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SPSS cannot calculate Cohen's f or d directly, but they may be obtained from partial Eta-squared. Cohen discusses the relationship between partial eta-squared and Cohen's f : eta^2 = f^2 / ( 1 + f^2 ) f^2 = eta^2 / ( 1 - eta^2 ) where f^2 is the square of the effect size, and eta^2 is the partial eta-squared calculated by SPSS. (cf. [Cohen], pg. 281.) Therefore, f = sqr( eta^2 / ( 1 - eta^2 ) ). If the model is a Univariate ANOVA with two groups, and the number of observations in each group is equal, then the standardized range of population means, Cohen's d, is given by d = 2*f ([Cohen], pg. 276.) When there are more than two means, Cohen considers three patterns of dispersion: Pattern 1: Minimum variability Pattern 2: Intermediate variability Pattern 3: Maximum variability Henceforth we will take there to be k means, where k > 2. For Pattern 1, the dispersion is minimized when the intermediate means are all at the midpoint of the range, and then: d = f * sqr(2*k) ([Cohen], pg. 277.) For Pattern 2, it is assumed that the k means are equally spaced through the range. Then: d = 2 * f * sqr(3*(k-1)/(k+1)) ([Cohen], pg. 279.) For Pattern 3, maximum dispersion for an even number of means occurs with half at one extreme and the other half at the other: d = 2 * f (k even) while for an odd number of means, there will be one additional mean at one extreme: d = 2 * f * k / sqr(k^2 - 1) (k odd) ([Cohen], pp. 279-280). Discussion of the power associated with these effects is beyond the scope of this note. Please consult [Cohen] or another reference. REFERENCE: [Cohen]. Cohen, Jacob. Statistical Power Analysis for the Behavioral Sciences, 2nd ed., New Jersey: Lawrence Erlbaum Associates, Inc., 1988.
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