tutorial repeated measures anova
TRANSCRIPT
![Page 1: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/1.jpg)
Repeated Measures (ANOVA)
Conceptual Explanation
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How did you get here?
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How did you get here?So, you have decided to use a Repeated Measures ANOVA.
![Page 4: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/4.jpg)
How did you get here?So, you have decided to use a Repeated Measures ANOVA.Let’s consider the decisions you made to get here.
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First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
![Page 6: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/6.jpg)
First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
![Page 7: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/7.jpg)
First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
Sample of 30
![Page 8: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/8.jpg)
First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
Sample of 30
Generalizes to
![Page 9: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/9.jpg)
First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
Large Population of 30,000
Sample of 30
Generalizes to
![Page 10: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/10.jpg)
First of all, you must have noticed the problem to be solved deals with generalizing from a smaller sample to a larger population.
Therefore, you would determine that the problem deals with inferential not descriptive statistics.
Large Population of 30,000
Sample of 30
Generalizes to
![Page 11: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/11.jpg)
Therefore, you would determine that the problem deals with inferential not descriptive statistics.
![Page 12: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/12.jpg)
Therefore, you would determine that the problem deals with inferential not descriptive statistics.
Double check your problem to see if that is the case
![Page 13: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/13.jpg)
Therefore, you would determine that the problem deals with inferential not descriptive statistics.
Inferential Descriptive
Double check your problem to see if that is the case
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You would have also noticed that the problem dealt with questions of difference not Relationships, Independence nor Goodness of Fit. Inferential Descriptive
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You would have also noticed that the problem dealt with questions of difference not Relationships, Independence nor Goodness of Fit.
Double check your problem to see if that is the case
Inferential Descriptive
Difference
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You would have also noticed that the problem dealt with questions of difference not Relationships, Independence nor Goodness of Fit.
Double check your problem to see if that is the case
Inferential Descriptive
Difference Relationship
![Page 17: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/17.jpg)
You would have also noticed that the problem dealt with questions of difference not Relationships, Independence nor Goodness of Fit.
Double check your problem to see if that is the case
Inferential Descriptive
DifferenceDifference Relationship
![Page 18: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/18.jpg)
You would have also noticed that the problem dealt with questions of difference not Relationships, Independence nor Goodness of Fit.
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of FitDifference Relationship
![Page 19: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/19.jpg)
After checking the data, you noticed that the data was ratio/interval rather than extreme ordinal (1st, 2nd, 3rd place) or nominal (male, female)
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of FitDifference Relationship
![Page 20: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/20.jpg)
After checking the data, you noticed that the data was ratio/interval rather than extreme ordinal (1st, 2nd, 3rd place) or nominal (male, female)
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
Ratio/Interval
Difference Relationship
![Page 21: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/21.jpg)
After checking the data, you noticed that the data was ratio/interval rather than extreme ordinal (1st, 2nd, 3rd place) or nominal (male, female)
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
OrdinalRatio/Interval
Difference Relationship
![Page 22: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/22.jpg)
After checking the data, you noticed that the data was ratio/interval rather than extreme ordinal (1st, 2nd, 3rd place) or nominal (male, female)
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
NominalOrdinalRatio/Interval
Difference Relationship
![Page 23: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/23.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
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The distribution was more or less normal rather than skewed or kurtotic.
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The distribution was more or less normal rather than skewed or kurtotic.
![Page 26: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/26.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
![Page 27: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/27.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
Skewed
NominalOrdinalRatio/Interval
Difference Relationship
![Page 28: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/28.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
Skewed Kurtotic
NominalOrdinalRatio/Interval
Difference Relationship
![Page 29: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/29.jpg)
The distribution was more or less normal rather than skewed or kurtotic.
Double check your problem to see if that is the case
Inferential Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
NominalOrdinalRatio/Interval
Difference Relationship
![Page 30: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/30.jpg)
Only one Dependent Variable (DV) rather than two or more exist.
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Only one Dependent Variable (DV) rather than two or more exist.
DV #1
Chemistry Test Scores
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Only one Dependent Variable (DV) rather than two or more exist.
DV #1 DV #2
Chemistry Test Scores
Class Attendance
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Only one Dependent Variable (DV) rather than two or more exist.
DV #1 DV #2 DV #3
Chemistry Test Scores
Class Attendance
Homework Completed
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Only one Dependent Variable (DV) rather than two or more exist.
Inferential Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
Double check your problem to see if that is the case
NominalOrdinalRatio/Interval
Difference Relationship
![Page 35: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/35.jpg)
Only one Dependent Variable (DV) rather than two or more exist.
Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV
Double check your problem to see if that is the case
Inferential
NominalOrdinalRatio/Interval
Difference Relationship
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Only one Dependent Variable (DV) rather than two or more exist.
Inferential Descriptive
Difference Relationship Difference Goodness of Fit
Ratio/Interval Ordinal Nominal
Skewed Kurtotic Normal
1 DV 2+ DV
Double check your problem to see if that is the case
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Only one Independent Variable (DV) rather than two or more exist.
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Only one Independent Variable (DV) rather than two or more exist.
IV #1
Use of Innovative eBook
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Only one Independent Variable (DV) rather than two or more exist.
IV #1 IV #2
Use of Innovative eBook
Doing Homework to Classical Music
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Only one Independent Variable (DV) rather than two or more exist.
IV #1 IV #2 IV #3
Use of Innovative eBook
Doing Homework to Classical Music Gender
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Only one Independent Variable (DV) rather than two or more exist.
IV #1 IV #2 IV #3
Use of Innovative eBook
Doing Homework to Classical Music Gender
![Page 42: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/42.jpg)
Only one Independent Variable (DV) rather than two or more exist.
![Page 43: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/43.jpg)
Only one Independent Variable (DV) rather than two or more exist. Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV 2+ DV
Inferential
NominalOrdinalRatio/Interval
Difference Relationship
![Page 44: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/44.jpg)
Only one Independent Variable (DV) rather than two or more exist. Inferential Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV 2+ DV
1 IV
Inferential
NominalOrdinalRatio/Interval
Difference Relationship
![Page 45: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/45.jpg)
Only one Independent Variable (DV) rather than two or more exist. Descriptive
Difference Goodness of Fit
Nominal
Skewed Kurtotic Normal
1 DV 2+ DV
1 IV 2+ IV
Inferential
NominalOrdinalRatio/Interval
Difference Relationship Difference
![Page 46: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/46.jpg)
Only one Independent Variable (DV) rather than two or more exist. Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV 2+ DV
1 IV 2+ IV
Double check your problem to see if that is the case
Inferential
NominalOrdinalRatio/Interval
Difference Relationship Difference
![Page 47: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/47.jpg)
There are three levels of the Independent Variable (IV) rather than just two levels. Note – even though repeated measures ANOVA can analyze just two levels, this is generally analyzed using a paired sample t-test.
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There are three levels of the Independent Variable (DV) rather than just two levels. Note – even though repeated measures ANOVA can analyze just two levels, this is generally analyzed using a paired sample t-test.
Level 1
Before using the innovative ebook
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There are three levels of the Independent Variable (DV) rather than just two levels. Note – even though repeated measures ANOVA can analyze just two levels, this is generally analyzed using a paired sample t-test.
Level 1 Level 2
Before using the innovative ebook
Using the innovative ebook
for 2 months
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There are three levels of the Independent Variable (DV) rather than just two levels. Note – even though repeated measures ANOVA can analyze just two levels, this is generally analyzed using a paired sample t-test.
Level 1 Level 2 Level 3
Before using the innovative ebook
Using the innovative ebook
for 2 months
Using the innovative ebook
for 4 months
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Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV 2+ DVs
2+ IVs
Inferential
NominalOrdinalRatio/Interval
Difference Relationship
2 levels 3+ levels
1 IV
Difference
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The samples are repeated rather than independent. Notice that the same class (Chem 100 section 003) is repeatedly tested.
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The samples are repeated rather than independent. Notice that the same class (Chem 100 section 003) is repeatedly tested.
Chem 100 Section 003
January
Chem 100 Section 003
March
Chem 100 Section 003
May
Before using the innovative
ebook
Using the innovative ebook
for 2 months
Using the innovative ebook
for 4 months
![Page 54: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/54.jpg)
Descriptive
Difference Goodness of Fit
Skewed Kurtotic Normal
1 DV 2+ DVs
2+ IVs
Inferential
NominalOrdinalRatio/Interval
Difference Relationship
2 levels 3+ levels
1 IV
Difference
RepeatedIndependent
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If this was the appropriate path for your problem then you have correctly selected Repeated-measures ANOVA to solve the problem you have been presented.
