Calculating eta squared from F and df - Cross Validated most recent 30 from stats.stackexchange.com 2019-07-21T15:41:36Z https://stats.stackexchange.com/feeds/question/41861 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://stats.stackexchange.com/q/41861 7 Calculating eta squared from F and df octern https://stats.stackexchange.com/users/9816 2012-11-04T17:43:23Z 2018-02-16T15:22:34Z <p>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 $$\eta {2} = \frac{ss_{between}}{ss_{between} + ss_{error}}$$</p> <p>And the F value is: $$F = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$ <strong>UPDATE: Nope! the denominator is just [(k-1)*SSerror]. Thus, everything that follows is invalid. Back to first-years stats for me.</strong></p> <p>Where N = number of observations and k = number of groups. </p> <p><strong>Question 1:</strong> Does it follow that you can calculate eta squared as: $$\eta {2} = \frac{k-1}{N-k}F$$</p> <p><strong>Question 2:</strong> I tried checking this in some output from SPSS. Here's an example with k=4 and N=158:</p> <p><img src="https://dl.dropbox.com/u/5473621/spss_etasq_output2.png" alt="SPSS output with relevant values described below"></p> <p>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. </p> <p>Is SPSS subtly adjusting F somehow, or am I confused about how to calculate eta squared?</p> https://stats.stackexchange.com/questions/41861/-/41866#41866 1 Answer by rolando2 for Calculating eta squared from F and df rolando2 https://stats.stackexchange.com/users/2669 2012-11-04T18:18:02Z 2012-11-04T18:18:02Z <p>At <a href="http://publib.boulder.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=/com.ibm.spss.statistics.help/alg_glm-uni-multi_parameters_partial-eta.htm" rel="nofollow noreferrer">this IBM/SPSS help page</a> we find:</p> <p><img src="https://i.stack.imgur.com/hFJeR.png" alt="enter image description here"></p> <p>Terms are defined <a href="http://publib.boulder.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=/com.ibm.spss.statistics.help/alg_glm-uni-multi_parameters_partial-eta.htm" rel="nofollow noreferrer">elsewhere</a>. </p> <p><img src="https://i.stack.imgur.com/SuJqU.png" alt="enter image description here"></p> <p>It's beyond me, but maybe others can make heads or tails of it.</p> https://stats.stackexchange.com/questions/41861/-/45518#45518 4 Answer by octern for Calculating eta squared from F and df octern https://stats.stackexchange.com/users/9816 2012-12-09T20:10:59Z 2012-12-09T20:10:59Z <p>This question was based on a huge and very basic error. F is not $$F = \frac{(N-k)ss_{between}}{(k-1)(ss_{between} + ss_{error})}$$</p> <p>But rather $$F = \frac{(N-k)ss_{between}}{(k-1)ss_{error}}$$</p> <p>With this correction, everything makes sense. Unfortunately, I think it also means that there is no way to calculate etasq if all you know is F and df.</p> <p>Back to first-year stats for me!</p> https://stats.stackexchange.com/questions/41861/-/98998#98998 9 Answer by Hans Ivers for Calculating eta squared from F and df Hans Ivers https://stats.stackexchange.com/users/45678 2014-05-16T18:59:50Z 2014-05-16T19:21:59Z <ol> <li><p>We know that:</p> <p>$$F = \frac{MS_B} {MS_W} = \frac{SS_B/(k-1)} {SS_W/(N-k)}.$$</p> <p>Thus $SS_B = F \times MS_W \times (k-1)$, and $SS_W = MS_W \times (N-k)$.</p></li> <li><p>We also know that:</p> <p>$$\eta^2 = \frac{SS_B}{SS_B + SS_W}$$ </p></li> <li><p>Thus, if we substitute (1) in (2):</p> <p>$$\eta^2 = \frac{F \times MS_W \times (k-1)}{F \times MS_W \times (k-1) + MS_W \times (N-k)}$$ </p></li> <li><p>The $MS_W$ terms in both numerator and denominator can be removed (simplified), leaving: </p> <p>$$\eta^2 = \frac{F (k-1)}{F (k-1) + (N-k)} = \frac{F (df_B)}{F (df_B) + (df_W)}$$ </p></li> </ol> <p>So, it's possible to compute eta-squared using only F and degrees of freedom.</p> https://stats.stackexchange.com/questions/41861/-/241748#241748 0 Answer by statistic24h for Calculating eta squared from F and df statistic24h https://stats.stackexchange.com/users/135777 2016-10-22T13:27:53Z 2016-10-22T13:27:53Z <p>Forgive unearthing an old story, but...</p> <p>The main reason for confusion in this thread is that SPSS calculates the partial eta-squared instead of the normal eta-squared (and in some versions even incorrectly names it). Formulas which you used are correct, the calculations also, but you read an incorrect result in SPSS, and the problem is broadly described here:</p> <p>Levine, T. R., &amp; Hullett, C. R. (2002). Eta squared, partial eta squared, and misreporting of effect size in communication research. Human Communication Research, 28(4), 612-625.</p> <p><a href="https://msu.edu/~levinet/eta%20squared%20hcr.pdf" rel="nofollow">https://msu.edu/~levinet/eta%20squared%20hcr.pdf</a></p> https://stats.stackexchange.com/questions/41861/-/328998#328998 1 Answer by Carina for Calculating eta squared from F and df Carina https://stats.stackexchange.com/users/195623 2018-02-16T14:10:32Z 2018-02-16T15:22:34Z <p><a href="https://www.frontiersin.org/articles/10.3389/fpsyg.2013.00863/full" rel="nofollow noreferrer">This article</a> by Daniel Lakens explains how eta squared can be calculated from only F and degrees of freedom, but only in cases of one-way ANOVA. This is the example: </p> <blockquote> <p>For example, for an $F(1, 38) = 7.21$, $η2p = 7.21 \cdot 1/(7.21 \cdot 1 + 38) = 0.16$</p> </blockquote> <ul> <li>Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. <em>Frontiers in Psychology, 4</em>. </li> </ul>