practice as part of a program to reducing smoking, a national organization ran an advertising...
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Practice SubjectBeforeAfterTRANSCRIPT
Practice• As part of a program to reducing smoking, a
national organization ran an advertising campaign to convince people to quit or reduce their smoking. To evaluate the effectiveness of their campaign, they had 15 subjects record the average number of cigarettes smoked per day in the week before and the week after exposure to the advertisement. Determine if the advertisements reduced their smoking (Alpha = .05).
PracticeSubject Before After1 45 43
2 16 20
3 20 17
4 33 30
5 30 25
6 19 19
7 33 34
8 25 28
9 26 23
10 40 41
11 28 26
12 36 40
13 15 16
14 26 23
15 32 34
Practice• Dependent t-test• t = .45• Do not reject Ho
• The advertising campaign did not reduce smoking
Practice
• You wonder if there has been a significant change (.05) in grading practices over the years.
• In 1985 the grade distribution for the school was:
Practice• Grades in 1985
• A: 14%• B: 26%• C: 31%• D: 19%• F: 10%
Observed
A 32
B 61
C 64
D 31
F 12
Total 200
Grades last semester
Step 1: State the Hypothesis
• H0: The data do fit the model– i.e., Grades last semester are distributed the
same way as they were in 1985.
• H1: The data do not fit the model– i.e., Grades last semester are not distributed the
same way as they were in 1985.
Step 2: Find 2 critical
• df = number of categories - 1
Step 2: Find 2 critical
• df = number of categories - 1
• df = 5 - 1 = 4 = .05
2 critical = 9.49
Step 3: Create the data table
Observed Expected Prop.
A 32 .14
B 61 .26
C 64 .31
D 31 .19
F 12 .10
Total 200
Step 4: Calculate the Expected Frequencies
Observed Expected Prop.
Expected Freq.
A 32 .14 28
B 61 .26 52
C 64 .31 62
D 31 .19 38
F 12 .10 20
Total 200
Step 5: Calculate 2
O = observed frequency
E = expected frequency
2
O E O - E (O - E)2 (O - E)2
E 32 28 4 16 .57 61 52 9 81 1.55 64 62 2 4 .06 31 38 -7 49 1.29 12 20 -8 64 3.2
6.67
Step 6: Decision
• Thus, if 2 > than 2critical
– Reject H0, and accept H1
• If 2 < or = to 2critical
– Fail to reject H0
Step 6: Decision
• Thus, if Thus, if 22 > than > than 22criticalcritical
– Reject HReject H00, and accept H, and accept H11
• If 2 < or = to 2critical
– Fail to reject H0
2 = 6.67
2 crit = 9.49
Step 7: Put answer into words
• H0: The data do fit the model
• Grades last semester are distributed the same way (.05) as they were in 1985.
The Three Goals of this Course
• 1) Teach a new way of thinking
• 2) Self-confidence in statistics
• 3) Teach “factoids”
Mean
r =
r =
tobs = (X - ) / Sx
What you have learned!
• Introduced to statistics and learned key words
– Scales of measurement– Populations vs. Samples
What you have learned!
• Learned how to organize scores of one variable using:
– frequency distributions– graphs– measures of central tendency
What you have learned!
• Learned about the variability of distributions
– range– standard deviation– variance
What you have learned!
• Learned about combination statistics
– z-scores– effect sizes– box plots
What you have learned!
• Learned about examining the relation between two continous variables
– correlation (expresses relationship)– regression (predicts)
What you have learned!
• Learned about probabilities
What you have learned!
• Learned about the sampling distribution
– central limit theorem– determine probabilities of sample means– confidence intervals
What you have learned!
• Learned about hypothesis testing
– using a t-test for to see if the mean of a single sample came from a population value
What you have learned!
• Extended hypothesis testing to two samples
– using a t-test for to see if two means are different from each other
• independent• dependent
What you have learned!
• Extended hypothesis testing to three or more samples
– using an ANOVA to determine if three or means are different from each other
What you have learned!
• Extended ANOVA to two or more IVs
– Factorial ANOVA– Interaction
What you have learned!
• Learned how to examine nominal variables
– Chi-Square test of independence– Chi-Square test of goodness of fit
• CRN: 33496.0
Next Step
• Nothing new to learn!
• Just need to learn how to put it all together
Four Step When Solving a Problem
• 1) Read the problem
• 2) Decide what statistical test to use
• 3) Perform that procedure
• 4) Write an interpretation of the results
Four Step When Solving a Problem
• 1) Read the problem1) Read the problem
• 2) Decide what statistical test to use
• 3) Perform that procedure3) Perform that procedure
• 4) Write an interpretation of the results4) Write an interpretation of the results
Four Step When Solving a Problem
• 1) Read the problem
• 2) Decide what statistical test to use2) Decide what statistical test to use
• 3) Perform that procedure
• 4) Write an interpretation of the results
How do you know when to use what?
• If you are given a word problem, would you know which statistic you should use?