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Repeated Measures ANOVA –
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Repeated Measures ANOVA –Another use of analysis of variance is to test whether a single group of people change over time.
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Repeated Measures ANOVA –Another use of analysis of variance is to test whether a single group of people change over time.
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In this case, the distributions that are compared to each other are not from different groups
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In this case, the distributions that are compared to each other are not from different groups
versus
Group 1 Group 2
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In this case, the distributions that are compared to each other are not from different groups
versus
Group 1 Group 2
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In this case, the distributions that are compared to each other are not from different groups
But from different times.
versus
Group 1 Group 2
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In this case, the distributions that are compared to each other are not from different groups
But from different times.
versus
Group 1 Group 2
Group 1 Group 1: Two Months Later
versus
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For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
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For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
January FebruaryApril
Exam 1Exam 2
Exam 3
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For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
The overall F-ratio will reveal whether there are differences somewhere among three time periods.
January FebruaryApril
Exam 1Exam 2
Exam 3
![Page 67: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/67.jpg)
For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
The overall F-ratio will reveal whether there are differences somewhere among three time periods.
January FebruaryApril
Exam 1Exam 2
Exam 3
![Page 68: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/68.jpg)
For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
The overall F-ratio will reveal whether there are differences somewhere among three time periods.
January FebruaryApril
Exam 1Exam 2
Exam 3
Average Score
Average Score
Average Score
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For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
The overall F-ratio will reveal whether there are differences somewhere among three time periods.
January FebruaryApril
Exam 1Exam 2
Exam 3
Average Score
Average Score
Average Score
![Page 70: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/70.jpg)
For example, an instructor might administer the same test three times throughout the semester to ascertain whether students are improving in their skills.
The overall F-ratio will reveal whether there are differences somewhere among three time periods.
January FebruaryApril
Exam 1Exam 2
Exam 3
Average Score
Average Score
Average Score
There is a difference but
we don’t know where
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Post hoc tests will reveal exactly where the differences occurred.
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Post hoc tests will reveal exactly where the differences occurred.
January FebruaryApril
Exam 1Exam 2
Exam 3
Average Score 35
Average Score 38
Average Score 40
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Post hoc tests will reveal exactly where the differences occurred.
January FebruaryApril
Exam 1Exam 2
Exam 3
Average Score 35
Average Score 38
Average Score 40
There is a statistically significant
difference only between Exam 1
and Exam 3
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In contrast, with the One-way analysis of Variance (ANOVA) we were attempting to determine if there was a statistical difference between 2 or more (generally 3 or more) groups.
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In contrast, with the One-way analysis of Variance (ANOVA) we were attempting to determine if there was a statistical difference between 2 or more (generally 3 or more) groups.In our One-way ANOVA example in another presentation we attempted to determine if there was any statistically significant difference in the amount of Pizza Slices consumed by three different player types (football, basketball, and soccer).
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The data would be set up thus:
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The data would be set up thus:Football Players
Pizza Slices
Consumed
Basketball Players
Pizza Slices Consumed
Soccer Players
Pizza Slices Consumed
Ben 5 Cam 6 Dan 5
Bob 7 Colby 4 Denzel 8
Bud 8 Conner 8 Dilbert 8
Bubba 9 Custer 4 Don 1
Burt 10 Cyan 2 Dylan 2
![Page 78: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/78.jpg)
The data would be set up thus:
Notice how the individuals in these groups are different (hence different names)
Football Players
Pizza Slices
Consumed
Basketball Players
Pizza Slices Consumed
Soccer Players
Pizza Slices Consumed
Ben 5 Cam 6 Dan 5
Bob 7 Colby 4 Denzel 8
Bud 8 Conner 8 Dilbert 8
Bubba 9 Custer 4 Don 1
Burt 10 Cyan 2 Dylan 2
![Page 79: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/79.jpg)
The data would be set up thus:
Notice how the individuals in these groups are different (hence different names)
Football Players
Pizza Slices
Consumed
Basketball Players
Pizza Slices Consumed
Soccer Players
Pizza Slices Consumed
Ben 5 Cam 6 Dan 5
Bob 7 Colby 4 Denzel 8
Bud 8 Conner 8 Dilbert 8
Bubba 9 Custer 4 Don 1
Burt 10 Cyan 2 Dylan 2
![Page 80: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/80.jpg)
The data would be set up thus:
Notice how the individuals in these groups are different (hence different names)A Repeated Measures ANOVA is different than a One-Way ANOVA in one simply way: Only one group of person or observations is being measured, but they are measured more than one time.
Football Players
Pizza Slices
Consumed
Basketball Players
Pizza Slices Consumed
Soccer Players
Pizza Slices Consumed
Ben 5 Ben 6 Ben 5
Bob 7 Bob 4 Bob 8
Bud 8 Bud 8 Bud 8
Bubba 9 Bubba 4 Bubba 1
Burt 10 Burt 2 Burt 2
![Page 81: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/81.jpg)
The data would be set up thus:
Notice how the individuals in these groups are different (hence different names)A Repeated Measures ANOVA is different than a One-Way ANOVA in one simply way: Only one group of persons or observations is being measured, but they are measured more than one time.
Football Players
Pizza Slices
Consumed
Basketball Players
Pizza Slices Consumed
Soccer Players
Pizza Slices Consumed
Ben 5 Ben 6 Ben 5
Bob 7 Bob 4 Bob 8
Bud 8 Bud 8 Bud 8
Bubba 9 Bubba 4 Bubba 1
Burt 10 Burt 2 Burt 2
![Page 82: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/82.jpg)
Notice the different times football player pizza consumption is being measured.
Football Players
Pizza Slices
Consumed
Pizza Slices Consumed
Pizza Slices Consumed
Ben 5 Ben 6 Ben 5
Bob 7 Bob 4 Bob 8
Bud 8 Bud 8 Bud 8
Bubba 9 Bubba 4 Bubba 1
Burt 10 Burt 2 Burt 2
![Page 83: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/83.jpg)
Notice the different times football player pizza consumption is being measured.
Football Players
Pizza Slices
ConsumedBefore the
Season
Pizza Slices Consumed
During the Season
Pizza Slices Consumed
After the Season
Ben 5 Ben 6 Ben 5
Bob 7 Bob 4 Bob 8
Bud 8 Bud 8 Bud 8
Bubba 9 Bubba 4 Bubba 1
Burt 10 Burt 2 Burt 2
![Page 84: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/84.jpg)
Since only one group is being measured 3 times, each time is dependent on the previous time. By dependent we mean there is a relationship.
![Page 85: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/85.jpg)
Since only one group is being measured 3 times, each time is dependent on the previous time. By dependent we mean there is a relationship.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 86: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/86.jpg)
Since only one group is being measured 3 times, each time is dependent on the previous time. By dependent we mean there is a relationship.
The relationship between the scores is that we are comparing the same person across multiple observations.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 87: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/87.jpg)
So, Ben’s before-season and during-season and after-season scores have one important thing in common:
![Page 88: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/88.jpg)
So, Ben’s before-season and during-season and after-season scores have one important thing in common:
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 89: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/89.jpg)
So, Ben’s before-season and during-season and after-season scores have one important thing in common: THESE SCORES ALL BELONG TO BEN.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 90: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/90.jpg)
So, Ben’s before-season and during-season and after-season scores have one important thing in common: THESE SCORES ALL BELONG TO BEN.
They are subject to all the factors that are special to Ben when consuming pizza, including how much he likes or dislikes, the toppings that are available, the eating atmosphere, etc.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 91: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/91.jpg)
What we want to find out is – how much the BEFORE, DURING, and AFTER season pizza consuming sessions differ.
![Page 92: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/92.jpg)
What we want to find out is – how much the BEFORE, DURING, and AFTER season pizza consuming sessions differ.But we have to find a way to eliminate the variability that is caused by individual differences that linger across all three eating sessions. Once again we are not interested in the things that make Ben, Ben while eating pizza (like he’s a picky eater). We are interested in the effect of where we are in the season (BEFORE, DURING, and AFTER on Pizza consumption.)
