1. Two Sample t test
Chapter 9

2. Two sample t test
We want to test whether the means of two samples are statistically significantly different from each other
Example: Student-motivation data
Test whether the ‘males and females in the study have similar mean academic ability score?’
t test

3. Student t test for 2 samples
Two independent samples
Samples drawn randomly from different populations
Hypothesis : Population means are same
Where S is the standard deviation

4. Two independent Sample t test
If both population are found to have equal variance
Pooled variance estimate is computed
If both population are found to have unequal variance
An exact t cannot be estimated
Only an approximation can be computed
First test if population variance are equal

5. F test for population variance
Testing for equality of population variance
F statistics is computed from sample variance
Known as Levene’s test for equality of variance

6. Testing mean for our example
Test whether the ‘males and females have similar mean academic ability score?’
Academic ability score = OLTS
Testing the mean value of OLTS grouped by gender variable

7. Two independent sample t test: SPSS
Analyze > Compare means > Independent sample t test
Test variable : OLTS
Grouping variable : Gender
Click on Define groups

8. Two independent sample t test: SPSS

9. Two independent sample test: SPSS Output
First part of the table gives the Levene’s test
Decision Rule: P value < 0.05
Reject the H0

10. P value: level of significance
H0: Samples are from population with equal variance
In our example P value = 0.56 > 0.05
Hence we cannot reject the H0
The samples are drawn from populations with equal variances

11. Independent Samples Test
SPSS output
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means F
Sig. t df
Sig. (2-tailed)
Online Test Score
Equal variances assumed
.345
.560
-.286 48
.776
Equal variances not assumed
45.174
The Significance level (P value) > 0.05
We cannot reject the H0 that the mean OLTS for Male and Females are same

12. Exercise on Pg 73
Exercise 2, 3 and 5

13. Paired t test

14. Paired t test The sample relate to same set of respondents
Before After test
Test whether mean performance of a set of respondents before and after a treatment is same
Set of employees undergoing training
Students undergoing MBA course work

15. Paired t test Test performance over time
Test the performance of an organization from the response of same set respondents over time
Feedback about the institute from same set of students in their 1st year and 2nd year of MBA

16. Paired t test Example on pg69
Scores of 20 individuals before and after the training programme
H0: There is no difference in the mean performance of individuals before and after the training programme
H1: There is difference in the mean performance of individual before and after the training programme

17. Paired t test: SPSS Hypothesis
Analyze > Compare means > Paired t test
Select both the variables

18. SPSS output

19. Paired t test: SPSS Results for the t test
Significance level (P value) = < 0.05 (α)
Hence we reject the null hypothesis at 5% level of significance
There is a significant difference in the mean performance of individuals before and after the training.

20. A Classification of Hypothesis Testing Procedures for Examining Differences
Hypothesis Tests
Parametric Tests (Metric Tests)
Non-parametric Tests (Nonmetric Tests)
One Sample
Two or More Samples
* t test
* Z test
Chi-Square
* K-S
* Runs
* Binomial
Independent Samples
Paired Samples
* Two-Group t test
* Z test
* Paired
t test
* Chi-Square
* Mann-Whitney
* Median
* K-S
* Sign
* Wilcoxon
* McNemar
Chi-Square

21. Exercise
Exercise 1 on pg 72
Exercise 4 on Pg 73