T-Test for Independent Samples by Groups - Options Tab

Select the Options tab of the T-Test for Independent Samples by Groups dialog box to access options to determine the detail and formatting of the t-test for independent samples results spreadsheet.

Display long variable names

Select this check box to display the long variable names (if any, see Variable Specs Editor) along with the short names in the first column of the result spreadsheets. If no long variable names have been specified for any of the selected variables, the setting of this check box will have no effect.

Test w/ separate variance estimates

Select this check box to add the t-test with separate variance estimates to the result spreadsheet that is displayed when you click the Summary button. In order to compute the t-test for independent samples, STATISTICA estimates the variance of the difference for the respective dependent variable. By default, this variance is estimated from the pooled (averaged) within-group variances. If the variances in the two groups are widely different, and the number of observations in each group also differs, the t-test computed in this manner may not accurately reflect the statistical significance of the difference. In this case, you should use this option to compute the t-test with separate variance estimates and approximate degrees of freedom (see Blalock, 1972; this test is also called the Welch t; see Welch, 1938).

Multivariate test (Hotelling's T2)

Select this check box to add the Hotelling T2 test to the Header of the result spreadsheet that is displayed when you click the Summary button.

The Hotelling T2 test is a multivariate test for differences in means between two groups. This test will only be computed if more than one dependent variable is selected. Because this test is based on the within-group variance/covariance matrices for the dependent variables, it will automatically exclude missing data casewise from the computations. That is, this test will be computed only for cases that have complete data for all dependent variables in the selected list. If the Test w/ separate variance estimates check box (see above) is cleared, the covariance matrices of the selected dependent variables will be pooled across the two groups to estimate the common population covariance matrix; if the Test w/ separate variance estimates check box is selected, the covariance matrices will not be pooled together.

Equivalence test (TOST)

Select this check box to add the Schuirmann's two one-sided test (TOST) of statistical equivalence to the results spreadsheet that is displayed when you click the Summary button.

This test enables you to determine if the means between two groups are practically equivalent within some interval of equivalence/indifference. Click the adjacent button to display the Enter equivalence values dialog box, where you can specify the interval of equivalence/indifference for each variable by entering an equivalence value; e.g., a value of 0.1 defines an interval of [-0.1,0.1].

A small p-value gives evidence to suggest that the difference between the means are contained within the interval of equivalence. If you select the Test w/ separate variance estimates check box (see above), the variances will not be pooled together and the results will be based on the one sided t-tests using separate variances. See the Equivalence Test topic for more information.

p-value for highlighting

The default p-value for highlighting is .05. You can adjust this p-value by entering a new value in the edit box or using the microscroll buttons. For more details on p-value, see Elementary Concepts.

CI for estimates

Select this check box to compute confidence interval estimates for the differences between means. You can request confidence limits for any p-value using the corresponding field.

By default, the 95% confidence limits (p=.05) is computed. If the Test w/ separate variance estimates check box (see above) is cleared, the variance used in the calculation of the confidence limits is estimated from the pooled (averaged) within-group variances; if the Test w/ separate variance estimates check box is selected, separate variance estimates with the approximate degrees of freedom are used in calculating the confidence limits. For more information on confidence limits, see Descriptive Statistics - "True" Mean and Confidence Interval.

Homogeneity of variances

Two tests for the homogeneity of variance assumption are available in this group box. For more information on the importance of the homogeneity of variance assumption, see Homogeneity of variances in the ANOVA/MANOVA module.

Levene's test

Click the Levene's test button to add the Levene test to the result spreadsheet that is displayed when you click the Summary button.

The standard t-test for independent samples is based on the assumption that the variances in the two groups are the same (homogeneous). A powerful statistical test of this assumption is Levene's test (however, see also the description of the Brown-Forsythe modification of this test below). For each dependent variable, an analysis of variance is performed on the absolute deviations of values from the respective group means.

If the Levene test is statistically significant, then the hypothesis of homogeneous variances should be rejected. However, note that the t-test for independent samples is a robust test as long as the N per group is greater than 30 (and, in particular, in the case of equal N); thus, a significant Levene test does not necessarily call into question the validity of the t-test (see also the general overview to the t-test for independent samples). Also, in the case of unbalanced designs (i.e., unequal N per group), the Levene test is itself not very robust, as has recently been pointed out in, for example, Glass and Hopkins (1996; see also the next paragraph).

Brown & Forsythe test

Click the Brown & Forsythe test button to add the Brown & Forsythe test to the result spreadsheet that is displayed when you click the Summary button.

Recently, some authors (e.g., Glass and Hopkins, 1996) have called into question the power of the Levene test for unequal variances. Specifically, the absolute deviation (from the group means) scores can be expected to be highly skewed; thus, the normality assumption for the ANOVA of those absolute deviation scores is usually violated. This poses a particular problem when there is unequal N in the two (or more) groups that are to be compared.

A more robust test that is very similar to the Levene test has been proposed by Brown and Forsythe (1974). Instead of performing the ANOVA on the deviations from the mean, one can perform the analysis on the deviations from the group medians. Olejnik and Algina (1987) have shown that this test will give quite accurate error rates even when the underlying distributions for the raw scores deviate significantly from the normal distribution.

However, recently, Glass and Hopkins (1996, p. 436) have pointed out that both the Levene test as well as the Brown-Forsythe modification suffer from what those authors call a fatal flaw, namely, that both tests themselves rely on the homogeneity of variances assumption (of the absolute deviations from the means or medians); and hence, it is not clear how robust these tests are themselves in the presence of significant variance heterogeneity and unequal N. In most cases, when one suspects a violation of the homogeneity of variances assumption, it is probably advisable to interpret the Test /w separate variance estimates described above.