PHARM/PCS V5 · Procedure 36 ANOVA and Comparisons
Newman-Keuls Test
After a significant ANOVA, find which pairs of group means differ, using the studentized range, with groups of any size.
What it computes
After ANOVA shows significance, tests all pairwise differences using the studentized range statistic q. Supports unequal group sizes. Critical q values are computed automatically from the studentized range distribution using the within-sample degrees of freedom.
Inputs and outputs
You provide
- The values for each group, entered as separate blocks; groups may differ in size
- Optionally, your own q critical values in place of the computed ones
PHARM/PCS reports
- The underlying ANOVA: F, mean square error, and degrees of freedom
- Critical q values at 95% and 99%
- Every pairwise difference, marked by significance level
- A chart of the means grouped into homogeneous subsets
When to use it
As a follow-up after a significant one-way ANOVA (Procedure 33) when you want to know which pairs differ and you're comparing all groups against each other. Duncan (Procedure 37) and LSD (Procedure 38) are alternative all-pairs methods; Dunnett (Procedure 44) is the choice when every comparison is against a single control.
Reading the results
Newman-Keuls is stepwise, more powerful than a blanket LSD but less strict about false positives across many comparisons than the more conservative range tests: fine for exploratory work, less so when a single false claim is costly. Never run it without a significant ANOVA first, since the omnibus test is the gate.
No q table needed
The 1986 program read critical values prepared from the book's Table A.13. V5 computes them from the studentized range distribution, the same approach R and SciPy use, and agrees with Table A.13 to within about 0.008. An override field lets you enter table values directly.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.