Option Description Reference Nonparametric Menu Option Each Pair, Student’s t 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. Nonparametric > Nonparametric Multiple Comparisons > Wilcoxon Each Pair All Pairs, Tukey HSD 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). Nonparametric > Nonparametric Multiple Comparisons > Steel-Dwass All Pairs With Best, Hsu MCB Tests whether the means are less than the unknown maximum or greater than the unknown minimum. This is the Hsu MCB test (Hsu, 1996 and Hsu, 1981). none With Control, Dunnett’s Tests whether the means are different from the mean of a control group. This is Dunnett’s test (Dunnett 1955). Nonparametric > Nonparametric Multiple Comparisons > Steel With Control
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.
Related Information
 • Example Contrasting All of the Compare Means Tests
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
 • Circles for means that are significantly different either do not intersect, or intersect slightly, so that the outside angle of intersection is less than 90 degrees.
 • If the circles intersect by an angle of more than 90 degrees, or if they are nested, the means are not significantly different.
Angles of Intersection and Significance
Highlighting Comparison Circles
Related Information
 • Statistical Details for Comparison Circles
The Each Pair, Student’s t test shows the Student’s t-test for each pair of group levels and tests only individual comparisons.
Related Information
 • Example of the Each Pair, Student’s t Test
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.
Related Information
 • Example of the All Pairs, Tukey HSD Test
The With Best, Hsu MCB test determines whether the mean for a given level exceeds the maximum mean of the remaining levels, or is smaller than the minimum mean of the remaining levels. See Hsu, 1996.
The report shows p-values for one-sided Dunnett tests. For each level other than the best, the p-value given is for a test that compares the mean of the sample best level to the mean of each remaining level treated as a control (potentially best) level. The p-value for the sample best level is obtained by comparing the mean of the second sample best level to the mean of the sample best level treated as a control.
For each level of the categorical variable, this column gives a p-value for a test that the mean of that level exceeds the maximum mean of the remaining levels. Use the tests in this column to screen out levels whose means are significantly smaller than the (unknown) largest true mean.
For each level of the categorical variable, this column gives a p-value for a test that the mean of that level is smaller than the minimum mean of the remaining levels. Use the tests in this column to screen out levels whose means are significantly greater than the (unknown) smallest true mean.
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.
Related Information
 • Example of the With Best, Hsu MCB Test
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.
Related Information
 • Example of the With Control, Dunnett’s Test
 Difference Matrix Shows a table of all differences of means. Confidence Quantile Shows the t-value or other corresponding quantiles used for confidence intervals. LSD Threshold Matrix Shows a matrix showing if a difference exceeds the least significant difference for all comparisons. Connecting Letters Report Shows the traditional letter-coded report where means that are not sharing a letter are significantly different. Ordered Differences Report Shows all the positive-side differences with their confidence interval in sorted order. For the Student’s t and Tukey-Kramer comparisons, an Ordered Difference report appears below the text reports. This report shows the ranked differences, from highest to lowest, with a confidence interval band overlaid on the plot. Confidence intervals that do not fully contain their corresponding bar are significantly different from each other. Detailed Comparisons Report 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.