Computes individual pairwise comparisons using Student’s t-tests. If you make many pairwise tests, there is no protection across the inferences. Therefore, the alpha-size (Type I error rate) across the hypothesis tests is higher than that for individual tests.
Shows a test that is sized for all differences among the means. This is the Tukey or Tukey-Kramer HSD (honestly significant difference) test. (Tukey 1953, Kramer 1956). This test is an exact alpha-level test if the sample sizes are the same, and conservative if the sample sizes are different (Hayter 1984).
Note: If you have specified a Block column, then the multiple comparison methods are performed on data that has been adjusted for the Block means.
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Each multiple comparison test begins with a comparison circles plot, which is a visual representation of group mean comparisons. Visual Comparison of Group Means shows the comparison circles for the All Pairs, Tukey HSD method. Other comparison tests lengthen or shorten the radii of the circles.
Visual Comparison of Group Means
Angles of Intersection and Significance
Highlighting Comparison Circles
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The Each Pair, Student’s t test shows the Student’s t-test for each pair of group levels and tests only individual comparisons.
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The All Pairs, Tukey HSD test (also called Tukey-Kramer) protects the significance tests of all combinations of pairs, and the HSD intervals become greater than the Student’s t pairwise LSDs. Graphically, the comparison circles become larger and differences are less significant.
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The With Best, Hsu MCB test determines whether a mean can be rejected as the maximum or minimum among the means. The Hsu’s MCB test is given for each level versus the maximum, and each level versus the minimum.
If a mean has means significantly separated above it, it is not regarded as the maximum.
If a mean has means significantly separated below it, it is not regarded as the minimum.
If a mean is significantly separated above all other means, it is regarded as the maximum.
If a mean is significantly separated below all other means, it is regarded as the minimum.
For the maximum report, a column shows the row mean minus the column mean minus the LSD. If a value is positive, the row mean is significantly higher than the mean for the column, and the mean for the column is not the maximum.
For the minimum report, a column shows the row mean minus the column mean plus the LSD. If a value is negative, the row mean is significantly less than the mean for the column, and the mean for the column is not the minimum.
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The With Control, Dunnett’s test compares a set of means against the mean of a control group. The LSDs that it produces are between the Student’s t and Tukey-Kramer LSDs, because they are sized to refrain from an intermediate number of comparisons.
In the Dunnett’s report, the quantile appears, and can be used in a manner similar to a Student’s t-statistic. The LSD threshold matrix shows the absolute value of the difference minus the LSD. If a value is positive, its mean is more than the LSD apart from the control group mean and is therefore significantly different.
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Shows the t-value or other corresponding quantiles used for confidence intervals.
Shows a detailed report for each comparison. Each section shows the difference between the levels, standard error and confidence intervals, t-ratios, p-values, and degrees of freedom. A plot illustrating the comparison appears on the right of each report.