Publication date: 11/10/2021

The With Best, Hsu MCB test determines whether the mean for a given level exceeds the maximum mean of the remaining levels, or is smaller than the minimum mean of the remaining levels. See Hsu (1996). For an example of this test, see Example of the With Best, Hsu MCB Test.

The quantiles for the Hsu MCB test vary by the level of the categorical variable. Unless the sample sizes are equal across levels, the comparison circle technique is not exact. The radius of a comparison circle is given by the standard error of the level multiplied by the largest quantile value. Use the p-values of the tests to obtain precise assessments of significant differences. See Comparison with Max and Min.

Note: Means that are not regarded as the maximum or the minimum by MCB are also the means that are not contained in the selected subset of Gupta (1965) of potential maximums or minimum means.

This report gives the quantiles for each level of the categorical variable. These correspond to the specified value of Alpha.

The report shows p-values for one-sided Dunnett tests. For each level other than the best, the p-value given is for a test that compares the mean of the sample best level to the mean of each remaining level treated as a control (potentially best) level. The p-value for the sample best level is obtained by comparing the mean of the second sample best level to the mean of the sample best level treated as a control.

The report shows three columns.

Level

The level of the categorical variable.

with Max p-Value

For each level of the categorical variable, this column gives a p-value for a test that the mean of that level exceeds the maximum mean of the remaining levels. Use the tests in this column to screen out levels whose means are significantly smaller than or equal to the (unknown) largest true mean.

with Min p-Value

For each level of the categorical variable, this column gives a p-value for a test that the mean of that level is smaller than the minimum mean of the remaining levels. Use the tests in this column to screen out levels whose means are significantly greater than or equal to the (unknown) smallest true mean.

The first report shown is for the maximum and the second is for the minimum.

For the maximum report, a column shows the row mean minus the column mean minus the LSD. If a value is positive, the row mean is significantly higher than the mean for the column, and the mean for the column is not the maximum.

For the minimum report, a column shows the row mean minus the column mean plus the LSD. If a value is negative, the row mean is significantly less than the mean for the column, and the mean for the column is not the minimum.

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