Question

The Independent Samples t-Test compares the means of two independent groups to determine whether there is statistical evidence that the associated population means are significantly different. The Independent Samples t-Test is a parametric test.

Give an example of two variables you would compare, what your theory is and the hypothesis, and how you would find the independent samples t-test in SPSS.

Answer 1

Suppose we wish to compare the mean score of girls and boys in a class test of 10th standard.

The scores obtained by girls in class test be X and that by boys be Y.

Then, X and Y are independent of each other as the two has no association and did not affect each other in any way.

Hence, here we will perform the independent samples t test.

For this, the random sample of scores of both the groups (boys and girls) are noted and the data [two variables i.e the score (scale) and gender(nominal) with value 1 for boys and 2 for girls] is entered in SPSS.

Hypothesis can be framed as :

Null hypothesis : There is no significant difference between the mean score of boys and girls.

Alternative hypothesis : There is significant difference between the mean score of boys and girls.

Assuming equal variances,

Test statistic is given by -

where, nx and ny are the sample sizes of girls and boys respectively.

sp is the pooled standard deviation given by -

Now, to perform independent t test in SPSS, we will click on Analyze, compare means, independent samples t test and then move scores in test variable and gender in comparing variables. In define groups, in use specified values enter 1 in group 1 and 2 in group 2 . Then, click on continue. Then, click OK.

The t table will appear and we have to consider the equal variances assumed.

Sigma two tailed Colomn will represent the p value.

Now, comparing p value with the level of significance, we can conclude whether to reject or not reject the null hypothesis.

If P-value < level of significance, then reject the null hypothesis otherwise not.