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Lists of requirements for one-way ANOVA include the following:

  • Samples should be mutually independent
  • Samples should be from a population with a normal distribution
  • Samples should have the same variance (though if the max standard deviation is less than twice the smallest, it's "close enough")
  • The samples should be simple random samples from their population (according to Sullivan, 5ed, pg. 620; though Wikipedia seems to disagree)

Many statistical analyses (e.g. Student's t-test) require that a sample's size be small relative to its population (often, $n \le 0.05 N$ is used as a rule of thumb). This allows individuals within a given sample to be treated as approximately independent of each other.

I am curious why the $n \le 0.05 N$ requirement doesn't appear in the list for ANOVA. Is the assumption/approximation of a small sample size relative to the population size at all relevant to ANOVA? If so, how is it relevant? If not, why not?

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The n < 0.05N rule of thumb is with regards to applying a finite population correction factor (FPC) for estimating a standard error. You are correct that just about any analysis, in which you have sampled a sizable proportion of the finite population, will have a smaller true standard error than the one estimated under the assumption that N is infinite. Just do the thought experiment where you ask "what should my standard error be when n=N?" If your answer is 0, then an FPC adjustment may be appropriate.

There is a good discussion of the FPC in this thread. Explanation of finite correction factor

In many settings we think of N being infinite, so the FPC does not apply.

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  • $\begingroup$ Neat! Thanks. Why is it not used for ANOVA then? $\endgroup$
    – jvriesem
    Dec 12, 2019 at 18:27
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    $\begingroup$ Methodological development for the analysis of survey data has extended finite population corrections to additional settings. $\endgroup$ Dec 12, 2019 at 22:14

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