PHARM/PCS V5 · Procedure 33 ANOVA and Comparisons
Analysis of Variance I: One-Way
Test whether three or more group means differ in one omnibus test, rather than a string of t-tests, with groups of any size.
What it computes
Tests whether the means of three or more groups differ significantly. Computes the between-groups and within-groups sums of squares, F-ratio, and compares to the F-distribution critical value. Groups may have unequal sizes.
Inputs and outputs
You provide
- The values for each group, entered as separate blocks; groups may differ in size
PHARM/PCS reports
- Between-groups, within-groups, and total sums of squares
- The F ratio with its exact p-value
- Critical F at the 95% and 99% levels
- A chart of group means with standard errors
When to use it
When one factor splits your data into three or more independent groups (a vehicle control plus several dose groups, or a set of competing treatments) and you want a single omnibus test of whether any group differs, instead of running many pairwise t-tests and inflating your false-positive rate. For two factors at once, see Procedures 34 and 35.
Reading the results
A significant F says at least one group mean stands apart, but not which; that takes a follow-up multiple-comparison test (Newman-Keuls, Duncan, or LSD, and Dunnett when comparing against a control: Procedures 36-38 and 44). The F-test assumes roughly normal residuals and similar variances across groups; markedly unequal spread or strongly skewed data weaken it, in which case a variance-stabilizing transform or a nonparametric analysis is the safer path.
No F table needed
The 1986 program looked up critical values in the book's Table A.11. V5 computes the F distribution directly and reports an exact p-value alongside the 95% and 99% critical values.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.