

Here is a brief description of how the Holm multiple comparison test works:
1.If you are using the test as a followup to ANOVA, P values for each comparison are computed as they are for the Fisher's LSD test. These are not corrected for multiple comparisons.
2.The P values are ranked from smallest to largest.
3.Set a value for the significance level, alpha. This is often set to 5%.
4.Define K equal to the number of comparisons you are making.
5.Start with the smallest P value and set i=K. Ask: Is the smallest P value less than alpha/i?
If No: Conclude that none of the comparisons are statistically significant, and you are done.
If Yes: Conclude that this comparison is statistically significant, and continue.
6.The second to smallest P value is compared next. Set i=K1. Is the P value less than alpha/i?
If No: Conclude that this comparison (and all with larger P values) is not statistically significant. You are done.
If Yes: Conclude that this comparison is statistically significant, and continue.
7.The third to smallest P value is compared next. Set i=K2. Compare the P value to alpha/i...
8.Continue until you find a comparison that is not statistically significant.
Prism actually uses the Šídák modification, so computes the HolmŠídák test. At steps 57 above, the P value is not compared to to alpha/i but rather to 1(1alpha)(1/i)
To compute the adjusted P value, called Padj(i), from the P value, called P(i), use the equations below where, the P values are sorted so P(1) is the smallest, k is the number of comparisons (number of P values) and max is a function that returns the larger of two values.
PAdj(1) = 1  (1  P(1))^k
PAdj(2) = max(PAdj(1), 1  (1  P(2))^(k1))
..........
PAdj(j) = max(PAdj(j1), 1  (1  P(j))^(kj+1))
..........
PAdj(k) = max(PAdj(k1), 1  (1  P(k))^(kk+1)) = max(PAdj(k1), P(k))
Note that in some cases successive adjusted P values will be identical, even when the original P values are not.