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Analysing Binomial Data in a Two‐Factor Experiment with Unequal Observations Per Cell
Author(s) -
Butcher D. F.,
Kemp K. E.
Publication year - 1974
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2346999
Subject(s) - statistics , binomial (polynomial) , factor (programming language) , mathematics , econometrics , binomial distribution , computer science , programming language
Summary Binomial data were generated for a two‐factor experiment with both factors at three levels using unequal numbers of observations per cell. Three n ‐patterns were used. The number of observations per cell ranged from 30 to 90 for two n ‐patterns and from 38 to 98 for the third n ‐pattern. The mean number of observations per cell was 60 for all n ‐patterns. Samples were generated for values of μ p of 0·05, 0·10, 0·15, 0·20, 0·30, 0·40 and 0·50 to determine the effects of n ‐pattern and of the binomial parameter (μ p ) on α‐level for four methods of analysis. Methods of analysis considered were: two analyses of variance, one using percentage data; the other, the angular transformation for percentage data; a three‐factor χ 2 analysis; and Friedman's (1937) non‐parametric two‐way analysis of variance. Because Friedman's test generally showed erratic α‐levels, no comparisons of power were made with Friedman's test. Of the remaining tests, the three‐factor χ 2 was more powerful than the parametric analysis of variance procedures. There was no apparent difference between the parametric analyses of variance with respect to power, raising some doubt as to the usefulness of the arc‐sine transformation for percentage data.