![Page 93: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/93.jpg)
What we want to find out is – how much the BEFORE, DURING, and AFTER season pizza consuming sessions differ.But we have to find a way to eliminate the variability that is caused by individual differences that linger across all three eating sessions. Once again we are not interested in the things that make Ben, Ben while eating pizza (like he’s a picky eater). We are interested in the effect of where we are in the season (BEFORE, DURING, and AFTER on Pizza consumption.)
![Page 94: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/94.jpg)
What we want to find out is – how much the BEFORE, DURING, and AFTER season pizza consuming sessions differ.But we have to find a way to eliminate the variability that is caused by individual differences that linger across all three eating sessions. Once again we are not interested in the things that make Ben, Ben while eating pizza (like he’s a picky eater). We are interested in the effect of where we are in the season (BEFORE, DURING, and AFTER on Pizza consumption.)
![Page 95: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/95.jpg)
That way we can focus just on the differences that are related to WHEN the pizza eating occurred.
![Page 96: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/96.jpg)
That way we can focus just on the differences that are related to WHEN the pizza eating occurred. After running a repeated-measures ANOVA, this is the output that we will get:
![Page 97: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/97.jpg)
That way we can focus just on the differences that are related to WHEN the pizza eating occurred. After running a repeated-measures ANOVA, this is the output that we will get:
Tests of Within-Subjects Effects
Measure: Pizza slices
Source
Type III Sum of
Squares dfMean
Square F Sig.
Between Subjects 21.333 4
Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 98: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/98.jpg)
This output will help us determine if we reject the null hypothesis:
![Page 99: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/99.jpg)
This output will help us determine if we reject the null hypothesis:There is no significant difference in the amount of pizza consumed by football players before,
during, and/or after the season.
![Page 100: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/100.jpg)
This output will help us determine if we reject the null hypothesis:There is no significant difference in the amount of pizza consumed by football players before,
during, and/or after the season.Or accept the alternative hypothesis:
![Page 101: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/101.jpg)
This output will help us determine if we reject the null hypothesis:There is no significant difference in the amount of pizza consumed by football players before,
during, and/or after the season.Or accept the alternative hypothesis:There is a significant difference in the amount of
pizza consumed by football players before, during, and/or after the season.
![Page 102: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/102.jpg)
To do so, let’s focus on the value .008
![Page 103: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/103.jpg)
To do so, let’s focus on the value .008Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 104: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/104.jpg)
To do so, let’s focus on the value .008Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source
Type III Sum of
Squares dfMean
Square F Sig.Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033Total 49.333 14
![Page 105: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/105.jpg)
To do so, let’s focus on the value .008
This means that if we were to reject the null hypothesis, the probability that we would be wrong is 8 times out of 1000. As you remember, if that were to happen, it would be called a Type 1 error.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source
Type III Sum of
Squares dfMean
Square F Sig.Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033Total 49.333 14
![Page 106: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/106.jpg)
To do so, let’s focus on the value .008
This means that if we were to reject the null hypothesis, the probability that we would be wrong is 8 times out of 1000. As you remember, if that were to happen, it would be called a Type 1 error.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source
Type III Sum of
Squares dfMean
Square F Sig.Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033Total 49.333 14
![Page 107: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/107.jpg)
But it is so unlikely, that we would be willing to take that risk and hence reject the null hypothesis.
![Page 108: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/108.jpg)
But it is so unlikely, that we would be willing to take that risk and hence we reject the null hypothesis.
There IS NO statistically significant difference between the number of slices of pizza consumed
by football players before, during, or after the football season.
![Page 109: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/109.jpg)
But it is so unlikely, that we would be willing to take that risk and hence we reject the null hypothesis.
There IS NO statistically significant difference between the number of slices of pizza consumed
by football players before, during, or after the football season. REJE
CT
![Page 110: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/110.jpg)
And accept the alternative hypothesis:
![Page 111: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/111.jpg)
And accept the alternative hypothesis:
There IS A statistically significant difference between the number of slices of pizza consumed
by football players before, during, or after the football season.
![Page 112: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/112.jpg)
And accept the alternative hypothesis:
There IS A statistically significant difference between the number of slices of pizza consumed
by football players before, during, or after the football season. ACCEPT
![Page 113: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/113.jpg)
Now we do not know which of the three are significantly different from one another or if all three are different. We just know that a difference exists.
![Page 114: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/114.jpg)
Now we do not know which of the three are significantly different from one another or if all three are different. We just know that a difference exists.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 115: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/115.jpg)
Now we do not know which of the three are significantly different from one another or if all three are different. We just know that a difference exists.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 116: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/116.jpg)
Now we do not know which of the three are significantly different from one another or if all three are different. We just know that a difference exists.
Later, we can run what is called a “Post-hoc” test to determine where the difference lies.
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 117: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/117.jpg)
From this point on – we will delve into the actual calculations and formulas that produce a Repeated-measures ANOVA. If such detail is of interest or a necessity to know, please continue.
![Page 118: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/118.jpg)
How was a significance value of .008 calculated?
![Page 119: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/119.jpg)
How was a significance value of .008 calculated?Let’s begin with the calculation of the various sources of Sums of Squares
![Page 120: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/120.jpg)
How was a significance value of .008 calculated?Let’s begin with the calculation of the various sources of Sums of Squares
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source
Type III Sum of
Squares dfMean
Square F Sig.Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033Total 49.333 14
![Page 121: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/121.jpg)
We do this so that we can explain what is causing the scores to vary or deviate.
![Page 122: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/122.jpg)
We do this so that we can explain what is causing the scores to vary or deviate.• Is it error?
![Page 123: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/123.jpg)
We do this so that we can explain what is causing the scores to vary or deviate.• Is it error?• Is it differences between times (before,
during, and after)?
![Page 124: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/124.jpg)
We do this so that we can explain what is causing the scores to vary or deviate.• Is it error?• Is it differences between times (before,
during, and after)?Remember, the full name for sum of squares is the sum of squared deviations about the mean. This will help us determine the amount of variation from each of the possible sources.
![Page 125: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/125.jpg)
Let’s begin by calculating the total sums of squares.
![Page 126: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/126.jpg)
Let’s begin by calculating the total sums of squares.
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
![Page 127: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/127.jpg)
Let’s begin by calculating the total sums of squares.
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
![Page 128: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/128.jpg)
Let’s begin by calculating the total sums of squares.
