4 deleted 2 characters in body edited Feb 16 '14 at 17:35 octern 33011 gold badge44 silver badges1414 bronze badges I'm trying to compute ANOVA effect sizes from papers that provide an F value without other information. If I understand correctly, the effect size for a single-factor ANOVA is $$\eta {2} = \frac{ss_{between}}{ss_{between} + ss_{error}}$$ And the F value is: $$F = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$ UPDATE: Nope! the denominator is just [(k-1)*SSbetween]*SSerror]. Thus, everything that follows is invalid. Back to first-years stats for me. Where N = number of observations and k = number of groups. Question 1: Does it follow that you can calculate eta squared as: $$\eta {2} = \frac{k-1}{N-k}F$$ Question 2: I tried checking this in some output from SPSS. Here's an example with k=4 and N=158: I'm aware that SPSS gives partial eta squared, but for a single-factor ANOVA that should be the same as eta squared, right? And indeed, the ratio of the sums of squares is $$\frac{342.872}{(342.872+6133.519)} = .05294$$. But using F, we get $$2.870*3/154 = .05591$$, which is off by much more than rounding error. Is SPSS subtly adjusting F somehow, or am I confused about how to calculate eta squared? I'm trying to compute ANOVA effect sizes from papers that provide an F value without other information. If I understand correctly, the effect size for a single-factor ANOVA is $$\eta {2} = \frac{ss_{between}}{ss_{between} + ss_{error}}$$ And the F value is: $$F = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$ UPDATE: Nope! the denominator is just [(k-1)*SSbetween]. Thus, everything that follows is invalid. Back to first-years stats for me. Where N = number of observations and k = number of groups. Question 1: Does it follow that you can calculate eta squared as: $$\eta {2} = \frac{k-1}{N-k}F$$ Question 2: I tried checking this in some output from SPSS. Here's an example with k=4 and N=158: I'm aware that SPSS gives partial eta squared, but for a single-factor ANOVA that should be the same as eta squared, right? And indeed, the ratio of the sums of squares is $$\frac{342.872}{(342.872+6133.519)} = .05294$$. But using F, we get $$2.870*3/154 = .05591$$, which is off by much more than rounding error. Is SPSS subtly adjusting F somehow, or am I confused about how to calculate eta squared? I'm trying to compute ANOVA effect sizes from papers that provide an F value without other information. If I understand correctly, the effect size for a single-factor ANOVA is $$\eta {2} = \frac{ss_{between}}{ss_{between} + ss_{error}}$$ And the F value is: $$F = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$ UPDATE: Nope! the denominator is just [(k-1)*SSerror]. Thus, everything that follows is invalid. Back to first-years stats for me. Where N = number of observations and k = number of groups. Question 1: Does it follow that you can calculate eta squared as: $$\eta {2} = \frac{k-1}{N-k}F$$ Question 2: I tried checking this in some output from SPSS. Here's an example with k=4 and N=158: I'm aware that SPSS gives partial eta squared, but for a single-factor ANOVA that should be the same as eta squared, right? And indeed, the ratio of the sums of squares is $$\frac{342.872}{(342.872+6133.519)} = .05294$$. But using F, we get $$2.870*3/154 = .05591$$, which is off by much more than rounding error. Is SPSS subtly adjusting F somehow, or am I confused about how to calculate eta squared? 3 added 138 characters in body edited Dec 9 '12 at 20:06 octern 33011 gold badge44 silver badges1414 bronze badges I'm trying to compute ANOVA effect sizes from papers that provide an F value without other information. If I understand correctly, the effect size for a single-factor ANOVA is $$\eta {2} = \frac{ss_{between}}{ss_{between} + ss_{error}}$$ And the F value is: $$F = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$ UPDATE: Nope! the denominator is just [(k-1)*SSbetween]. Thus, everything that follows is invalid. Back to first-years stats for me. Where N = number of observations and k = number of groups. Question 1: Does it follow that you can calculate eta squared as: $$\eta {2} = \frac{k-1}{N-k}F$$ Question 2: I tried checking this in some output from SPSS. Here's an example with k=4 and N=158: I'm aware that SPSS gives partial eta squared, but for a single-factor ANOVA that should be the same as eta squared, right? And indeed, the ratio of the sums of squares is $$\frac{342.872}{(342.872+6133.519)} = .05294$$. But using F, we get $$2.870*3/154 = .05591$$, which is off by much more than rounding error. Is SPSS subtly adjusting F somehow, or am I confused about how to calculate eta squared? I'm trying to compute ANOVA effect sizes from papers that provide an F value without other information. If I understand correctly, the effect size for a single-factor ANOVA is $$\eta {2} = \frac{ss_{between}}{ss_{between} + ss_{error}}$$ And the F value is: $$F = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$ Where N = number of observations and k = number of groups. Question 1: Does it follow that you can calculate eta squared as: $$\eta {2} = \frac{k-1}{N-k}F$$ Question 2: I tried checking this in some output from SPSS. Here's an example with k=4 and N=158: I'm aware that SPSS gives partial eta squared, but for a single-factor ANOVA that should be the same as eta squared, right? And indeed, the ratio of the sums of squares is $$\frac{342.872}{(342.872+6133.519)} = .05294$$. But using F, we get $$2.870*3/154 = .05591$$, which is off by much more than rounding error. Is SPSS subtly adjusting F somehow, or am I confused about how to calculate eta squared? I'm trying to compute ANOVA effect sizes from papers that provide an F value without other information. If I understand correctly, the effect size for a single-factor ANOVA is $$\eta {2} = \frac{ss_{between}}{ss_{between} + ss_{error}}$$ And the F value is: $$F = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$ UPDATE: Nope! the denominator is just [(k-1)*SSbetween]. Thus, everything that follows is invalid. Back to first-years stats for me. Where N = number of observations and k = number of groups. Question 1: Does it follow that you can calculate eta squared as: $$\eta {2} = \frac{k-1}{N-k}F$$ Question 2: I tried checking this in some output from SPSS. Here's an example with k=4 and N=158: I'm aware that SPSS gives partial eta squared, but for a single-factor ANOVA that should be the same as eta squared, right? And indeed, the ratio of the sums of squares is $$\frac{342.872}{(342.872+6133.519)} = .05294$$. But using F, we get $$2.870*3/154 = .05591$$, which is off by much more than rounding error. Is SPSS subtly adjusting F somehow, or am I confused about how to calculate eta squared? 2 fixed typo of $\eta^2$ for $F$ edited Nov 4 '12 at 17:49 Peter Flom♦ 79.2k1313 gold badges114114 silver badges225225 bronze badges I'm trying to compute ANOVA effect sizes from papers that provide an F value without other information. If I understand correctly, the effect size for a single-factor ANOVA is $$\eta {2} = \frac{ss_{between}}{ss_{between} + ss_{error}}$$ And the F value is: $$\eta {2} = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$$$F = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$ Where N = number of observations and k = number of groups. Question 1: Does it follow that you can calculate eta squared as: $$\eta {2} = \frac{k-1}{N-k}F$$ Question 2: I tried checking this in some output from SPSS. Here's an example with k=4 and N=158: I'm aware that SPSS gives partial eta squared, but for a single-factor ANOVA that should be the same as eta squared, right? And indeed, the ratio of the sums of squares is $$\frac{342.872}{(342.872+6133.519)} = .05294$$. But using F, we get $$2.870*3/154 = .05591$$, which is off by much more than rounding error. Is SPSS subtly adjusting F somehow, or am I confused about how to calculate eta squared? I'm trying to compute ANOVA effect sizes from papers that provide an F value without other information. If I understand correctly, the effect size for a single-factor ANOVA is $$\eta {2} = \frac{ss_{between}}{ss_{between} + ss_{error}}$$ And the F value is: $$\eta {2} = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$ Where N = number of observations and k = number of groups. Question 1: Does it follow that you can calculate eta squared as: $$\eta {2} = \frac{k-1}{N-k}F$$ Question 2: I tried checking this in some output from SPSS. Here's an example with k=4 and N=158: I'm aware that SPSS gives partial eta squared, but for a single-factor ANOVA that should be the same as eta squared, right? And indeed, the ratio of the sums of squares is $$\frac{342.872}{(342.872+6133.519)} = .05294$$. But using F, we get $$2.870*3/154 = .05591$$, which is off by much more than rounding error. Is SPSS subtly adjusting F somehow, or am I confused about how to calculate eta squared? I'm trying to compute ANOVA effect sizes from papers that provide an F value without other information. If I understand correctly, the effect size for a single-factor ANOVA is $$\eta {2} = \frac{ss_{between}}{ss_{between} + ss_{error}}$$ And the F value is: $$F = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$ Where N = number of observations and k = number of groups. Question 1: Does it follow that you can calculate eta squared as: $$\eta {2} = \frac{k-1}{N-k}F$$ Question 2: I tried checking this in some output from SPSS. Here's an example with k=4 and N=158: I'm aware that SPSS gives partial eta squared, but for a single-factor ANOVA that should be the same as eta squared, right? And indeed, the ratio of the sums of squares is $$\frac{342.872}{(342.872+6133.519)} = .05294$$. But using F, we get $$2.870*3/154 = .05591$$, which is off by much more than rounding error. Is SPSS subtly adjusting F somehow, or am I confused about how to calculate eta squared? 1 asked Nov 4 '12 at 17:43 octern 33011 gold badge44 silver badges1414 bronze badges