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In ANOVA the assumption is made that the population variances of the different groups are the same. Assuming $H_0$ is correct, all population means are also the same. In this case, would it not be easier to simply assume that all observations come from the same single population? I do not see how this makes a difference in calculation, but conceptually a single population is easier to imagine and work with. Did I miss something?

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  • $\begingroup$ I don't really understand what you ask about. Could uou clarify? But see stats.stackexchange.com/questions/76151/… $\endgroup$ Apr 8, 2021 at 13:36
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    $\begingroup$ "Come from the same single population" will work but is (far) more restrictive unless you also assume all distributions are Normal. $\endgroup$
    – whuber
    Apr 8, 2021 at 14:28
  • $\begingroup$ @whuber: and the normal distribution assumption is not always made? (I implicitly assumed it is.) $\endgroup$ Apr 8, 2021 at 18:02
  • $\begingroup$ It is rare for the Normal distribution assumption to hold exactly. What matters is that the sampling distributions of the ANOVA statistics be close enough to their reference distributions (usually F ratio distributions) to produce reliable p-values. This permits a (much) broader application of ANOVA than would otherwise be possible. $\endgroup$
    – whuber
    Apr 8, 2021 at 18:07

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