Introduction
Post-Hoc, or posterior, tests allow to identify among X groups which group differs, the Hypothesis Testing Having slept and already indicated that there was a difference.
This is typical of clinical trials: We have many different groups and our challenge is to determine which group is different.
You can use multiple tests based on the level of complexity of our problem and the previous text:
- If you want to compare all the averages 2 to 2, you can use the HSD Test of Tukey.
- If we want to compare groups in personalized ways (1 group with 1 control group, 2 groups with 3 other groups…), we will use the Scheffé test.
- We did an ANOVA and we want to know which groups are different. The list below presents the tests that can be done from the most lax to the most conservative.
Name of the post HOC test |
Comment |
Fisher’s Least significant difference (LSD) – test of the smallest difference |
To be used for a comparison of 3 samples |
Student Newman-Keuls PPAS-smaller significant amplitude |
For 3 to 5 samples maximum, because the error level increases almost linearly with the number of pairs of samples to be tested. |
Tukey Honestly significant difference (HSD) – Really significant difference Test |
Very conservative, it will allow to calculate the probability of error at the level of risk chosen. Attention, it can only be used if the data is normal. |
The procedure REGW test Q and F-Ryan-Einot-Gabriel-Welsch |
This test requires the use of software because the calculation requires automation. |
Duncan new multiple range test (MRT) |
Derived from the Newman-Keuls test, this test is more protective against the second species error with the consequence of having a greater risk of first species. |
Dunnett |
This test is used when you want to compare 1 sample with all the others. |
The Bonferroni procedure (Bonferonni correction) |
Probably the most used but it lacks power. |
Holm Bonferroni |
More powerful than the Bonferroni procedure, this method provides a correction that allows to be more restrictive and to detect weaker deviations. |
Scheffé |
Derived from Student’s T, ultra Conservative, it will be used for complex comparisons. |