Example
• An investigator wants to predict a male adult’s height from his length at birth. He obtains records of both measures from a sample of males.
Possible Answers
a. Independent t-test k. Regressionb. Dependent t-test l. Standard
Deviationc. One-Sample t-test m. Z-scored. Goodness of fit Chi-Square n. Modee. Independence Chi-Square n o. Meanf. Confidence Interval p. Mediang. Correlation (Pearson r) q. Bar Graphh. Scatter Plot r. Rangei. Line Graph s. ANOVAj. Frequency Polygon t. Factorial ANOVA
Example
• An investigator wants to predict a male adult’s height from his length at birth. He obtains records of both measures from a sample of males.
• Use regression
Decision Tree
• First Question:
• Descriptive vs. Inferential• Perhaps most difficult part
– Descriptive - a number or figure that summarizes a set of data
– Inferential - use a sample to conclude something about a population
• hint: these use confidence intervals or probabilities!
Decision Tree: Descriptive
• One or Two Variables
Decision Tree: Descriptive: Two Variables
• Graph, Relationship, or Prediction
– Graph - visual display – Relationship – Quantify the relation between two
continuous variables (CORRELATION)– Prediction – Predict a score on one variable from a
score on a second variable (REGRESSION)
Decision Tree: Descriptive: Two Variables: Graph
• Scatterplot vs. Line graph
– Scatterlot– Linegraph
• Both are used to show the relationship between two variables (it is usually subjective which one is used)
Scatter Plot
0
5
10
15
20
25
0 2 4 6 8 10
Happiness Score
Neu
rotic
ism
Sco
re
Line Graph
0
5
10
15
20
25
0 2 4 6 8 10
Happiness Score
Neu
rotic
ism
Sco
re
Decision Tree: Descriptive: One Variable
• Central Tendency, Variability, Z-Score, Graph
– Central Tendency – one score that represents an entire group of scores
– Variability – indicates the spread of scores– Z-Score – converts a score so that is conveys the sore’s
relationship to the mean and SD of the other scores.– Graph – Visual display
Decision Tree: Descriptive: One Variable: Central Tendency
• Mean, Median, Mode
Decision Tree: Descriptive: One Variable: Central Tendency
• Mean, Median, Mode Mean Median Mode
Nominal NO NO OK
Ordinal NO OK OK
Interval OK OK OK
Ratio OK OK OK
Decision Tree: Descriptive: One Variable: Variability
• Variance, Standard Deviation, Range/IQR
– Variance– Standard Deviation
• Uses all of the scores to compute a measure of variability– Range/IQR
• Only uses two scores to compute a measure of variability
• In general, variance and standard deviation are better to use a measures of variability
Decision Tree: Descriptive: One Variable: Graph
• Frequency Polygon, Histogram, Bar Graph
– Frequency Polygon– Histogram
• Interchangeable graphs – both show frequency of continuous variables
– Bar Graph• Displays the frequencies of a qualitative (nominal) variable
Frequency Polygon
02468
101214161820
8 11 14 17 20 23 26 29 32 35 38
Neuroticism Score
Freq
uenc
y
Histogram
02468
101214161820
8 11 14 17 20 23 26 29 32 35 38
Neuroticism Score
Freq
uenc
y
Bar Graph
0
5
10
15
20
25
30
Biology History Math Psychology Sociology
Major
Freq
uenc
y
Decision Tree: Inferential:
• Frequency Counts vs. Means w/ One IV vs. Means w/ Two or more IVs
– Frequency Counts – data is in the form of qualitative (nominal) data
– Means w/ one IV – data can be computed into means (i.e., it is interval or ratio) and there is only one IV
– Means w/ two or more IVs – data can be computed into means (i.e., it is interval or ratio) and there are two or more IVs
– Confidence Interval - with some degree of certainly (usually 95%) you establish a range around a mean
Decision Tree: Inferential: Frequency Counts
• Goodness of Fit vs. Test of Independence
– Goodness of Fit – Used to determine if there is a good fit between a qualitative theoretical distribution and the qualitative data.
– Test of Independence – Tests to determine if two qualitative variables are independent – that there is no relationship.
Decision Tree: Inferential: Means with two or more IVs
– Factorial ANOVA
Decision Tree: Inferential: Means with one IV
• One Sample, Two Samples, Three or more
– One Sample – Used to determine if a single sample is different, >, or < than some value (usually a known population mean; ONE-SAMPLE t-TEST)
– Two Samples – Used to determine if two samples are different, >, or < than each other
– Two or more – Used to determine if three or more samples are different than each other (ANOVA).
Decision Tree: Inferential: Means with one IV: Two Samples
• Independent vs. Dependent
– Independent – there is no logical reason to pair a specific score in one sample with a specific score in the other sample
– Paired Samples – there is a logical reason to pair specific scores (e.g., repeated measures, matched pairs, natural pairs, etc.)
Cookbook
• Due: Final exam
• Early grade: Wednesday!
• Tuesday: Work on Practice Test and Cookbook (no class)!