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means one pizza eating observation for person “I” (e.g., Ben) on
time “j” (e.g., before)
![Page 129: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/129.jpg)
For example:
![Page 130: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/130.jpg)
For example: Pizza Slices Consumed
Football Players Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 131: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/131.jpg)
For example: Pizza Slices Consumed
Football Players Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 132: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/132.jpg)
For example:
OR
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 133: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/133.jpg)
For example:
OR
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 134: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/134.jpg)
For example:
OR
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 135: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/135.jpg)
For example:
OR
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 136: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/136.jpg)
For example:
OR
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 137: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/137.jpg)
For example:
ETC
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 138: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/138.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
![Page 139: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/139.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means the average of all of the
observations
![Page 140: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/140.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means the average of all of the
observationsThis means one pizza eating observation for
person “I” (e.g., Ben) on time “j” (e.g., before)
![Page 141: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/141.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means the average of all of the
observations
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
This means one pizza eating observation for
person “I” (e.g., Ben) on time “j” (e.g., before)
![Page 142: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/142.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means the average of all of the
observations
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Average of All Observations
This means one pizza eating observation for
person “I” (e.g., Ben) on time “j” (e.g., before)
![Page 143: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/143.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means sum or add
everything up
![Page 144: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/144.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means sum or add
everything up
This means the average of
all of the observations
�́�𝑿
![Page 145: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/145.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
This means sum or add
everything up
This means the average of
all of the observations
This means one pizza eating observation for
person “I” (e.g., Ben) on time “j” (e.g., before)
![Page 146: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/146.jpg)
Let’s calculate total sums of squares with this data set:
![Page 147: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/147.jpg)
Let’s calculate total sums of squares with this data set:
Pizza Slices ConsumedFootball Players Before the
SeasonDuring the
SeasonAfter the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 148: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/148.jpg)
To do so we will rearrange the data like so:
![Page 149: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/149.jpg)
To do so we will rearrange the data like so:Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
![Page 150: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/150.jpg)
To do so we will rearrange the data like so:Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
![Page 151: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/151.jpg)
To do so we will rearrange the data like so:Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
![Page 152: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/152.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
![Page 153: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/153.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
![Page 154: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/154.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
Each observation
![Page 155: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/155.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.Here is how we
compute the Grand Mean =
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
![Page 156: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/156.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.Here is how we
compute the Grand Mean =
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
![Page 157: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/157.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.Here is how we
compute the Grand Mean =
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Pizza Slices ConsumedFootball Players
Before the Season
During the Season
After the Season
Ben 5 4 4Bob 7 5 5Bud 8 7 6
Bubba 9 8 4Burt 10 7 6
![Page 158: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/158.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.Here is how we
compute the Grand Mean =
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Pizza Slices ConsumedFootball Players
Before the Season
During the Season
After the Season
Ben 5 4 4Bob 7 5 5Bud 8 7 6
Bubba 9 8 4Burt 10 7 6
Average of All Observations =
6.3
![Page 159: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/159.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Football Players
Season Slices of Pizza
Ben Before 5 -Bob Before 7 -Bud Before 8 -
Bubba Before 9 -Burt Before 10 -Ben During 4 -Bob During 5 -Bud During 7 -
Bubba During 8 -Burt During 7 -Ben After 4 -Bob After 5 -Bud After 6 -
Bubba After 4 -Burt After 6 -
![Page 160: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/160.jpg)
To do so we will rearrange the data like so:We will
subtract each of these values from
the grand mean, square the
result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Football Players
Season Slices of Pizza
Ben Before 5 -Bob Before 7 -Bud Before 8 -
Bubba Before 9 -Burt Before 10 -Ben During 4 -Bob During 5 -Bud During 7 -
Bubba During 8 -Burt During 7 -Ben After 4 -Bob After 5 -Bud After 6 -
Bubba After 4 -Burt After 6 -
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
![Page 161: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/161.jpg)
𝑆𝑆𝑡𝑜𝑡𝑎𝑙=Σ(𝑋 𝑖𝑗− �́� )2
To do so we will rearrange the data like so:We
will subtract each of these values from the
grand mean, square the result and sum
them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Football Players
Season Slices of Pizza
Ben Before 5 -Bob Before 7 -Bud Before 8 -
Bubba Before 9 -Burt Before 10 -Ben During 4 -Bob During 5 -Bud During 7 -
Bubba During 8 -Burt During 7 -Ben After 4 -Bob After 5 -Bud After 6 -
Bubba After 4 -Burt After 6 -
Football Players
Season Slices of Pizza
Grand Mean
Ben Before 5 - 6.3Bob Before 7 - 6.3Bud Before 8 - 6.3
Bubba Before 9 - 6.3Burt Before 10 - 6.3Ben During 4 - 6.3Bob During 5 - 6.3Bud During 7 - 6.3
Bubba During 8 - 6.3Burt During 7 - 6.3Ben After 4 - 6.3Bob After 5 - 6.3Bud After 6 - 6.3
Bubba After 4 - 6.3Burt After 6 - 6.3
![Page 162: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/162.jpg)
To do so we will rearrange the data like so:
We will subtract each of these values
from the grand mean,
square the result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Football Players
Season Slices of Pizza
Ben Before 5 -Bob Before 7 -Bud Before 8 -
Bubba Before 9 -Burt Before 10 -Ben During 4 -Bob During 5 -Bud During 7 -
Bubba During 8 -Burt During 7 -Ben After 4 -Bob After 5 -Bud After 6 -
Bubba After 4 -Burt After 6 -
Football Players
Season Slices of Pizza
Grand Mean
Ben Before 5 - 6.3Bob Before 7 - 6.3Bud Before 8 - 6.3
Bubba Before 9 - 6.3Burt Before 10 - 6.3Ben During 4 - 6.3Bob During 5 - 6.3Bud During 7 - 6.3
Bubba During 8 - 6.3Burt During 7 - 6.3Ben After 4 - 6.3Bob After 5 - 6.3Bud After 6 - 6.3
Bubba After 4 - 6.3Burt After 6 - 6.3
Football Players
Season Slices of Pizza
Grand Mean
Ben Before 5 - 6.3 =Bob Before 7 - 6.3 =Bud Before 8 - 6.3 =
Bubba Before 9 - 6.3 =Burt Before 10 - 6.3 =Ben During 4 - 6.3 =Bob During 5 - 6.3 =Bud During 7 - 6.3 =
Bubba During 8 - 6.3 =Burt During 7 - 6.3 =Ben After 4 - 6.3 =Bob After 5 - 6.3 =Bud After 6 - 6.3 =
Bubba After 4 - 6.3 =Burt After 6 - 6.3 =
![Page 163: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/163.jpg)
To do so we will rearrange the data like so:
We will subtract each of these values
from the grand mean,
square the result and sum them all up.
Football Players
BenBobBud
BubbaBurtBenBobBud
BubbaBurtBenBobBud
BubbaBurt
Football Players
Season
Ben BeforeBob BeforeBud Before
Bubba BeforeBurt BeforeBen DuringBob DuringBud During
Bubba DuringBurt DuringBen AfterBob AfterBud After
Bubba AfterBurt After
Football Players
Season Slices of Pizza
Ben Before 5Bob Before 7Bud Before 8
Bubba Before 9Burt Before 10Ben During 4Bob During 5Bud During 7
Bubba During 8Burt During 7Ben After 4Bob After 5Bud After 6
Bubba After 4Burt After 6
Football Players
Season Slices of Pizza
Ben Before 5 -Bob Before 7 -Bud Before 8 -
Bubba Before 9 -Burt Before 10 -Ben During 4 -Bob During 5 -Bud During 7 -
Bubba During 8 -Burt During 7 -Ben After 4 -Bob After 5 -Bud After 6 -
Bubba After 4 -Burt After 6 -
Football Players
Season Slices of Pizza
Grand Mean
Ben Before 5 - 6.3Bob Before 7 - 6.3Bud Before 8 - 6.3
Bubba Before 9 - 6.3Burt Before 10 - 6.3Ben During 4 - 6.3Bob During 5 - 6.3Bud During 7 - 6.3
Bubba During 8 - 6.3Burt During 7 - 6.3Ben After 4 - 6.3Bob After 5 - 6.3Bud After 6 - 6.3
Bubba After 4 - 6.3Burt After 6 - 6.3
Football Players
Season Slices of Pizza
Grand Mean
Ben Before 5 - 6.3 =Bob Before 7 - 6.3 =Bud Before 8 - 6.3 =
Bubba Before 9 - 6.3 =Burt Before 10 - 6.3 =Ben During 4 - 6.3 =Bob During 5 - 6.3 =Bud During 7 - 6.3 =
Bubba During 8 - 6.3 =Burt During 7 - 6.3 =Ben After 4 - 6.3 =Bob After 5 - 6.3 =Bud After 6 - 6.3 =
Bubba After 4 - 6.3 =Burt After 6 - 6.3 =
Football Players
Season Slices of Pizza
Grand Mean
Deviation
Ben Before 5 - 6.3 = -1.3Bob Before 7 - 6.3 = 0.7Bud Before 8 - 6.3 = 1.7
Bubba Before 9 - 6.3 = 2.7Burt Before 10 - 6.3 = 3.7Ben During 4 - 6.3 = -2.3Bob During 5 - 6.3 = -1.3Bud During 7 - 6.3 = 0.7
Bubba During 8 - 6.3 = 1.7Burt During 7 - 6.3 = 0.7Ben After 4 - 6.3 = -2.3Bob After 5 - 6.3 = -1.3Bud After 6 - 6.3 = -0.3
Bubba After 4 - 6.3 = -2.3Burt After 6 - 6.3 = -0.3
![Page 164: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/164.jpg)
To do so we will rearrange the data like so:
We will subtract each of these values from the grand mean, square the result and sum them all up.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
![Page 165: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/165.jpg)
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
To do so we will rearrange the data like so:
We will subtract each of these values from the grand mean, square the result and sum them all up.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
![Page 166: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/166.jpg)
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
To do so we will rearrange the data like so:
Then –
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
![Page 167: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/167.jpg)
To do so we will rearrange the data like so:
Then – we place the total sums of squares result in the ANOVA table.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
![Page 168: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/168.jpg)
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
To do so we will rearrange the data like so:
Then – we place the total sums of squares result in the ANOVA table.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
![Page 169: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/169.jpg)
Then – we place the total sums of squares result in the ANOVA table.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
![Page 170: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/170.jpg)
Then – we place the total sums of squares result in the ANOVA table.
