Two Sample t test Chapter 9

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

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

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

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

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

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

Two independent sample t test: SPSS

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

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

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

Exercise on Pg 73 Exercise 2, 3 and 5

Paired t test

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

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

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

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

SPSS output

Paired t test: SPSS Results for the t test Significance level (P value) = 0.000 < 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.

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

Exercise Exercise 1 on pg 72 Exercise 4 on Pg 73