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.

This “stepdown” procedure works by first ordering group means from smallest to largest. The smallest mean and the largest mean are then tested for a significant difference with an F-test.

- 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)**, when k < g – 1^{k/g}

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.

## REGWQ

A similar test to the REGWF is the REGWQ, which is based on the Q or studentized range. REGWQ is less computationally intensive, but less powerful.

**References**:

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.

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