# Duncan’s New Multiple Range Test

The test statistic is:

where:

- 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

- Computing either:
- Column Comparisons
- A Planned Tests Of Statistical Significance for a row or column of a table.

- This test has been selected in the Statistical Assumptions setting of Multiple comparison correction > Column comparisons