Timeline for What measure of effect size in ANOVA has mode at zero under the null (unlike $\eta^2$ that does not)?

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Dec 23, 2014 at 17:30	comment	added	amoeba		@gung: I edited my question to remove my confusion about "biasedness" and to add an explanation of why I care about the mode of the distribution of effect sizes.
Dec 23, 2014 at 12:15	comment	added	amoeba		What you essentially explain there is that the sign is always positive. I would argue that in some cases there can be more meaningful conventions. I commented there.
Dec 23, 2014 at 12:00	comment	added	Silverfish		@amoeba In fact the sign on $R$, i.e. $\eta$, is not arbitrary, as I explained here! $R$ is the correlation between the fitted and observed values of the dependent variable.
Dec 23, 2014 at 11:11	comment	added	amoeba		Thanks, gung. Your answer and @Silverfish'es comments above made it clear and obvious that $\eta^2$ is biased for a trivial reason of being constrained to be positive. If one chooses any way of assigning sign to $\pm \sqrt{\eta^2}$, then such $\eta$ will be symmetrically distributed around zero under $H_0$ and hence unbiased. However, what concerns me is that distribution of $\eta^2$ has a non-zero mode for $k>3$ groups; therefore the distribution of my $\eta$ will be bimodal. My actual question is if there is any measure of effect size without this weird property. I will edit to clarify.
Dec 23, 2014 at 2:32	history	edited	gung - Reinstate Monica	CC BY-SA 3.0	added 20 characters in body
Dec 23, 2014 at 2:24	history	answered	gung - Reinstate Monica	CC BY-SA 3.0