Following is a small example of output from a between groups design involving sex differences on a measure of anxiety. The output presents the results of a t-test, which is a common statistical test. While the output from a common factor analysis, MANOVA, or some other analysis may result in different output, we still make an effort to explain what the output means. See below.
The following analysis represents an independent samples t-test your data. An independent samples t-test is an appropriate statistical method because you have a single dependent variable (Anxiety) which is continuous and a single independent variable with two categories (Sex). The t-test is used to see if there are statistically significant differences between the two independent groups on the continuous dependent variable.
Use the following guide to decide if a given statistic was significant or if it was due to chance. The “Sig” column represents the probability that the observed statistic is due to chance. An observed statistic was “significant” when the value of “Sig” was less than the chosen probability of type 1 error, alpha (commonly .05). If the value of “Sig” is greater than alpha (commonly .05), the corresponding statistic may have arisen due to chance.
Following are descriptive statistics for males and females on anxiety. A majority of this sample was female. Note that the mean for males was higher than the mean for females.
You may recall that one of the assumptions of a t-test is equal variances among the groups of the independent variable. This assumption is sometimes referred to as homogeneity of variance. In the context of your research, it means that the spread of scores for the male and female groups is approximately equal. A Levene’s test can be used to test this assumption. A non-significant Levene’s test suggests that the variance of the anxiety scores is approximately equal for the male and female groups. If the Levene’s test is nonsignificant, the researcher could report the results of the row "equal" variances assumed. If the Levene's test is significant, this implies that the variance of the anxiety scores is not equal for the male and female groups. If this is the case, the researcher could report the results of the row labeled "equal variances not assumed."
The following table presents a Levene's test for homogeneity of variance and a t-test test of the difference between the means males and females. Since the Levene’s test was nonsignificant, this is evidence that the assumption of equal variances was not violated. Therefore, we suggest interpreting the results in the row labeled "equal variances assumed." Note that the t test corresponding to the difference between males and females on anxiety was not statistically significant.
Optionally, the client can request high resolution graphs to help examine these differences. Following is an example of an "error-bar" graph. The horizontal axis shows the male and female groups. The means in this graph are the same as the values previously reported within the descriptive statistics table. The vertical axis shows a range of possible scores on the dependent variable anxiety. The box in the middle of the brackets shows the mean for each group and the brackets above and below represent the 95% confidence interval about the mean. Note that the confidence interval for the males and females overlap, which is consistent with the non significant t-test that was reported above.
Figure 1
Summary: The hypothesis that there would be significant sex differences on anxiety was not supported by this data. Although the mean for men was higher than the mean for women, the difference was not large enough to be statistically significant.
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