Criticisms
Duncan's test has been criticised as being too liberal by many statisticians including Henry Scheffé, and John W. Tukey. Duncan argued that a more liberal procedure was appropriate because in real world practice the global null hypothesis H0= "All means are equal" is often false and thus traditional statisticians overprotect a probably false null hypothesis against type I errors. Duncan later developed the Duncan–Waller test which is based on Bayesian principles. It uses the obtained value of F to estimate the prior probability of the null hypothesis being true.
The main criticisms raised against Duncan's procedure are:
- Duncan's MRT does not control family wise error rate at the nominal alpha level, a problem it inherits from Student–Newman–Keuls method.
- The increased power of Duncan's MRT over Newman–Keuls comes from intentionally raising the alpha levels (Type I error rate) in each step of the Newman–Keuls procedure and not from any real improvement on the SNK method.
Read more about this topic: Duncan's New Multiple Range Test
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