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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.

The pairs whose mean difference is larger than the critical value are significant.

For our example, the only mean differences in the first two columns are significant.

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.

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statistic becomes Note that the Real Statistics Tukey HSD data analysis tool described above actually performs the Tukey-Kramer Test when the sample sizes are unequal.

The Real Statistics Resource Pack also provides the following functions which provide estimates for the Studentized range distribution and its inverse based on a somewhat complicated algorithm. Observation: Note that the values calculated by QCRIT and QINV will be similar, at least within the range of alpha values in the table of critical values. QINV(.015,4,18,2) = 4.82444 while QCRIT(4,18,.015,2) = 4.75289. Real Statistics Data Analysis Tool: The Real Statistics Resource Pack contains a Tukey’s HSD Test data analysis tool which produces output very similar to that shown in Figure 2.

For example, to produce the first test in Figure 2, follow the following steps: Enter Ctrl-m and select the Analysis of Variance data analysis tool from the list.

The following table shows the same comparisons for all pairs of variables: From Figure 1 we see that the only significant difference in means is between women taking the drug and men in the control group (i.e. We can also use the t-statistic to calculate the 95% confidence interval as described above.

In Figure 2 we compute the confidence interval for the comparison requested in the example as well as for the variables with maximum difference.