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I am trying to calculate how many samples I need for an ANOVA with 2 groups, effect size of 0.3, significance of 0.05 and power of 0.8.

'''pwr.anova.test(k=2, f=.4, sig.level =.05, power =.8)

Balanced one-way analysis of variance power calculation

          k = 2
          n = 44.58577
          f = 0.3
  sig.level = 0.05
      power = 0.8

NOTE: n is number in each group.'''

I tried different effect sizes and when I increase the effect size, 'n' decreases, whereas I would expect that more samples would be required to achieve a greater effect size? I'm confused...am I missing something here?

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  • $\begingroup$ When the effect size is huge, how many samples do you really need to see it?? $\endgroup$
    – whuber
    Mar 4 '20 at 17:01
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I think you may be confused about some concepts:

  • The effect size is a (standardized) measure of the magnitude of the phenomenon that you are investigating - in other words, it is a property of the world, not of the statistical test, so it does not change if you increase or decrease your sample size.
  • The statistical power is instead a property of the statistical test: specifically it is the probability that such a test would reject the null hypothesis if performed in an hypothetical world in which the alternative hypothesis is true. Thus, increasing the sample size does achieve a larger statistical power.

In your code you are telling R to calculate the smallest sample size such that your test achieve a statistical power of 80%, assuming that the effect you are investigating is real and has the specified effect size. It follows that if you increase the effect size, then the sample size necessary to achieve 80% power decreases.

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  • $\begingroup$ Thank you for your response, I was getting confused, now I understand! $\endgroup$
    – user134543
    Mar 6 '20 at 10:31
  • $\begingroup$ You're welcome. Please mark the answer as accepted if it cleared up your doubts. $\endgroup$
    – matteo
    Mar 27 '20 at 9:21

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