Football Players
Season Slices of Pizza
Grand Mean
Deviation Squared
Ben Before 5 - 6.3 = -1.3 1.8Bob Before 7 - 6.3 = 0.7 0.4Bud Before 8 - 6.3 = 1.7 2.8
Bubba Before 9 - 6.3 = 2.7 7.1Burt Before 10 - 6.3 = 3.7 13.4Ben During 4 - 6.3 = -2.3 5.4Bob During 5 - 6.3 = -1.3 1.8Bud During 7 - 6.3 = 0.7 0.4
Bubba During 8 - 6.3 = 1.7 2.8Burt During 7 - 6.3 = 0.7 0.4Ben After 4 - 6.3 = -2.3 5.4Bob After 5 - 6.3 = -1.3 1.8Bud After 6 - 6.3 = -0.3 0.1
Bubba After 4 - 6.3 = -2.3 5.4Burt After 6 - 6.3 = -0.3 0.1
= 49.3
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 171: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/171.jpg)
We have now calculated the total sums of squares. This is a good starting point. Because now we want to know of that total sums of squares how many sums of squares are generated from the following sources:
![Page 172: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/172.jpg)
We have now calculated the total sums of squares. This is a good starting point. Because now we want to know of that total sums of squares how many sums of squares are generated from the following sources:• Between subjects (this is the variance we
want to eliminate)
![Page 173: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/173.jpg)
We have now calculated the total sums of squares. This is a good starting point. Because now we want to know of that total sums of squares how many sums of squares are generated from the following sources:• Between subjects (this is the variance we
want to eliminate)• Between Groups (this would be between
BEFORE, DURING, AFTER)
![Page 174: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/174.jpg)
We have now calculated the total sums of squares. This is a good starting point. Because now we want to know of that total sums of squares how many sums of squares are generated from the following sources:• Between subjects (this is the variance we
want to eliminate)• Between Groups (this would be between
BEFORE, DURING, AFTER)• Error (the variance that we cannot explain
with our design)
![Page 175: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/175.jpg)
With these sums of squares we will be able to compute our F ratio value and then statistical significance.
![Page 176: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/176.jpg)
With these sums of squares we will be able to compute our F ratio value and then statistical significance.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 177: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/177.jpg)
With these sums of squares we will be able to compute our F ratio value and then statistical significance.
Let’s calculate the sums of squares between subjects.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 178: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/178.jpg)
Remember if we were just computing a one way ANOVA the table would go from this:
![Page 179: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/179.jpg)
Remember if we were just computing a one way ANOVA the table would go from this:
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 180: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/180.jpg)
Remember if we were just computing a one way ANOVA the table would go from this:
To this:
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 181: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/181.jpg)
Remember if we were just computing a one way ANOVA the table would go from this:
To this:
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 2.669 .078
Error 29.600 8 3.700
Total 49.333 14
![Page 182: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/182.jpg)
Remember if we were just computing a one way ANOVA the table would go from this:
To this:
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 2.669 .078
Error 29.600 8 3.700
Total 49.333 14
![Page 183: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/183.jpg)
All of that variability goes into the error or within groups sums of squares (29.600) which makes the F statistic smaller (from 9.548 to 2.669), the significance value no longer significant (.008 to .078).
![Page 184: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/184.jpg)
All of that variability goes into the error or within groups sums of squares (29.600) which makes the F statistic smaller (from 9.548 to 2.669), the significance value no longer significant (.008 to .078).But the difference in within groups variability is not a function of error, it is a function of Ben, Bob, Bud, Bubba, and Burt’s being different in terms of the amount of slices they eat regardless of when they eat!
![Page 185: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/185.jpg)
All of that variability goes into the error or within groups sums of squares (29.600) which makes the F statistic smaller (from 9.548 to 2.669), the significance value no longer significant (.008 to .078).But the difference in within groups variability is not a function of error, it is a function of Ben, Bob, Bud, Bubba, and Burt’s being different in terms of the amount of slices they eat regardless of when they eat!
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 5 4 4 4.3Bob 7 5 5 5.7Bud 8 7 6 7.0
Bubba 9 8 4 7.0Burt 10 7 6 7.7
![Page 186: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/186.jpg)
Here is a data set where there are not between group differences, but there is a lot of difference based on when the group eats their pizza:
![Page 187: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/187.jpg)
Here is a data set where there are not between group differences, but there is a lot of difference based on when the group eats their pizza:
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 1 5 9 5.0Bob 2 5 8 5.0Bud 3 5 7 5.0
Bubba 1 5 9 5.0Burt 2 5 8 5.0
![Page 188: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/188.jpg)
Here is a data set where there are not between group differences, but there is a lot of difference based on when the group eats their pizza:
There is no variability between subjects (they are all 5.0).
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 1 5 9 5.0Bob 2 5 8 5.0Bud 3 5 7 5.0
Bubba 1 5 9 5.0Burt 2 5 8 5.0
![Page 189: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/189.jpg)
Look at the variability between groups:
![Page 190: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/190.jpg)
Look at the variability between groups: Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average
Ben 1 5 9 5.0Bob 2 5 8 5.0Bud 3 5 7 5.0
Bubba 1 5 9 5.0Burt 2 5 8 5.0
1.8 5.0 8.2
![Page 191: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/191.jpg)
Look at the variability between groups:
They are very different from one another.
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 1 5 9 5.0Bob 2 5 8 5.0Bud 3 5 7 5.0
Bubba 1 5 9 5.0Burt 2 5 8 5.0
1.8 5.0 8.2
![Page 192: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/192.jpg)
Here is what the ANOVA table would look like:
![Page 193: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/193.jpg)
Here is what the ANOVA table would look like:Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 0.000 4Between Groups 102.400 2 51.200 73.143 .000
Error 5.600 8 0.700
Total 49.333 14
![Page 194: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/194.jpg)
Here is what the ANOVA table would look like:
Notice how there are no sum of squares values for the between subjects source of variability!
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 0.000 4Between Groups 102.400 2 51.200 73.143 .000
Error 5.600 8 0.700
Total 49.333 14
![Page 195: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/195.jpg)
Here is what the ANOVA table would look like:
Notice how there are no sum of squares values for the between subjects source of variability!But there is a lot of sum of squares values for the between groups.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 0.000 4Between Groups 102.400 2 51.200 73.143 .000
Error 5.600 8 0.700
Total 49.333 14
![Page 196: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/196.jpg)
Here is what the ANOVA table would look like:
Notice how there are no sum of squares values for the between subjects source of variability!But there is a lot of sum of squares values for the between groups.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 0.000 4Between Groups 102.400 2 51.200 73.143 .000
Error 5.600 8 0.700
Total 49.333 14
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 0.000 4Between Groups 102.400 2 51.200 73.143 .000
Error 5.600 8 0.700
Total 49.333 14
![Page 197: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/197.jpg)
What would the data set look like if there was very little between groups (by season) variability and a great deal of between subjects variability:
![Page 198: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/198.jpg)
What would the data set look like if there was very little between groups (by season) variability and a great deal of between subjects variability:Here it is:
![Page 199: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/199.jpg)
What would the data set look like if there was very little between groups (by season) variability and a great deal of between subjects variability:Here it is:
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average
Ben 3 3 3 3.0
Bob 5 5 5 5.0
Bud 7 7 7 7.0
Bubba 8 8 8 8.0
Burt 12 12 13 12.3
Between Subjects
![Page 200: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/200.jpg)
In this case the between subjects (Ben, Bob, Bud . . .), are very different.
![Page 201: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/201.jpg)
In this case the between subjects (Ben, Bob, Bud . . .), are very different.When you see between SUBJECTS averages that far away, you know that the sums of squares for between groups will be very large.
![Page 202: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/202.jpg)
In this case the between subjects (Ben, Bob, Bud . . .), are very different.When you see between SUBJECTS averages that far away, you know that the sums of squares for between groups will be very large.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 148.267 4Between Groups 0.133 2 0.067 1.000 .689
Error 0.533 8 0.067
Total 148.933 14
![Page 203: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/203.jpg)
Notice, in contrast, as we compute the between group (seasons) average how close they are.
