We can also use the Real Statistics function QCRIT(4,44,.05,2, FALSE), as described below, to get the same result of 3.7775.

The critical value for differences in means is Since the difference between the means for women taking the drug and women in the control group is 5.83 – 3.83 = 1.75 and 1.75 is smaller than 1.8046, we conclude that the difference is not significant (just barely).

Note too that in the previous example we found that QCRIT(4,44,.05,2, FALSE) = 3.7775 using linear interpolation (between the table values of = 48). To get the usual cdf value for the Studentized range distribution, you need to divide the result from QDIST by 2, which for this example is .0075, as confirmed by the fact that QINV(.0075,4,18,1) = 4.82444.

One continues in this manner until no subsets remain to be tested.

First we arrange the sample means in descending order There are three tables in Figure 7.

Although the Bonferroni and Dunn/Sidák correction factors can be used, since we are considering unplanned tests, we must assume that all pairwise tests will be made (or at least taken into account). General guidelines are: then the two means are significantly different.

This test is equivalent to Picking the largest pairwise difference in means allows us to control the experiment-wise for all possible pairwise contrasts; in fact, Tukey’s HSD keeps experiment-wise , and similarly for other pairs.

Here the standard error becomes Thus we use different pooled variances for each pair instead of the same pooled variance as defined in Two Sample t-Test with Unequal Variances, namely In this way we also take care of the case where the variances are unequal in exactly the same manner as in Theorem 1 of Two Sample t-Test with Unequal Variances, except that we now use the q-statistic instead of the t-statistic.

Note that the supplemental function DF_POOLED can be used to calculate The Ryan, Einot, Gabriel, Welsh Studentized Range Q (REGWQ) test uses what is known as a step-down approach. First, the equality of all of the means is tested at the means is considered not to differ significantly and none of its subsets is tested.

The key issue is to correct for experiment-wise error. We also describe the Scheffé test, which can be used for non-pairwise comparisons. Where the variances are unequal we can also use the Brown-Forsythe F* Test.

Fisher’s LSD, Student Newman-Keuls (SNK) and Tukey’s B) are not very accurate and usually should not be used. These tests are designed only for pairwise comparisons (i.e. We also describe extensions to Tukey’s HSD test (Tukey-Kramer and Games and Howell) where the sample sizes or variances are unequal.

This means that there is a significant difference between women who take the drug and men in the control (first column) and there is also a significant difference between women who take the drug and women in the control.

This test is used when we want to compare one group (usually the control treatment) with the other groups.

= TRUE (default) harmonic interpolation is used; otherwise linear interpolation is used.

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