Conventions for Defining Effect Sizes PSY441my.ilstu.edu/~czimmer/psy441/powerEShandout.pdf ·...
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Conventions for Defining Effect Sizes PSY441 Adapted from Table 2.2 in Murphy & Myors (2004). PV d R 2 f 2 (eta) η 2 (omega) ω 2 r Small effect .01 .20 .01 .02 .01 .01 .10 Medium effect .10 .50 .06 .15 .06 .06 .30 Large effect .25 .80 .15 .35 .14 .15+ .50 Some Notes: d 12 = Y 1 – Y 2 (for 2 groups; see p. 160 of Keppel & Wickens) s 12 R 2 = SS A /SS total OR R 2 = (a-1)F / (a-1)F + a(n-1) PV = (df hyp * F) / ([df hyp * F ] + df err ) Omega-squared: est. ω 2 = (a – 1)(F A – 1) / (a – 1)(F A – 1) + (a)(n) SPSS will compute Eta-squared (η 2 ) or partial eta-squred for a number of statistical tests (e.g., independent t, paired-samples t, anova, etc. and formula varies by test; see Green & Salkind, 2003). Values range from 0 to 1, 0 indicates no effect, a value of 1 indicates difference between at least two of the means on the DV. In general η 2 or partial η 2 is interpreted as the proportion of variance in the DV that is related to a factor (a main effect or interaction, excluding other sources). Values in the table above for η 2 are too large for partial-η 2 (i.e., conventions are specific to η 2 ). Cohen’s f 2 = (df hyp * F) / df err Cohen’s f 2 = R 2 / (1 – R 2 ) Translating between f or f 2 and omega ω 2 f = √ ω 2 / (1 - ω 2 ) [entire equation is under the square root] ω 2 = f 2 / (f 2 + 1) To convert eta-squared to Cohen’s f 2 f 2 = η 2 / (1 - η 2 ) To convert f 2 into PV (percentage of variance associated with an effect): PV = f 2 / (1 + f 2 ) References: Keppel, G., & Wickens, T. D. (2004). Design and analysis: A researcher’s handbook (4 th ed.) Murphy, K. R., & Myors, B. (2004). Statistical power analysis (2 nd ed.) Green & Salkind (2003). Using SPSS for Windows and Macintosh (3rd ed.). Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2 nd ed.).
Transcript of Conventions for Defining Effect Sizes PSY441my.ilstu.edu/~czimmer/psy441/powerEShandout.pdf ·...
Conventions for Defining Effect Sizes PSY441 Adapted from Table 2.2 in Murphy & Myors (2004).
PV d R2 f2 (eta) η2 (omega) ω2 r Small effect
.01 .20 .01 .02 .01 .01 .10
Medium effect
.10 .50 .06 .15 .06 .06 .30
Large effect
.25 .80 .15 .35 .14 .15+ .50
Some Notes:
d12= Y1 – Y2 (for 2 groups; see p. 160 of Keppel & Wickens) s12
R2 = SSA/SStotal OR R2 = (a-1)F / (a-1)F + a(n-1) PV = (dfhyp * F) / ([dfhyp * F ] + dferr) Omega-squared: est. ωωωω2 = (a – 1)(FA – 1) / (a – 1)(FA – 1) + (a)(n) SPSS will compute Eta-squared (ηηηη2) or partial eta-squred for a number of statistical tests (e.g., independent t, paired-samples t, anova, etc. and formula varies by test; see Green & Salkind, 2003). Values range from 0 to 1, 0 indicates no effect, a value of 1 indicates difference between at least two of the means on the DV. In general η2 or partial η2 is interpreted as the proportion of variance in the DV that is related to a factor (a main effect or interaction, excluding other sources). Values in the table above for η2 are too large for partial-η2 (i.e., conventions are specific to η2). Cohen’s f2 = (dfhyp * F) / dferr Cohen’s f2 = R2 / (1 – R2) Translating between f or f2 and omega ω2 f = √ ω2/ (1 - ω2) [entire equation is under the square root] ω2 = f2 / (f2 + 1)
To convert eta-squared to Cohen’s f2 f2 = η2 / (1 - η2) To convert f2 into PV (percentage of variance associated with an effect): PV = f2 / (1 + f2) References: Keppel, G., & Wickens, T. D. (2004). Design and analysis: A researcher’s handbook (4th ed.) Murphy, K. R., & Myors, B. (2004). Statistical power analysis (2nd ed.) Green & Salkind (2003). Using SPSS for Windows and Macintosh (3rd ed.). Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.).