![Page 204: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/204.jpg)
Notice, in contrast, as we compute the between group (seasons) average how close they are.
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 3 3 3 3.0Bob 5 5 5 5.0Bud 7 7 7 7.0
Bubba 8 8 8 8.0Burt 12 12 13 12.3
7.0 7.0 7.2
![Page 205: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/205.jpg)
Notice, in contrast, as we compute the between group (seasons) average how close they are.
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 3 3 3 3.0Bob 5 5 5 5.0Bud 7 7 7 7.0
Bubba 8 8 8 8.0Burt 12 12 13 12.3
7.0 7.0 7.2
Between Groups
![Page 206: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/206.jpg)
Notice, in contrast, as we compute the between group (seasons) average how close they are.
Pizza Slices Consumed Football Players
Before the Season
During the Season
After the Season
Average
Ben 3 3 3 3.0Bob 5 5 5 5.0Bud 7 7 7 7.0
Bubba 8 8 8 8.0Burt 12 12 13 12.3
7.0 7.0 7.2
Between Groups
![Page 207: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/207.jpg)
When you see between group averages this close you know that the sums of squares for between groups will be very small.
![Page 208: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/208.jpg)
When you see between group averages this close you know that the sums of squares for between groups will be very small.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 148.267 4Between Groups 0.133 2 0.067 1.000 .689
Error 0.533 8 0.067
Total 148.933 14
![Page 209: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/209.jpg)
When you see between group averages this close you know that the sums of squares for between groups will be very small.
Now that we have conceptually considered the sources of variability as described by the sum of squares, let’s begin calculating between subjects, between groups, and the error sources.
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 148.267 4Between Groups 0.133 2 0.067 1.000 .689
Error 0.533 8 0.067
Total 148.933 14
![Page 210: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/210.jpg)
We will begin with calculating Between Subjects sum of squares.
![Page 211: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/211.jpg)
We will begin with calculating Between Subjects sum of squares.To do so, let’s return to our original data set:
![Page 212: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/212.jpg)
We will begin with calculating Between Subjects sum of squares.To do so, let’s return to our original data set:
Pizza Slices ConsumedFootball Players
Before the Season
During the Season
After the Season
Ben 5 4 4Bob 7 5 5Bud 8 7 6
Bubba 9 8 4Burt 10 7 6
![Page 213: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/213.jpg)
We will begin with calculating Between Subjects sum of squares.To do so, let’s return to our original data set:
Here is the formula for calculating SS between subjects.
Pizza Slices ConsumedFootball Players
Before the Season
During the Season
After the Season
Ben 5 4 4Bob 7 5 5Bud 8 7 6
Bubba 9 8 4Burt 10 7 6
![Page 214: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/214.jpg)
We will begin with calculating Between Subjects sum of squares.To do so, let’s return to our original data set:
Here is the formula for calculating SS between subjects.
Pizza Slices ConsumedFootball Players
Before the Season
During the Season
After the Season
Ben 5 4 4Bob 7 5 5Bud 8 7 6
Bubba 9 8 4Burt 10 7 6
𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑢𝑏𝑗𝑒𝑐𝑡𝑠=𝑘∗ Σ(𝑋𝑏𝑠− �́� )2
![Page 215: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/215.jpg)
𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑢𝑏𝑗𝑒𝑐𝑡𝑠=𝑘∗ Σ(𝑿𝒃𝒔− �́� )2
![Page 216: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/216.jpg)
𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑢𝑏𝑗𝑒𝑐𝑡𝑠=𝑘∗ Σ(𝑿𝒃𝒔− �́� )2 Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average
Ben 5 4 4 4.3
Bob 7 5 5 5.7
Bud 8 7 6 7.0
Bubba 9 8 4 7.0
Burt 10 7 6 7.7
![Page 217: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/217.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average
Ben 5 4 4 4.3
Bob 7 5 5 5.7
Bud 8 7 6 7.0
Bubba 9 8 4 7.0
Burt 10 7 6 7.7
𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑢𝑏𝑗𝑒𝑐𝑡𝑠=𝑘∗ Σ(𝑿𝒃𝒔− �́� )2This means the average of between
subjects
![Page 218: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/218.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average minus
Ben 5 4 4 4.3 -
Bob 7 5 5 5.7 -
Bud 8 7 6 7.0 -
Bubba 9 8 4 7.0 -
Burt 10 7 6 7.7 -
𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑢𝑏𝑗𝑒𝑐𝑡𝑠=𝑘∗ Σ(𝑿𝒃𝒔− �́� )2
![Page 219: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/219.jpg)
This means the average of all of the observations
![Page 220: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/220.jpg)
Here is how we calculate the grand mean again:
![Page 221: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/221.jpg)
Here is how we calculate the grand mean again: Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Average of All Observations =
6.3
![Page 222: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/222.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.
![Page 223: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/223.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average minus Grand Mean
Ben 5 4 4 4.3 - 6.3
Bob 7 5 5 5.7 - 6.3
Bud 8 7 6 7.0 - 6.3
Bubba 9 8 4 7.0 - 6.3
Burt 10 7 6 7.7 - 6.3
This means the average of all of the observations
![Page 224: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/224.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean.
![Page 225: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/225.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean.
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average minus Grand Mean
Deviation
Ben 5 4 4 4.3 - 6.3 -2.0
Bob 7 5 5 5.7 - 6.3 -0.6
Bud 8 7 6 7.0 - 6.3 0.7
Bubba 9 8 4 7.0 - 6.3 0.7
Burt 10 7 6 7.7 - 6.3 1.4
![Page 226: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/226.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.
![Page 227: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/227.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.
![Page 228: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/228.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
![Page 229: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/229.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.Then we sum all of these squared deviations.
![Page 230: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/230.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.Then we sum all of these squared deviations.
![Page 231: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/231.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.Then we sum all of these squared deviations.
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Sum up
![Page 232: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/232.jpg)
Here is how we calculate the grand mean again:Now we subtract each subject or person average from the Grand Mean.This gives us the person’s average score deviation from the total or grand mean. Now we will square the deviations.Then we sum all of these squared deviations.Finally, we multiply the sum all of these squared deviations by the number of groups:
![Page 233: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/233.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
![Page 234: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/234.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
Number of conditions
![Page 235: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/235.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
![Page 236: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/236.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
![Page 237: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/237.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
1 2 3
![Page 238: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/238.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
1 2 3
![Page 239: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/239.jpg)
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
1 2 3
![Page 240: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/240.jpg)
Pizza Slices Consumed
Football Players
Before the
Season
During the Season
After the Season
Average minus Grand Mean
Deviation Squared
Ben 5 4 4 4.3 - 6.3 -2.0 3.9
Bob 7 5 5 5.7 - 6.3 -0.6 0.4
Bud 8 7 6 7.0 - 6.3 0.7 0.5
Bubba 9 8 4 7.0 - 6.3 0.7 0.5
Burt 10 7 6 7.7 - 6.3 1.4 1.9
7.1
Times 3 groups
Sum of Squares Between Subjects 21.3
1 2 3
Tests of Within-Subjects Effects
Measure: Pizza slices consumed
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 241: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/241.jpg)
Now it is time to compute the between groups (seasons) sum of squares.
![Page 242: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/242.jpg)
Now it is time to compute the between groups’ (seasons) sum of squares.
Here is the equation we will use to compute it:
![Page 243: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/243.jpg)
Now it is time to compute the between groups’ (seasons) sum of squares.
Here is the equation we will use to compute it:
![Page 244: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/244.jpg)
Let’s break this down with our data set:
![Page 245: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/245.jpg)
Let’s break this down with our data set:
![Page 246: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/246.jpg)
Let’s break this down with our data set:
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 247: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/247.jpg)
We begin by computing the mean of each condition (k)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
![Page 248: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/248.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
We begin by computing the mean of each condition (k)
![Page 249: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/249.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8
We begin by computing the mean of each condition (k)
![Page 250: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/250.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8
We begin by computing the mean of each condition (k)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2
![Page 251: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/251.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8
We begin by computing the mean of each condition (k)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
![Page 252: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/252.jpg)
Then subtract each condition mean from the grand mean.
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
![Page 253: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/253.jpg)
Then subtract each condition mean from the grand mean.
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
![Page 254: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/254.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
Grand Mean
6.3 6.3 6.3
Then subtract each condition mean from the grand mean.
