GLM, GRM, and ANOVA More Results - Post-hoc Tab

Contrast Analysis

Select the Post-hoc tab of the GLM More Results or the ANOVA More Results dialogs to access options to perform post-hoc comparisons between the means in the design. A discussion of the rationale and applications of planned comparisons along with post-hoc tests is also provided in the Contrast Analysis and Post-Hoc Tests section in the context of the ANOVA/MANOVA module. Note that these options are only available if the current design contains effects for categorical predictor variables, or within (repeated measures) effect. For a general description of post-hoc comparisons and additional information on post-hoc tests involving random effects and repeated measures, see Post-hoc Tests in GLM, GRM, and ANOVA.

Effect. Select the desired effect from all of those effects in the current design in the Effect drop-down box. Post-hoc comparisons are performed on the marginal means (weighted observed) for effects involving only categorical predictor variables.

Dependent variables. Click the Dependent variables button to display the Variables for Post Hoc Tests dialog box, where you can select the dependent variables for which to compute the post-hoc tests; a results spreadsheet will be created for each dependent variable that is selected.

Display. The options in the Display group box control the manner in which the results for the requested post-hoc tests will be displayed. For detailed descriptions of the Significant differences, Homogeneous groups, Confidence intervals, and Critical ranges options, see Display Post-hoc Tests Results in GLM, GRM, and ANOVA.

Error term. Use the options in the Error term group box to select an error term (estimate of the error variance sigma) for the post-hoc comparisons. For detailed descriptions of the Between error, Within error, Between; within; pooled, and MS, df options, see Error Term for Post-hoc Tests in GLM, GRM, and ANOVA.

Fisher LSD. Click the Fisher LSD button to produce a spreadsheet containing the results of the Fisher LSD test. This test is equivalent to the t-test for independent or dependent samples (see also Basic Statistics and Tables), based on the N in the respective cells of the design involved in the comparison. It offers the least amount of protection against the increased alpha error rate due to multiple post-hoc comparisons. The results will be displayed in the format specified in the Display group box (see above).

Bonferroni. Click the Bonferroni button to produce a spreadsheet containing the results of the Bonferroni test. The Bonferroni procedure involves tests of multiple a priori hypotheses while controlling the experimenter-wise error rate; specifically, it can be shown that the type 1 error rate (alpha(exp)) for a set of comparisons will not exceed the sum of the error levels (alpha(ind)) for a set of m tests of significance; or alpha(exp) < m*alpha(ind). The Bonferroni procedure uses this inequality to adjust the significance levels for the individual post-hoc comparisons. The results will be displayed in the format specified in the Display group box (see above).

Scheffé. Click the Scheffé button to produce a spreadsheet with the post-hoc p-values for the Scheffé test. The Scheffé test is usually more conservative than the Newman-Keuls or Duncan's test (see Winer, 1962). The results will be displayed in the format specified in the Display group box (see above).

Tukey HSD. Click the Tukey HSD button to produce a spreadsheet containing the results of the Tukey HSD test. The Tukey HSD test falls between the Newman-Keuls (see below) and Scheffé (see above) procedures with regard to conservatism. The results will be displayed in the format specified in the Display group box (see above).

Unequal N HSD. Click the Unequal N HSD button to produce a spreadsheet containing the results of the Tukey Unequal N HSD test. This test is a generalization of Tukey's test to the case of unequal samples sizes (see Spjotvoll & Stoline, 1973, p. 975). The results will be displayed in the format specified in the Display group box (see above).

Range tests (multi-stage tests). The post-hoc tests contained in the Range tests group box test the significance of ranges, given the respective number of samples. The results will be displayed in the format specified in the Display group box (see above).

Newman-Keuls. Click the Newman-Keuls button to produce a spreadsheet containing the results of the Newman-Keuls test. This test is based on the studentized range statistic. Computationally, STATISTICA first sorts the means into ascending order. For each pair of means, STATISTICA then assesses the probability under the null hypothesis (no differences between means in the population) of obtaining differences between means of this (or greater) magnitude, given the respective number of samples. Thus, it actually tests the significance of ranges, given the respective number of samples. Note that STATISTICA does not merely report cut-off values for p, but will compute the actual probabilities based on the distribution of the studentized range statistics.

Crit. ranges. Click the Crit. ranges button to produce a spreadsheet containing the critical ranges for the Newman-Keuls test. This button is only active if you have selected Critical ranges in the Display group box (see above).

Duncan's. Click the Duncan's button to produce a spreadsheet containing the results of the Duncan's test. This test is based on the same logic as the Newman-Keuls procedure (see above); however, it uses a less conservative test criterion (see, for example, Milliken & Johnson, 1984).

Crit. ranges. Click the Crit. ranges button to produce a spreadsheet containing the critical ranges for Duncan's test. This button is only active if you have selected Critical ranges in the Display group box (see above).

Comparisons with a Control Group (CG). Use the options in the Comparisons with a Control Group group box to perform Dunnett's test.

Dunnett. Click the Dunnett button to produce a spreadsheet containing the results of the Dunnett's test. This procedure can be used to compare a set of k-1 treatment groups against a control group (see Dunnett, 1955). Note that the computations involved in the estimation of the p-values for the Dunnett test can be very time consuming, so large problems (many comparisons) may take some time to complete.

< CG. Select the < CG option button to indicate that the post-hoc comparisons (and associated p-values) should be one-sided (mean x(i) < x(control)).

> CG. Select the > CG option button to indicate that the post-hoc comparisons (and associated p-values) should be one-sided (mean x(i) > x(control).

<>CG. Select the <> CG option button to indicate that the post-hoc comparisons (and associated p-values) should be two-sided (x(i) ¹ x(control)).

CG cell #. Enter the number of the cell (treatment group) that you want to be used as the control group in the comparison in the CG cell # field. Refer to the spreadsheet of means (e.g., see the Means tab) for the numbers of cells in the current Effect (see above).

See also, GLM - Index, ANOVA/MANOVA Introductory Overview - Contrast Analysis and Post-hoc Tests, A-Priori Comparisons of Least Observed Squares Means vs. Post-hoc Comparisons of Means, and GLM Hypothesis Testing - Post-hoc Comparisons for additional details.