POSTHOC Subcommand (ONEWAY command)

POSTHOC produces post hoc tests for comparisons of all possible pairs of group means or multiple comparisons. In contrast to a priori analyses specified on the CONTRAST subcommand, post hoc analyses are usually not planned at the beginning of the study but are suggested by the data in the course of the study.

  • Twenty post hoc tests are available. Some detect homogeneity subsets among the groups of means, some produce pairwise comparisons, and others perform both. POSTHOC produces a Multiple Comparison table showing up to 10 test categories. Nonempty group means are sorted in ascending order, with asterisks indicating significantly different groups. In addition, homogeneous subsets are calculated and displayed in the Homogeneous Subsets table if the test is designed to detect homogeneity subsets.
  • When the number of valid cases in the groups varies, the harmonic mean of the group sizes is used as the sample size in the calculation for homogeneity subsets except for QREGW and FREGW. For QREGW and FREGW and tests for pairwise comparison, the sample sizes of individual groups are always used.
  • You can specify only one POSTHOC subcommand per ONEWAY command. If more than one is specified, the last specification takes effect.
  • You can specify one alpha value used in all POSTHOC tests using keyword ALPHA. The default is 0.05.

SNK. Student-Newman-Keuls procedure based on the Studentized range test. Used for detecting homogeneity subsets.

TUKEY. Tukey’s honestly significant difference. This test uses the Studentized range statistic to make all pairwise comparisons between groups. Used for pairwise comparison and for detecting homogeneity subsets.

BTUKEY. Tukey’s b. Multiple comparison procedure based on the average of Studentized range tests. Used for detecting homogeneity subsets.

DUNCAN. Duncan’s multiple comparison procedure based on the Studentized range test. Used for detecting homogeneity subsets.

SCHEFFE. Scheffé’s multiple comparison t test. Used for pairwise comparison and for detecting homogeneity subsets.

DUNNETT(refcat). Dunnett’s two-tailed t test. Used for pairwise comparison. Each group is compared to a reference category. You can specify a reference category in parentheses. The default is the last category. This keyword must be spelled out in full.

DUNNETTL(refcat). Dunnett’s one-tailed t test. Used for pairwise comparison. This test indicates whether the mean of each group (except the reference category) is smaller than that of the reference category. You can specify a reference category in parentheses. The default is the last category. This keyword must be spelled out in full.

DUNNETTR(refcat). Dunnett’s one-tailed t test. Used for pairwise comparison. This test indicates whether the mean of each group (except the reference category) is larger than that of the reference category. You can specify a reference category in parentheses. The default is the last category. This keyword must be spelled out in full.

BONFERRONI. Bonferroni t test. This test is based on Student’s t statistic and adjusts the observed significance level for the fact that multiple comparisons are made. Used for pairwise comparison.

LSD. Least significant difference t test. Equivalent to multiple t tests between all pairs of groups. Used for pairwise comparison. This test does not control the overall probability of rejecting the hypotheses that some pairs of means are different, while in fact they are equal.

SIDAK. Sidak t test. Used for pairwise comparison. This test provides tighter bounds than the Bonferroni test.

GT2. Hochberg’s GT2. Used for pairwise comparison and for detecting homogeneity subsets. This test is based on the Studentized maximum modulus test. Unless the cell sizes are extremely unbalanced, this test is fairly robust even for unequal variances.

GABRIEL. Gabriel’s pairwise comparisons test based on the Studentized maximum modulus test. Used for pairwise comparison and for detecting homogeneity subsets.

FREGW. Ryan-Einot-Gabriel-Welsch’s multiple stepdown procedure based on an F test. Used for detecting homogeneity subsets.

QREGW. Ryan-Einot-Gabriel-Welsch’s multiple stepdown procedure based on the Studentized range test. Used for detecting homogeneity subsets.

T2. Tamhane’s T2. Used for pairwise comparison. This test is based on a t test and can be applied in situations where the variances are unequal.

T3. Tamhane’s T3. Used for pairwise comparison. This test is based on the Studentized maximum modulus test and can be applied in situations where the variances are unequal.

GH. Games and Howell’s pairwise comparisons test based on the Studentized range test. Used for pairwise comparison. This test can be applied in situations where the variances are unequal.

C. Dunnett’s C. Used for pairwise comparison. This test is based on the weighted average of Studentized ranges and can be applied in situations where the variances are unequal.

WALLER(kratio). Waller-Duncan t test. Used for detecting homogeneity subsets. This test uses a Bayesian approach. The k-ratio is the Type 1/Type 2 error seriousness ratio. The default value is 100. You can specify an integer greater than 1 within parentheses.

Example

ONEWAY WELL BY EDUC6 
  /POSTHOC=SNK SCHEFFE ALPHA=.01.
  • ONEWAY requests two different post hoc tests. The first uses the Student-Newman-Keuls test and the second uses Scheffé’s test. Both tests use an alpha of 0.01.