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I am trying to determine the sample size using power analysis for ANOVA. That requires as inputs the number of groups, effect size, significance level and power. By default, the significance level is 0.05, the power is 0.8 and I use 10 groups. The only parameter left is the effect size. I have no idea how much influence one group would have on another so I use 0.2 (small effect) from Cohen (1988)'s guideline. However, it seems that I might have just made things up. If the 0.2 drops to 0.15 the sample size would go up by 30 observations. Is there a better way to choose an effect size?

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    $\begingroup$ If there are related existing studies in the literature then you might want to look at the effect sizes they found. This could give you a sense of what you might expect to see in your study. $\endgroup$
    – Ian_Fin
    Nov 28, 2016 at 9:46

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I think effect size is an issue separate from the sample size. It should be chosen as a difference worth detecting. This is something that should come out of an understanding of the problem. Then sample size is determined to be large enough to provide high power.

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  • $\begingroup$ I wonder if there is a way to decide an appropriate effect size based on the data that I am investigating. $\endgroup$
    – M八七
    Nov 30, 2016 at 22:08
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I would recommend that OP looks into the area/system in which the experiment would be taking place. If you are looking for differences that are significantly large than you do not need too much of an effect size. However, if you're experiment delves into differences that are very hard to tell then a stronger effect size is needed and therefore more replicates/ samples.

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  • $\begingroup$ A higher effect size should result less samples I think, I just tested pwr.anova.test in R. $\endgroup$
    – M八七
    Nov 28, 2016 at 4:30
  • $\begingroup$ I got my effect sizes mixed up! $\endgroup$
    – Leo Ohyama
    Nov 28, 2016 at 4:32

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