Effect size and eta squared

Abstract

Question: In Chapter 6 of the 2008 book on heritage language learning that you co-edited with Kimi-Kondo Brown, a study comparing how three different groups of informants use intersentential referencing is outlined. On page 147 of that book, a MANOVA with a partial eta 2 of .29 is outlined. There are several questions about this statistic. What does a " partial eta " measure? Are there other forms of eta that readers should know about? And how should one interpret a partial eta 2 value of .29? Answer: I will answer your question about partial eta 2 in two parts. I will start by defining and explaining eta 2 . Then I will circle back and do the same for partial eta 2 . Eta 2 Eta 2 can be defined as the proportion of variance associated with or accounted for by each of the main effects, interactions, and error in an ANOVA study (see Tabachnick & Fidell, 2001, pp. 54-55, and Thompson, 2006, pp. 317-319). Formulaically, eta 2 , or 2 η , is defined as follows: total effect SS SS = 2 η Where: SS effect = the sums of squares for whatever effect is of interest SS total = the total sums of squares for all effects, interactions, and errors in the ANOVA Eta 2 is most often reported for straightforward ANOVA designs that (a) are balanced (i.e., have equal cell sizes) and (b) have independent cells (i.e., different people appear in each cell). For example, in Brown (2007), I used an example ANOVA to demonstrate how to calculate power with SPSS. That was a 2 x 2 two-way ANOVA with anxiety and tension as the independent variables and trial 3 as the dependent variable (using the Anxiety 2.sav example file that comes with recent versions of the SPSS software). There were three people in each cell and the cells were independent. Notice in Table 1 that the p values (0.90, 0.55, & 0.10) indicate that there were no significant effects (i.e., no p values below .05) for Anxiety, Tension, or their interaction. Note also that there was not sufficient power to detect such effects (i.e., the power statistics of 0.05, 0.09, & 0.37 were not above .80 in any case). All of this led me to conclude that " the study lacked sufficient power to detect any significant effects even if they exist in reality " , which is reasonable given the very small sample size of 12. Table 1 Results of the Analysis Shown in Figure 3 of the Anxiety 2.sav used with SPSS Source SS df MS F p eta 2 Power Anxiety 0.08 1 0.08 0.02 0.90 0.0012 0.05 Tension 2.08 1 2.08 0.38 0.55 0.0324 0.09 Anxiety x Tension 18.75 1 18.75 3.46 0.10 0.2919 0.37 Error 43.33 8 5.42 0.6745 Total 64.24 12