# partial eta squared

Would it please be possible to help me with a statistics query. I have asked for the partial eta squared on the output of a one-way within subjects ANOVA from SPSS and it has given me the value .137. According to Cohen (1992) the classifications for effect sizes should be; r=.10 small, r=.30 medium and r=.50 large (I am unsure whether these classifications can be attributed to partial eta squared?)

I appreciate this is a basic question but please may I clarify my value falls in the small effect category? Additionally, does this suggest that the proportion of variance explained by the IV on the DV and not explained by other variables in the analysis is 13.7%?

Any help would be greatly appreciated!! Thank you!

• Partial Eta-squared of an effect is SSeffect/(SSeffect+SSerror) and, for quantitative IV (a covariate), equals partial r-squared. Mar 27 '13 at 10:50
• This might help you: stats.stackexchange.com/questions/15958/… Jun 17 '13 at 11:59
• Cohen never intended his proposals for guidelines for quantifying effect sizes to be used as definite categories.
– jona
Jun 19 '14 at 14:22

According to Richardson (2011), Cohen (1969, pp.278-280) provides partial eta squared values of .0099, .0588, and .1379 as benchmarks for small, medium, and large effect sizes, respectively.

Literature:

Richardson, J.T.E. (2011). Eta squared and partial eta squared as measurements of effect size in educational research. Educational Research Review, 6, 135-147.

Cohen, J. (1969). Statistical power analysis for the behavioural sciences. New York: Academic Press.

• Consider the whole section from Richardson (2011) you refer to. You get wrong exactly what they're talking about there in the very next sentence.
– jona
Jun 19 '14 at 14:19
• "Further confusion surrounds the benchmarks suggested by Cohen (1969, pp. 278–280) to define small, medium, and large effects. As was explained earlier, these were based upon values of f that correspond to values of partial $\eta^2$ of .0099, .0588, and .1379, respectively. ...
– jona
Jun 19 '14 at 14:19
• .. Nowadays, researchers often quote the latter values without explaining their derivation from values of f, which suggests a spurious degree of precision and makes them sound even more arbitrary than Cohen had originally intended. They are quoted as benchmark values for both partial $\eta^2$ and classical $\eta^2$, despite the fact that the former is typically greater than the latter." (p. 142)
– jona
Jun 19 '14 at 14:20
• I disagree: see the last sentence from the paragraph you cited above, as well as Table 3 in the paper of Richardson.
– skip
Jun 19 '14 at 15:14