tiedrank2

Tied-rank transformation across both dimensions

Function: tiedrank2

Usage: [RANKS, RESPONSE, TREATMENT, BLOCKS] = tiedrank2 (X, REPS, DIM)

The entire data matrix X is ranked from smallest to largest, where average ranks are assigned in the case of ties and NaN values are ignored. This is what Conover referred to as the RT-1 type procedure [1].

If there is more than one observation per row-column "cell", use the scalar argument REPS to indicate the (largest) number of observations per cell. Each cell corresponds to REPS consecutive rows in one column of X if DIM equals 1 (default), or REPS consecutive columns in one row of X if DIM equals 2.

The output from tiedrank2 can be used as input for the ANOVA functions as a more powerful alternative to using bespoke nonparametric tests [2].

Please see function help for example usage in a wide variety of tests.

References:
[1] Conover, W. J., & Iman, R. L. (1981).
Rank transformations as a bridge between parametric and nonparametric statistics.
American Statistician, 35, 124-129.

[2] Zimmerman, D. W., & Zumbo, Bruno, D. (1993).
Relative power of the Wilcoxon test, the Friedman test, and repeated-measures ANOVA on ranks.
Journal of Experimental Education, 62, 75-86.

[3] Conover, W. J., & Iman, R. L. (1982).
Analysis of Covariance using the Rank Transformations.
Biometrics, 38, 715-724.