![Page 255: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/255.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
Grand Mean
6.3 6.3 6.3
equals
Deviation 1.5 -0.1 -1.3
Then subtract each condition mean from the grand mean.
![Page 256: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/256.jpg)
Square the deviation.
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
Grand Mean
6.3 6.3 6.3
equals
Deviation 1.5 -0.1 -1.3
Squared Deviation
2.2 0.0 1.8
![Page 257: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/257.jpg)
Sum the Squared Deviations:
![Page 258: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/258.jpg)
Sum the Squared Deviations:
![Page 259: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/259.jpg)
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
Grand Mean
6.3 6.3 6.3
equals
Deviation 1.5 -0.1 -1.3
Squared Deviation
2.2 0.0 1.8
Sum
Sum the Squared Deviations:
![Page 260: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/260.jpg)
Bubba 9 8 4
Burt 10 7 6
Condition Mean
7.8 6.2 5.0
minus - - -
Grand Mean
6.3 6.3 6.3
equals
Deviation 1.5 -0.1 -1.3
Squared Deviation
2.2 0.0 1.8
Sum
Sum the Squared Deviations:
3.95
Sum of Squared Deviations
![Page 261: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/261.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
![Page 262: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/262.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
3.95
Sum of Squared Deviations
![Page 263: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/263.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
3.95
Sum of Squared Deviations
![Page 264: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/264.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
3.95
Sum of Squared Deviations
5
Number of observations
![Page 265: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/265.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
3.95
Sum of Squared Deviations
5
Number of observations
![Page 266: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/266.jpg)
Multiply by the number of observations per condition (number of pizza eating slices across before, during, and after).
3.95
Sum of Squared Deviations
5
Number of observations
19.7Weighted Sum of
Squared Deviations
![Page 267: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/267.jpg)
Let’s return to the ANOVA table and put the weighted sum of squared deviations.
![Page 268: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/268.jpg)
Let’s return to the ANOVA table and put the weighted sum of squared deviations.
Tests of Within-Subjects Effects
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 269: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/269.jpg)
Let’s return to the ANOVA table and put the weighted sum of squared deviations.
Tests of Within-Subjects Effects
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
3.95
Sum of Squared Deviations
5
Number of observations
19.7Weighted Sum of
Squared Deviations
![Page 270: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/270.jpg)
Let’s return to the ANOVA table and put the weighted sum of squared deviations.
Tests of Within-Subjects Effects
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
3.95
Sum of Squared Deviations
5
Number of observations
19.7Weighted Sum of
Squared Deviations
![Page 271: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/271.jpg)
So far we have calculated Total Sum of Squares along with Sum of Squares for Between Subjects, and Between Groups.
![Page 272: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/272.jpg)
So far we have calculated Total Sum of Squares along with Sum of Squares along with Sum of Squares for Between Subjects, Between Groups.
Tests of Within-Subjects Effects
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 273: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/273.jpg)
Now we will calculate the sum of squares associated with Error.
![Page 274: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/274.jpg)
Now we will calculate the sum of squares associated with Error.
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 275: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/275.jpg)
To do this we simply add the between subjects and between groups sums of squares.
![Page 276: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/276.jpg)
To do this we simply add the between subjects and between groups sums of squares.
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 277: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/277.jpg)
To do this we simply add the between subjects and between groups sums of squares.
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
21.333
Between Subjects Sum of Squares
19.733
Between Groups Sum of Squares
41.600
Between Subjects & Groups Sum of
Squares Combined
![Page 278: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/278.jpg)
Then we subtract the Between Subjects & Group Sum of Squares Combined (41.600) from the Total Sum of Squares (49.333)
![Page 279: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/279.jpg)
Then we subtract the Between Subjects & Group Sum of Squares Combined (41.600) from the Total Sum of Squares (49.333)
49.333
Total Sum of Squares
41.600 Between Subjects &
Groups Sum of Squares Combined
8.267
Sum of Squares Attributed to Error
or Unexplained
![Page 280: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/280.jpg)
Then we subtract the Between Subjects & Group Sum of Squares Combined (41.600) from the Total Sum of Squares (49.333)
49.333
Total Sum of Squares
41.600 Between Subjects &
Groups Sum of Squares Combined
8.267
Sum of Squares Attributed to Error
or Unexplained
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 281: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/281.jpg)
Now we have all of the information necessary to determine if there is a statistically significant difference between pizza slices consumed by football players between three different eating occasions (before, during or after the season).
![Page 282: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/282.jpg)
Now we have all of the information necessary to determine if there is a statistically significant difference between pizza slices consumed by football players between three different eating occasions (before, during or after the season).
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 283: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/283.jpg)
To calculate the significance level
![Page 284: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/284.jpg)
To calculate the significance levelSource
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 285: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/285.jpg)
We must calculate the F ratio
![Page 286: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/286.jpg)
We must calculate the F ratioSource
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 287: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/287.jpg)
Which is calculated by dividing the Between Groups Mean Square value (9.867) by the Error Mean Square value (1.033).
![Page 288: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/288.jpg)
Which is calculated by dividing the Between Groups Mean Square value (9.867) by the Error Mean Square value (1.033).
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
=
![Page 289: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/289.jpg)
Which is calculated by dividing the sum of squares between groups by its degrees of freedom, as shown below:
![Page 290: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/290.jpg)
Which is calculated by dividing the sum of squares between groups by its degrees of freedom, as shown below:
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
=
![Page 291: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/291.jpg)
Which is calculated by dividing the sum of squares between groups by its degrees of freedom, as shown below:
And
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
=
![Page 292: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/292.jpg)
Which is calculated by dividing the sum of squares between groups by its degrees of freedom, as shown below:
And
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14 =
=
![Page 293: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/293.jpg)
Which is calculated by dividing the sum of squares between groups by its degrees of freedom, as shown below:
And
Now we need to figure out how we calculate degrees of freedom for each source of sums of squares.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14 =
=
![Page 294: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/294.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
![Page 295: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/295.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
![Page 296: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/296.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 297: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/297.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
We take the number of subjects which, in this case, is 5 – 1 = 4
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 298: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/298.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
We take the number of subjects which, in this case, is 5 – 1 = 4
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 299: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/299.jpg)
Let’s begin with determining the degrees of freedom Between Subjects.
We take the number of subjects which, in this case, is 5 – 1 = 4
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Average
Ben 3 3 3 3.0
Bob 5 5 5 5.0
Bud 7 7 7 7.0
Bubba 8 8 8 8.0
Burt 12 12 13 12.3
Between Subjects
1
2
3
4
5
![Page 300: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/300.jpg)
Now – onto Between Groups Degrees of Freedom (df)
![Page 301: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/301.jpg)
Now – onto Between Groups Degrees of Freedom (df)
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 302: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/302.jpg)
Now – onto Between Groups Degrees of Freedom (df)
We take the number of groups which in this case is 3 – 1 = 2
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 303: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/303.jpg)
Now – onto Between Groups Degrees of Freedom (df)
We take the number of groups which in this case is 3 – 1 = 2
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 304: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/304.jpg)
Now – onto Between Groups Degrees of Freedom (df)
We take the number of groups which in this case is 3 – 1 = 2
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
1 2 3
![Page 305: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/305.jpg)
Now – onto Between Groups Degrees of Freedom (df)
We take the number of groups which in this case is 3 – 1 = 2
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
Pizza Slices Consumed
Football Players
Before the Season
During the Season
After the Season
Ben 5 4 4
Bob 7 5 5
Bud 8 7 6
Bubba 9 8 4
Burt 10 7 6
1 2 3
![Page 306: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/306.jpg)
The error degrees of freedom are calculated by multiplying the between subjects by the between groups degrees of freedom.
![Page 307: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/307.jpg)
The error degrees of freedom are calculated by multiplying the between subjects by the between groups degrees of freedom.
4
Between Subjects Degrees of Freedom
2
Between Groups Degrees of Freedom
8Error Degrees of
Freedom
![Page 308: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/308.jpg)
The error degrees of freedom are calculated by multiplying the between subjects by the between groups degrees of freedom.
4
Between Subjects Degrees of Freedom
2
Between Groups Degrees of Freedom
8Error Degrees of
Freedom
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 309: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/309.jpg)
The error degrees of freedom are calculated by multiplying the between subjects by the between groups degrees of freedom.
