9.3 Interpreting the Output The first table, Of greatest interest here are the mean performance scores for men (5.68) and for women (6.14). You might be tempted to conclude that this indicates that women had significantly higher average performance scores than men. However, this would be premature - in fact, the whole point of the t-test is to determine whether this is a real difference (statistically significant), or one that could be attributed to random chance. To do this, we need to examine the next table,
- 9.3a Testing for Homogeneity of Variance
The first two columns labeled Sig., an abbreviation for significance) provides this test. If the probability of the value (i.e., FSig.) is less than or equal to .05, then the variances in the groups being compared are different, and the condition of homogeneity of variance has not been satisfied. The results of the Equal variances assumed rows or the Equal variances not assumed rows in evaluating the t statistic. The decision rule for determining which rows to use is as follows:-
**If the variances for the two groups are equal**(i.e,**Sig. > .05**), then use the output in therows. These rows represent the more conventional method of evaluating the**Equal variances assumed****t**value based upon degrees of freedom (**df**) equal to the total number of scores minus 2 (this is the method that is described in most introductory statistics or research methods textbooks). **If the variances for the two groups are significantly different**(i.e,**Sig. < .05**), then use the output in therow. Evaluation of the**Equal variances not assumed****t**statistic in this row is based upon an adjusted degrees of freedom which takes into account the dissimilar variances in the two groups.
Since the probability ( .05. Thus, the variances of the two groups are not equal, and therefore the output in the Equal variances row should be used. not assumed- 9.3b Testing the null hypothesis: Interpreting the significance of the t-value
To determine if the difference in performance between men and women is significant, we need to look in the columns labeled Sig. (2-tailed). Looking in the Equal variances row, we see a not assumed value of 1.46. The probability in the tSig. (2-tailed) column in the (p = .146) is greater than .05, meaning that we need to retain the null hypothesis of no differences, concluding that there was no significant difference in leadership performance between male and female EZ employees.The following sentence illustrates how these results would be written according to APA format.
Note that while researchers generally are interested in finding "significant differences," sometimes the - 9.3c Additional Information in the t-table
There is additional information in the t-table that might be of use to you. The first is the As mentioned, there are numerous other hypotheses we could test using the independent samples t-test on the data from our EZ Manufacturing study. The exercise at the end of the chapter illustrates one of these, and you are encouraged to explore others on your own. In the next chapter we will discuss a similar approach to hypothesis testing using the |