PHARM/PCS V5 · Procedure 37 ANOVA and Comparisons
Duncan Multiple Range Test
After a significant ANOVA with equal group sizes, compare every pair of means using Duncan's graduated protection levels.
What it computes
Alternative to Newman-Keuls for pairwise comparisons after ANOVA. Requires equal group sizes. Qp values are computed automatically from the studentized range distribution at Duncan's protection level, so there is no need to enter values from Table A.14.
Inputs and outputs
You provide
- The values for each group, entered as separate blocks of equal size
- A significance level of 5% or 1%
- Optionally, your own Qp values
PHARM/PCS reports
- The underlying ANOVA and the sorted means
- Qp and the shortest significant ranges Rp
- Which pairs differ and which do not
- A chart of the means grouped into homogeneous subsets
When to use it
After a significant ANOVA (Procedure 33) for all-pairs comparisons when groups are equal in size and you want a somewhat more liberal test than Newman-Keuls (Procedure 36). If group sizes differ, use Newman-Keuls; for control comparisons, Dunnett (Procedure 44).
Reading the results
Duncan's graduated protection level makes it more willing to declare differences than Newman-Keuls: more power, more false positives. That trade-off suits screening, but state it plainly in a writeup, since reviewers vary in how they regard Duncan's.
No Table A.14 needed
The 1986 program loaded Duncan's values from a disk file. V5 computes them from the studentized range distribution at Duncan's protection level, and matches every printed cell of Table A.14 to within 0.01 at both the 5% and 1% levels.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.