The Shine-Bower error term is used to form approximate F ratios for testing various effects in the Shine-Bower single-subject ANOVA and the Shine Combined ANOVA. The distribution governing the general case of any one of these F ratios is the double non-central F distribution which has both a numerator and a denominator noncentrality parameter. It is rigorously shown that the approximate nature of these F ratios makes them no worse than conservative with respect to the probability of a Type I error. It is also shown that the approximate nature of these F ratios reduces their power.
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References
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Shine, L. C.Removing the restriction of an even number of trials for the Shine-Bower single-subject ANOVA. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT , 1977, 37, 873-875.
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