t-Test Application Testing Assumptions:

The Levene Test The homogeneity of variance assumption is tested with the Levene test. The Levene test is automatically generated in SPSS when an independent samples t-test is conducted. The null hypothesis for the Levene test is that group variances are equal. A significant Levene test (p < .05) indicates that the homogeneity of variance assumption is violated.

In this case, report the "Equal variances not assumed" row of the t-test output from SPSS. This version of the t-test uses a more conservative adjusted degrees of freedom (df) that compensates for the homogeneity violation. The adjusted df can often result in a decimal number (such as df = 13.4), which is commonly rounded to a whole number in reporting (df = 13). If the Levene test is not significant (that is, homogeneity is assumed), report the "Equal variances assumed" row.. Proper Reporting of the Independent Samples t-test Reporting a t-test requires an understanding of several elements, including the statistical notation for an independent samples t-test (t), the degrees of freedom in parentheses, the t value, and the probability value.

To provide context, provide the means and standard deviations for each group. For example, you might report: The mean test score for Class A (M = 93.32, SD = 2.1) was higher than the mean test score for Class B (M = 81.46 SD = 1.9). This was a statistically significant difference, t(98) = 2.75, p = .013. t, Degrees of Freedom, and t Value The statistical notation for an independent samples t-test is t, and following it is the degrees of freedom for this statistical test. The degrees of freedom for t is n1 + n2 2, where n1 equals the number of participants in Group 1 and n2 equals the number of participants in Group 2.

In the example above, there are 50 people in each group: N = 100 ( n1 = 50; n2 = 50), so the df = 98 [(n1 + n2 ) 2]. It is not recommended that the t-test be conducted with groups of fewer than 10 members. The t value is a ratio of the difference in group means divided by the standard error of the difference in sample means. The t value can be either positive or negative. 21 Probability Value SPSS determined the exact p value to be .013. This p value is less than .05, which indicates that the null hypothesis should be rejected for the alternative hypothesisthat is, the two groups are significantly different in test scores.