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InfluxDB
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So you are testing for the same thing, but the TukeyHSD and HSD.test functions use different ways to compensate for unbalanced designs. TukeyHSD applies an adjustment for "mildly unbalanced designs" by effectively padding the sample sizes (at least that is my understanding of the source code at a quick glance) where:
HSD.test adjusts the p-value where:
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