spss2 comparing means_two_groups
TRANSCRIPT
COMPARING MEANS:ONE OR TWO SAMPLES T-
TESTS
Dr. Vipul Patel
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T-tests answer a very simple question—are two scores the same or different?
T test is used to determine whether there is a significant difference between two sets of scores.
Examples of t test3
A major department store chain is having an end of season sale on refrigerators. Is there any evidence that an average of more than 50 refrigerators per store were sold during this sale?
Is there a significant difference between male and female on their grade in research methodology subject?
Is there any difference between people who are allowed to sleep for only four hours and people who are allowed to sleep for eight hours on a cognitive skills test.
Costumer preferences for Lux bathing soap were obtained on 11- point Likert scale. The same consumes were then shown a commercial about Lux. After the commercial, preferences for Lux were again measured. Has the commercial be successful in inducing a change in the preferences.
T-test4
There are three different types of t-tests: One sample t-test, Independent samples t-test, and Dependent (paired) samples t-test
One Sample T test5
The one-sample t-test is used for comparing sample results with a known value.
Specifically, in this type of test, a single sample is collected, and the resulting sample mean is compared with a value of interest, that is not based on the current sample.
The purpose of the one-sample t-test is to determine whether there is sufficient evidence to conclude that the mean of the population from which the sample is taken is different from the specified value.
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Examples of one sample t test A teacher wants to know if the average
weight of student in the class is different from 45 kgs.
An economist wants to know if the per capita income of a particular region is same as the national average.
The Quality Control department wants to know if the mean dimensions of a particular product have shifted significantly away from the original specifications.
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Case: One Sample t-test
Case: checkout time
The null hypothesis: H0: Checkout time of customer in the
store is eight minutes.
SPSS output: Case 18
Conclusion: p > 0.05. Thus, do not reject the null hypothesis at 5% significance level
Narration of Result 9
A one sample t test was performed to test the hypothesis that the average checkout time of customers at Kisan Retail store is eight minutes. The null hypothesis is not rejected, t (75) = - 0.397, p = 0.639
Independent Sample t test 10
An independent sample t test is used when you want to compare the mean score, on some continuous variable, for two different groups of subjects.
To conduct independent sample t test, you require: One categorical variable (independent
variable) One continuous variable (dependent
variable)
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Examples of independent sample t test An economist wants to compare the per
capita income of two different regions. A labor union wants to compare the
productivity levels of workers for two different groups.
An aspiring MBA student wants to compare the salaries offered to the graduates of two business schools.
Assumptions of Independent Sample t test
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Independence of group: participants should appear in only one group and these groups are unrelated.
Homogeneity of variance: the group should come from populations with equal variance. To test homogeneity of variance, SPSS uses the Levene Test for equality of variance.
The dependent variable is normally distributed within each population.
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Case 2: Gender Difference in Self Esteem Score
Two variables: Categorical Variable: Gender: Male – 1;
Female – 2 Continuous Variable: Total Self Esteem -
Tslfest: Summated score that participate recorded on a ten item self esteem scale. Null Hypothesis: There is no significant
difference in the mean self esteem scores of males and females.
SPSS output: Case 214
sex N Mean Std. Deviation Std. Error Meantotal self esteem MALES 184 34.02 4.911 0.362
FEMALES 252 33.17 5.705 0.359
Independent Samples Test
Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t dfSig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the
Difference
Lower Uppertotal self esteem
Equal variances assumed
3.506 0.062 1.622 434 0.105 0.847 0.522 -0.179 1.873
Equal variances not assumed
1.661 422.349 0.098 0.847 0.510 -0.156 1.850
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If the significance level of Levene’s test is p=0.05 or less, this means that the variance for the two groups are not the same. Then, refer equal variance not assumed.
If the significance level of Levene’s test is greater than p=0.05, this means that the variance for the two groups are the same. Then, refer equal variance assumed.
