Statisticians and experimenters are gradually calling for a replacement of the sacred alpha at 0.05 with more of an emphasis on beta. Alpha gives the probability of finding differences as extreme as observed sampling out of a totally mixed, random common population. Beta, or "power", centers more around effect size and the probability of making an error in calling out the observed differences if they come out of distinct populations. Alpha tends to "pass" inconsequential effects, while beta is more realistic.
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