9.3 Interpreting the Output

The first table, Group Statistics, is shown in Figure 9.5. This table includes descriptive statistics for each group. Specifically, the table includes the number of cases (N), the mean leader performance score, the standard deviation, and the estimated standard error of the mean (the standard deviation divided by N).

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, Independent Samples Test (Figure 9.6).

• 9.3a Testing for Homogeneity of Variance

The first two columns labeled Levene's Test for Equality of Variances provides a test of one of the assumptions of the t-test, i.e., that the variance in the two groups are equal (i.e., similar or homogenious). If this assumption is violated in the data, a statistical adjustment needs to be made. The F statistic in the first column and its probability in the second column (Sig., an abbreviation for significance) provides this test. If the probability of the F value (i.e., Sig.) 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 F test determine whether to use 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 the Equal variances assumed rows. These rows represent the more conventional method of evaluating the 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 the Equal variances not assumed row. Evaluation of the 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 (Sig. = .000) for the F value is less than .05. Thus, the variances of the two groups are not equal, and therefore the output in the Equal variances not assumed row should be used.

• 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 t-test for equality of Means. We are currently only interested in the obtained t-value and its probability, which can be seen in the columns labeled t and Sig. (2-tailed). Looking in the Equal variances not assumed row, we see a t value of 1.46. The probability in the Sig. (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.

The results indicate that there was no significant difference in performance between women and men, t (195) = 1.46, p = .15. That is, the average performance score of women (M = 6.14, SD = 1.94) was not significantly different from that of men (M = 5.69, SD = 2.74).

Note that while researchers generally are interested in finding "significant differences," sometimes the absence of a significant difference is of either theoretical or practical value. That certainly is the case here. In particular, these results indicate that there is no reliable difference in performance between men and women at EZ Manufacturing. This is an important because this information may be useful in calming the anxieties of upper-level executives who might adhere to the stereotype that women are less capable of men in leadership situations

• 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 Mean Difference. This is simply the difference between the two means. The Standard Error of the Mean Difference is the denominator used in computing the t-statistic. Finally, the 95% Confidence Interval for the Difference consists of two numbers indicating the lower and the upper bound of the confidence interval. We can be 95% confident that the difference between the two means falls between the lower and upper bounds.

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 correlated samples t-test.

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