PHARM/PCS V5 · Procedure 38 ANOVA and Comparisons
Least Significant Difference Test
After a significant ANOVA, compute a single least significant difference and see which pairs of means exceed it.
What it computes
After one-way ANOVA shows significance, computes the LSD for pairwise comparisons of means. Requires equal group sizes. LSD = t·√(2·s2p/n).
Inputs and outputs
You provide
- The values for each group, entered as separate blocks of equal size
PHARM/PCS reports
- The underlying ANOVA and the sorted means
- The LSD at the 5% and 1% levels
- Every pairwise difference, marked by significance
- A chart of the means grouped into homogeneous subsets
When to use it
As the simplest post-hoc after a significant ANOVA (Procedure 33), one yardstick you compare every mean difference against. Handy for a quick read; the range-based tests (Procedures 36, 37) and Dunnett (44) offer more principled control of multiplicity.
Reading the results
LSD applies no correction for the number of comparisons, so across many pairs it inflates the false-positive rate; its validity leans hard on the protected requirement that the ANOVA was significant first. Use it for a few planned comparisons; for many unplanned ones, prefer a range test.
Uses your actual group size
The LSD is computed from the group size in the data you enter, and every pairwise difference is shown with its significance marker. For the book example it returns 1.3251, which the book rounds to 1.33.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.