# Maximum sample size for one-way ANOVA?

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?