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I used the SNK.test (Student Newman Keuls Test) to compare different factor:

    model<-aov(d12~treatment, data=data)
    out <- SNK.test(model,"treatment", console=TRUE,main="main titel", alpha = 0.05)


    "           d12 groups
    n2 0.020114011      a
    b1 0.017675491      a
    d  0.010821398     ab
    w1 0.007966960     ab
    n4 0.001480165      b"

Here, n4 is in the same group as d.

But if I just compare the two of them:

    dn4   =subset (data, subset = ordre %in% c(3,7))

    model<-aov(d12~treatment, data=dn4)
    out <- SNK.test(model,"treatment", console=TRUE,main="main titel", alpha = 0.05)


    "           d12 groups
    d  0.010821398      a
    n4 0.001480165      b"

N4 and d are not in the same group!!

How is that possible? On which basis is the SNK test doing those groups?

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Several multiple-range tests, including SNK, correct for type I error by essentially requiring the minimum difference for significance to be larger for more comparisons. SNK also adds a ranking and stepwise comparisons. The specifics of how they impose that requirement vary from method to method. So, when you are only comparing d to n4, you are doing one comparison. This is mathematically equivalent to (heck, it is) a t test.

When you compare 5 groups, you are doing ten pairwise comparisons. The minimum threshold for a difference to be "significant" at p <= 0.05 increases. Whatever else SNK does, as you have more comparisons, the necessary difference between adjacent groups increases.

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