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If the value in the Sig. (2 tailed) column is less than 0.05, reject the null hypothesis. It means there is significant difference in the man scores on the dependent variable for each of the two groups.
If the value is above 0.05, do not reject the null hypothesis. It means there is no significant difference between the two groups.
Conclusion of Case 217
SPSS Output of the case 2 shows that Significance level for Levene’s test is above 0.05. Therefore, variance for the two groups are the same.
Refereeing the row of equal variance assumed, sig. (2 tailed) value is above 0.05, do not reject the null hypothesis, so it can be concluded that there is not a significant difference in the mean self esteem scores of males an females.
Effect Size for Independent Samples t test
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Eta square represents the proportion of variance in the dependent variable that is explained by the independent (group) variable.
The guidelines (Cohen, 1988) for interpreting this value are: 0.01= small effect; 0.06=moderate effect and 0.14 = large effect
Eta squared in our case is 0.006 (i.e., small effect). Only 0.6% of variance in self esteem is explained by gender.
Presenting the results for Independent Sample t test (Case 2).
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An independent samples t test was conducted to compare the self esteem scores for males and females. The null hypothesis was not rejected, t (434)=1.62, p=0.11. There was no significant difference in scores for males and female. The magnitude of the differences in the means was very small ( eta squared = 0.006).
Paired sample t test20
The paired t-test is appropriate for data in which the two samples are paired in some way.
Pairs consist of before and after measurements on a single groups of subjects.
Two measurements on the same subject or entity (right and left eye, for example) are paired.
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Examples of paired sample t test: The HR manager wants to know if a
particular training program had any impact in increasing the motivation level of the employees.
The production manager wants to know if a new method of handling machines helps in reducing the break down period.
An educationist wants to know if interactive teaching helps students learn more as compared to one-way lecturing.
Case 3: Paired Sample t Test 22
This case explore the impact of an intervention designed to increase students’ confidence in their ability to survive a compulsory statistics course.
Students were asked to complete a Fear of Statistics Test (FOST) both before (Time 1) and after (Time 2) intervention.
Open SPSS data file: experim.sav
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Here we have two variables: One categorical independent variable :
Time – before (Time 1) and after (Time 2). One continuous dependent variable: Fear of
Statistics Test Score, measured on two different occasions or under different conditions.
Null Hypothesis: there is no significant difference in the mean score of Fear of Statistics Test for before and after intervention.
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SPSS output: Case 3
Paired Samples Statistics
Mean N Std. Deviation Std. Error MeanPair 1 fear of stats time1 40.17 30 5.160 .942
fear of stats time2 37.50 30 5.151 .940
Paired Samples Test
Paired Differences
t dfSig. (2-tailed)Mean
Std. Deviation
Std. Error Mean
95% Confidence Interval of the
Difference
Lower UpperPair 1 fear of stats
time1 - fear of stats time2
2.667 2.708 .494 1.655 3.678 5.394 29 .000
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If the value in the Sig. (2 tailed) column is less than 0.05, reject the null hypothesis. So it can be concluded that there is significance difference between two scores.
If the value is above 0.05, do not reject the null hypothesis. It means there is no significant difference between the two scores.
Conclusion of Case 226
SPSS output for case 3 shows that sig. (2 tailed) value is less than 0.05, reject the null hypothesis. So it can be concluded that there is a significant difference in the Fear of Statistics test (FOST) scores at Time 1 and at Time 2.
In this case, the mean FOST score at Time 1 was 40.17 and the mean score for Time 2 was 37.50. Therefore, it can be concluded that there was a significant decrease in FOST scores from Time 1 (before intervention) to Time 2 (After Intervention).
Presenting the results for Paired Sample t test (Case 3).
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A paired samples t test was conducted to evaluate the impact of the intervention on students’ scores on the Fear of Statistics Test (FOST). There was a statistically significant decrease in FOST scores from Time 1 to Time 2, t(29) = 5.39, p<0.05.
