One-way ANOVA: Post hoc tests
The Post hoc test dialog provides options for specifying which post hoc test are included in the procedure and for specifying how the significance level (alpha) is handled for post hoc tests. Once you have determined that differences exist among the means, post hoc range tests and pairwise multiple comparisons can determine which means differ. Range tests identify homogeneous subsets of means that are not different from each other. Pairwise multiple comparisons test the difference between each pair of means and yield a matrix where asterisks indicate significantly different group means at an alpha level of 0.05.
- Perform post hoc tests
- Use the toggle control to enable or disable post hoc tests.
- Equal variances assumed
- Provides multiple comparison and range tests when equal variances are assumed. Tukey's honestly
significant difference test, Hochberg's GT2, Gabriel, and Scheffé are multiple comparison tests and
range tests. Other available range tests are Tukey's b, S-N-K (Student-Newman-Keuls), Duncan,
R-E-G-W F (Ryan-Einot-Gabriel-Welsch F test), R-E-G-W Q
(Ryan-Einot-Gabriel-Welsch range test), and Waller-Duncan. Available multiple comparison tests are
Bonferroni, Tukey's honestly significant difference test, Sidak, Gabriel, Hochberg, Dunnett,
Scheffé, and LSD (least significant difference).
- LSD
- Uses t tests to perform all pairwise comparisons between group means. No adjustment is made to the error rate for multiple comparisons.
- Bonferroni
- Uses t tests to perform pairwise comparisons between group means, but controls overall error rate by setting the error rate for each test to the experimentwise error rate divided by the total number of tests. Hence, the observed significance level is adjusted for the fact that multiple comparisons are being made.
- Sidak
- Pairwise multiple comparison test based on a t statistic. Sidak adjusts the significance level for multiple comparisons and provides tighter bounds than Bonferroni.
- Scheffe
- Performs simultaneous joint pairwise comparisons for all possible pairwise combinations of means. Uses the F sampling distribution. Can be used to examine all possible linear combinations of group means, not just pairwise comparisons.
- R-E-G-W F
- Ryan-Einot-Gabriel-Welsch multiple stepdown procedure based on an F test.
- R-E-G-W Q
- Ryan-Einot-Gabriel-Welsch multiple stepdown procedure based on the Studentized range.
- S-N-K
- Makes all pairwise comparisons between means using the Studentized range distribution. With equal sample sizes, it also compares pairs of means within homogeneous subsets, using a stepwise procedure. Means are ordered from highest to lowest, and extreme differences are tested first.
- Tukey
- Uses the Studentized range statistic to make all of the pairwise comparisons between groups. Sets the experimentwise error rate at the error rate for the collection for all pairwise comparisons.
- Tukey's b
- Uses the Studentized range distribution to make pairwise comparisons between groups. The critical value is the average of the corresponding value for the Tukey's honestly significant difference test and the Student-Newman-Keuls.
- Duncan
- Makes pairwise comparisons using a stepwise order of comparisons identical to the order used by the Student-Newman-Keuls test, but sets a protection level for the error rate for the collection of tests, rather than an error rate for individual tests. Uses the Studentized range statistic.
- Hochberg's GT2
- Multiple comparison and range test that uses the Studentized maximum modulus. Similar to Tukey's honestly significant difference test.
- Gabriel
- Pairwise comparison test that used the Studentized maximum modulus and is generally more powerful than Hochberg's GT2 when the cell sizes are unequal. Gabriel's test may become liberal when the cell sizes vary greatly.
- Waller-Duncan
- Multiple comparison test based on a t statistic; uses a Bayesian approach.
- Dunnett
- Pairwise multiple comparison t test that compares a set of treatments against a single control mean. The last category is the default control category. Alternatively, you can choose the first category. 2-sided tests that the mean at any level (except the control category) of the factor is not equal to that of the control category. < Control tests if the mean at any level of the factor is smaller than that of the control category. > Control tests if the mean at any level of the factor is greater than that of the control category.
- Equal variances not assumed
- Provides multiple comparison and range tests when equal variances are not assumed. Multiple
comparison tests that do not assume equal variances are Tamhane's T2, Dunnett's T3, Games-Howell,
and Dunnett's C.
- Tamhane's T2
- Conservative pairwise comparisons test based on a t test. This test is appropriate when the variances are unequal.
- Dunnett's T3
- Pairwise comparison test based on the Studentized maximum modulus. This test is appropriate when the variances are unequal.
- Games-Howell
- Pairwise comparison test that is sometimes liberal. This test is appropriate when the variances are unequal.
- Dunnett's C
- Pairwise comparison test based on the Studentized range. This test is appropriate when the variances are unequal.
- Null hypothesis test
- Specifies how the significance level (alpha) is handled for the post hoc test. You can choose to use the same significance level that is defined in the Options dialog, or specify a different significance level.
Obtaining post hoc tests for One-way ANOVA
This feature requires Statistics Base Edition.
- From the menus choose:
- In the One-way ANOVA dialog, expand the Additional settings menu and click Post hoc tests.