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Rodger's method
Rodger’s method is a statistical procedure for examining research data post hoc following an 'omnibus' analysis (e.g., after an analysis of variance – anova). The various components of this methodology were fully worked out by R. S. Rodger in the 1960s and 70s, and seven of his articles about it were published in the British Journal of Mathematical and Statistical Psychology between 1967 and 1978.〔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.〕〔Rodger, R. S. (1969). Linear hypotheses in 2xa frequency tables. British Journal of Mathematical and Statistical Psychology, 22, 29–48.〕〔Rodger, R. S. (1967a). Type I errors and their decision basis. British Journal of Mathematical and Statistical Psychology, 20, 51–62.〕〔Rodger, R. S. (1967b). Type II errors and their decision basis. British Journal of Mathematical and Statistical Psychology, 20, 187–204.〕
Statistical procedures for finding differences between groups, along with interactions between the groups that were included in an experiment or study, can be classified along two dimensions: 1) were the statistical contrasts that will be evaluated decided upon prior to collecting the data (planned) or while trying to figure out what those data are trying to reveal (''post hoc''), and 2) does the procedure use a decision-based (i.e., per contrast) error rate or does it instead use an experiment-wise error rate. Rodger’s method, and some others, are classified according to these dimensions in the table below.
==Statistical power==
In early 1990s, one set of researchers made this statement about their decision to use Rodger’s method: “We chose Rodger’s method because it is the most powerful ''post hoc'' method available for detecting true differences among groups. This was an especially important consideration in the present experiments in which interesting conclusions could rest on null results” (Williams, Frame, & LoLordo, 1992, p. 43).〔Williams, D. A., Frame, K. A., & LoLordo, V. M. (1992). Discrete signals for the unconditioned stimulus fail to overshadow contextual or temporal conditioning. Journal of Experimental Psychology: Animal Behavior Processes, 18(1), 41–55.〕 The most definitive evidence for the statistical power advantage that Rodger's method possesses (as compared with eight other multiple comparison procedures) is provided in a 2013 article by Rodger and Roberts.〔Rodger, R.S. and Roberts, M. (2013). (Comparison of power for multiple comparison procedures. ) Journal of Methods and Measurement in the Social Sciences, 4(1), 20–47.〕
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