4
Between Subjects Degrees of Freedom
2
Between Groups Degrees of Freedom
8Error Degrees of
Freedom
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 310: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/310.jpg)
The degrees of freedom for total sum of squares is calculated by adding all of the degrees of freedom from the other three sources.
![Page 311: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/311.jpg)
The degrees of freedom for total sum of squares is calculated by adding all of the degrees of freedom from the other three sources.
4 2 8 14
![Page 312: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/312.jpg)
The degrees of freedom for total sum of squares is calculated by adding all of the degrees of freedom from the other three sources.
4 2 8 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 313: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/313.jpg)
The degrees of freedom for total sum of squares is calculated by adding all of the degrees of freedom from the other three sources.
4 2 8 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 314: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/314.jpg)
We will compute the Mean Square values for just the Between Groups and Error. We are not interested in what is happening with Between Subjects. We calculated the Between Subjects sum of squares only take out any differences that are a function of differences that would exist regardless of what group we were looking at.
![Page 315: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/315.jpg)
Once again, if we had not pulled out Between Subjects sums of squares, then the Between Subjects would be absorbed in the error value:
![Page 316: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/316.jpg)
Once again, if we had not pulled out Between Subjects sums of squares, then the Between Subjects would be absorbed in the error value:
Tests of Within-Subjects Effects
Measure: Pizza_slices
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
![Page 317: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/317.jpg)
Once again, if we had not pulled out Between Subjects sums of squares, then the Between Subjects would be absorbed in the error value:
Tests of Within-Subjects Effects
Measure: Pizza_slices
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047Within Groups 29.600 8 1.033
Total 49.333 14
![Page 318: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/318.jpg)
Once again, if we had not pulled out Between Subjects sums of squares, then the Between Subjects would be absorbed in the error value:
Tests of Within-Subjects Effects
Measure: Pizza_slices
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047Within Groups 29.600 8 1.033
Total 49.333 14
![Page 319: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/319.jpg)
Once again, if we had not pulled out Between Subjects sums of squares, then the Between Subjects would be absorbed in the error value:
Tests of Within-Subjects Effects
Measure: Pizza_slices
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047Within Groups 29.600 8 1.033
Total 49.333 14
Within Groups is another way of
saying Error
![Page 320: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/320.jpg)
And that would have created a larger error mean square value:
![Page 321: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/321.jpg)
And that would have created a larger error mean square value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
![Page 322: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/322.jpg)
And that would have created a larger error mean square value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
![Page 323: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/323.jpg)
Which in turn would have created a smaller F value:
![Page 324: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/324.jpg)
Which in turn would have created a smaller F value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
![Page 325: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/325.jpg)
Which in turn would have created a smaller F value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
=
=
![Page 326: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/326.jpg)
Which in turn would have created a larger significance value:
![Page 327: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/327.jpg)
Which in turn would have created a larger significance value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
![Page 328: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/328.jpg)
Which in turn would have created a larger significance value:
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4 Between Groups 19.733 2 9.867 9.548 .008
Error 8.267 8 1.033
Total 49.333 14
Measure: Pizza_slices
Source Type III Sum of Squares df
Mean Square F Sig.
Between Groups 19.733 2 9.867 4.000 .047
Error 29.600 12 2.467
Total 49.333 14
=
=
![Page 329: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/329.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.
![Page 330: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/330.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.It is for that reason that we calculate the Between Subjects sums of squares and pull it out of the error sums of squares to get an uncontaminated error value…
![Page 331: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/331.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.It is for that reason that we calculate the Between Subjects sums of squares and pull it out of the error sums of squares to get an uncontaminated error value…
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 332: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/332.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.It is for that reason that we calculate the Between Subjects sums of squares and pull it out of the error sums of squares to get an uncontaminated error value…
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 333: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/333.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.It is for that reason that we calculate the Between Subjects sums of squares and pull it out of the error sums of squares to get an uncontaminated error value…
And a more accurate F value…
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 334: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/334.jpg)
With a larger significance value it makes it less likely to reject the null hypothesis.It is for that reason that we calculate the Between Subjects sums of squares and pull it out of the error sums of squares to get an uncontaminated error value…
And a more accurate F value…
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 335: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/335.jpg)
…as well as a more accurate Significance value…
![Page 336: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/336.jpg)
…as well as a more accurate Significance value…Source
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 337: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/337.jpg)
…as well as a more accurate Significance value…
Therefore, we will only focus on mean square values for Between Groups and Error:
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 338: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/338.jpg)
…as well as a more accurate Significance value…
Therefore, we will only focus on mean square values for Between Groups and Error:
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 339: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/339.jpg)
As previously demonstrated, let’s continue with our calculations by dividing the Between Groups mean square value (9.867) by the Error mean square value (1.033).
![Page 340: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/340.jpg)
As previously demonstrated, let’s continue with our calculations by dividing the Between Groups mean square value (9.867) by the Error mean square value (1.033).
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 341: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/341.jpg)
As previously demonstrated, let’s continue with our calculations by dividing the Between Groups mean square value (9.867) by the Error mean square value (1.033).
Which gives us an F value of 9.548
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
=
![Page 342: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/342.jpg)
Because we are using statistical software we will also get a significance value of .008. This means that is we were to theoretically run this experiment 1000 times we would be wrong to reject the null hypothesis 8 times this incurring a type 1 error.
![Page 343: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/343.jpg)
Because we are using statistical software we will also get a significance value of .008. This means that is we were to theoretically run this experiment 1000 times we would be wrong to reject the null hypothesis 8 times this incurring a type 1 error.If we are willing to live with those odds of failure (8 out of 1000) then we would reject the null hypothesis.
![Page 344: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/344.jpg)
If we had set our alpha cut off at .05 that would mean we would be willing to take the risk of being wrong 50 out of 1000 or 5 out of 100 times.
![Page 345: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/345.jpg)
If we had set our alpha cut off at .05 that would mean we would be willing to take the risk of being wrong 50 out of 1000 or 5 out of 100 times.If we do not get a significance value (.008) then we could go to the F table to determine if our F value of 9.548 exceeds the F critical value in the F table.
![Page 346: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/346.jpg)
This F critical value is located using the degrees of freedom for error (8) and the degrees of freedom for between groups (2).
![Page 347: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/347.jpg)
This F critical value is located using the degrees of freedom for error (8) and the degrees of freedom for between groups (2).
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 348: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/348.jpg)
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
Error df
![Page 349: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/349.jpg)
This F critical value is located using the degrees of freedom for error (8) and the degrees of freedom for between groups (2).
![Page 350: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/350.jpg)
This F critical value is located using the degrees of freedom for error (8) and the degrees of freedom for between groups (2).
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 351: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/351.jpg)
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
BG df
![Page 352: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/352.jpg)
Now let’s put them together:
![Page 353: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/353.jpg)
Now let’s put them together:Source
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 354: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/354.jpg)
Now let’s put them together:Source
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
BG df
Error df
![Page 355: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/355.jpg)
Now let’s put them together:Source
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
BG df
Error df
![Page 356: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/356.jpg)
Now let’s put them together:Source
Type III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
BG df
Error df
![Page 357: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/357.jpg)
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
Now let’s put them together:
![Page 358: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/358.jpg)
Now let’s put them together:
Since 9.548 exceeds 4.46 at the .05 alpha level, we will reject the null hypothesis.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 359: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/359.jpg)
Now let’s put them together:
Since 9.548 exceeds 4.46 at the .05 alpha level, we will reject the null hypothesis.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 360: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/360.jpg)
Now let’s put them together:
Since 9.548 exceeds 4.46 at the .05 alpha level, we will reject the null hypothesis.Once again, we only show you the table as another way to determine if you have statistical significance.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14
![Page 361: Tutorial repeated measures ANOVA](https://reader038.vdocuments.site/reader038/viewer/2022102903/55c99c31bb61eb680a8b4751/html5/thumbnails/361.jpg)
Now let’s put them together:
Since 9.548 exceeds 4.46 at the .05 alpha level, we will reject the null hypothesis.Once again, we only show you the table as another way to determine if you have statistical significance.That’s it. You have now seen the inner workings of Repeated Measures ANOVA.
SourceType III Sum of Squares df
Mean Square F Sig.
Between Subjects 21.333 4Between Groups 19.733 2 9.867 9.548 .008Error 8.267 8 1.033
Total 49.333 14