Rodger's method

Rodger's Method

This entry is currently a "stub" that will be elaborated upon soon.

Rodger's method is the only post hoc statistical procedure that does not lose statistical power as ν₁ (the numerator degrees of freedom) increases. As a consequence of this fact, Rodger's method has more power than all other post hoc procedures to detect every sort of interaction effect. Importantly, though, it also permits completely ignoring every factorially-defined interaction (which are widely acknowledged to be difficult to interpret), and encourages focusing instead on "the interactions defined by common sense" (Rodger, 1974, p. 195).

Another very significant feature of Rodger's method is the fact that the unlimited amount of post hoc data snooping Rodger's method permits is accompanied by a guarantee that the long-run expectation of type 1 errors can never exceed Eα (i.e., .05 or .01]. Both the increased power that Rodger's method possesses, and the impossibility of type 1 error rate inflation, are obtained by using a decision-based (i.e., per contrast) error rate, which is identical to that used with planned t-tests.

Perhaps the most important of the very attractive features of Rodger's method is its specification of the 'implied means' (or some other type of population parameter) that are logically implied, and mathematically entailed, by the number of means minus one statistical decisions that the user of Rodger's method will make. These implied true population means that Rodger's method provides constitute a very precise statement about the outcome of one's research, and assist other researchers in determining the size of effect that their related research ought to seek.

Using Rodger's Method: A free computer program, Simple, Powerful Statistics (SPS), implements the most important features of Rodger's method and makes their use readily available to researchers. It can be downloaded from the website in the external link section.

Delving Deeper: The single best source for finding out more about Rodger's method is his 1974 article. The most easily accessed source is Roberts' 2011 article. Both are identified in the references section below.

References: Roberts, M. (2011). Simple, Powerful Statistics: An instantiation of a better 'mousetrap.' Journal of Methods and Measurement in the Social Sciences, Vol. 2 No. 2, p. 63-79.

Rodger, R. S. (1969). Linear hypotheses in 2xa frequency tables. British Journal of Mathematical and Statistical Psychology, 22, 29-48.

Rodger, R. S. (1974). Multiple contrasts, factors, error rate and power. British Journal of Mathematical and Statistical Psychology, 27, 179-198.

Rodger, R. S. (1975a). The number of non-zero, post hoc contrasts from ANOVA and error-rate I. British Journal of Mathematical and Statistical Psychology, 28, 71-78.

Rodger, R. S. (1975b). Setting rejection rate for contrasts selected post hoc when some nulls are false. British Journal of Mathematical and Statistical Psychology, 28, 214-232.

Rodger, R. S. (1978). Two-stage sampling to set sample size for post hoc tests in ANOVA with decision-based error rates. British Journal of Mathematical and Statistical Psychology, 31, 153-178.

External Link: Simple, Powerful Statistics: R.S. Rodger's Method