Duncan’s New Multiple Range Test

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The test statistic is:


and are the means of the two groups being compared and is the mean of the of groups,
when applying the test to Repeated Measures, each respondent’s average is initially subtracted from their data and it is this corrected data that constitutes of ,
is the number of observations in the th of groups,
is the Calibrated Weight for the th observation in the group,
is the Effective Sample Size for the group,
for Repeated Measures and otherwise.
is evaluated using a Tukey’s Studentized Range distribution with degrees of freedom for groups, where is determined by a step down analysis and the resulting p-value is adjusted using (see Duncan, D B.; Multiple range and multiple F tests. Biometrics 11:1–42, 1955).

Circumstances when this test is applied

See also