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

Enter A3: D15 in the Input Range, check Column headings included with data, select the Tukey HSD option and click on the OK button. We see that only MC-WD is significant, although WC-WD is close.

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.

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).

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 test can also be used when the group means are not equal via although, since Dunnett’s Table is based on equal group sizes, the above formula is only accurate if the group sizes are not too different.Real Statistics Function: The following function is provided in the Real Statistics Resource Pack: DCRIT( = TRUE (default) harmonic interpolation is used; otherwise linear interpolation is used.As described above, to control type I error, we can’t simply use the usual critical value for the distribution, but instead use a critical value based on the largest difference of the means.From these observations we can calculate confidence intervals in the usual way: or equivalently Example 1: Analyze the data from Example 3 of Planned Comparisons using Tukey’s HSD test to compare the population means of women taking the drug and the control group taking the placebo. Alternatively, we can employ Excel’s table lookup capabilities.Example 2: Analyze the data in range A3: D15 of Figure 4 using the Tukey-Kramer test to compare the population means of women taking the drug and the control group taking the placebo.

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