Hypothesis Testing > REGWF Test
What is the Ryan-Einot-Gabriel-Welsh F(REGWF) Procedure?
The REGWF procedure– a modification of the Student-Newman-Keuls (SNK) procedure — is a step-down pairwise comparison procedure for One-Way Anova. It is a way to control the familywise error rate in multi-stage tests. It is a conservative test, which means that the familywise error rate does not exceed the alpha level. The test controls the family-wise α error more strictly than the SNK, but it is less powerful.
How the Procedure Works
REGWF is recommended for balanced designs, which have even numbers of levels.
- If the two means are significantly different, the test repeats for the next smallest and largest mean.
- If the two means are not significantly different, the test stops.
The error rate is maintained at each step by adjusting the significance levels for each subset of means. If g is the number of means in the group being tested and k is the number of means in a subset, then the significance level is adjusted to:
- α, when k = g or k = g-1;
- 1 – (1 – α)k/g, when k < g – 1
The p-values are also adjusted, except for when k ≥ g – 1.
Assumptions for the Test
- ANOVA results do not have to be significant to run the test.
- Assumption of equal variances applies.
IBM Knowledge Center. Means Comparison. Retrieved March 10, 2017 from: https://www.ibm.com/support/knowledgecenter/SSRL5J_1.1.0/com.ibm.swg.ba.cognos.ug_cr_rptstd.10.1.1.doc/c_id_obj_anova.html
Toothaker, L. (1991). Multiple Comparisons for ‘Interrater reliability and agreement’ of Subjective Researchers. Newbury PArk, CA: Sage.
Wright, S. (1992). Adjusted P-Values for Simultaneous Inference. Biometrics 48, 1005-1013.
Stephanie Glen. "REGWF (Ryan-Einot-Gabriel-Welsh F) Procedure" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/regwf-procedure/
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