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    $\begingroup$ Welcome to Cross Validated! The ANOVA question at the end probably warrants its own post. $\endgroup$ Commented Feb 3, 2022 at 13:45
  • $\begingroup$ We can solve the problem with ANOVA quickly in a single commonent. It is not p-hacking. Multiple groups are compared but only a single hypothesis is tested. ANOVA computes a ratio of variances and a p-value can be computed for that ratio based on a single hypothesis. Possibly the idea of anova=p-hacking arises due to the confusing aspect that a hypothesis test is often not used to test a null hypothesis, but instead to prove the alternative hypothesis (which can be many at once). ANOVA also doesn't tell which of the many groups are different, but only that they are not the same. $\endgroup$ Commented Feb 3, 2022 at 14:44
  • $\begingroup$ You may want to look into Oaxaca-Blinder decomposition which is frequently sued for studying racial/gender/other biases. $\endgroup$ Commented Feb 4, 2022 at 8:32