The NPAR1WAY Procedure

Ratio Mean Deviations (RMD) Exact Test

If you specify the RMD option in the PROC NPAR1WAY statement or the EXACT statement, PROC NPAR1WAY computes the ratio mean deviations (RMD) exact test of scale differences for two-sample data (Higgins 2004). This test is based on the ratio of absolute deviations of the observations (response variable values) from their class medians. For more information, see Butar and Park (2008) and Richter and McCann (2017).

The RMD test statistic is computed as

normal upper R normal upper M normal upper D equals left-parenthesis sigma-summation Underscript j equals 1 Overscript n 1 Endscripts d Subscript 1 j Baseline slash n 1 right-parenthesis slash left-parenthesis sigma-summation Underscript j equals 1 Overscript n 2 Endscripts d Subscript 2 j Baseline slash n 2 right-parenthesis

where the absolute deviations for class i are

d Subscript i j Baseline equals StartAbsoluteValue upper X Subscript i j Baseline minus m Subscript i Baseline EndAbsoluteValue

and where m Subscript i is the sample median of class i, upper X Subscript i j are the observations in class i (j equals 1 comma ellipsis comma n Subscript i Baseline), and n Subscript i is the number of observations in class i (i equals 1 comma 2).

PROC NPAR1WAY uses the first class that is displayed in the "Deviations" table as class 1 and the second class as class 2. By default, the table displays class levels in the order in which they appear in the input data set. If you specify the ORDER=FORMATTED option, the table displays class levels in order of their formatted value.

The RMD p-value is computed by using an exact permutation test that is conditional on the observed deviations (Higgins 2004). PROC NPAR1WAY displays the exact one-sided p-value as the left-sided p-value (Pr <= RMD) when the value of the RMD statistic is less than or equal to 1; otherwise, PROC NPAR1WAY displays the right-sided p-value (Pr >= RMD).

If you specify the MIDP computation-option in the EXACT statement, PROC NPAR1WAY also provides the exact mid p-value for the RMD test. If you specify the POINT computation-option in the EXACT statement, PROC NPAR1WAY provides the exact point probability for the RMD test.

PROC NPAR1WAY computes the modified RMD two-sided statistic as

normal upper R normal upper M normal upper D Baseline 2 equals max left-parenthesis normal upper R normal upper M normal upper D comma 1 slash normal upper R normal upper M normal upper D right-parenthesis

The corresponding exact two-sided p-value is computed by using a permutation test for the RMD2 statistic.

To obtain Monte Carlo estimates of exact p-values for the RMD test, you can specify the MC computation-option together with the RMD statistic-option in the EXACT statement. For more information, see the section Exact Tests.

Last updated: December 09, 2022