Open AccessNOTE ON A NON‐PARAMETRIC TEST FOR CORRELATION FOR DATA EXPRESSED IN THE FORM OF RANK ORDERS WITHIN SUBGROUPS
Author(s) -
Torgerson Warren S.
Publication year - 1955
Publication title -
ets research bulletin series
Language(s) - English
Resource type - Journals
eISSN - 2333-8504
pISSN - 0424-6144
DOI - 10.1002/j.2333-8504.1955.tb00051.x
Subject(s) - rank (graph theory) , mathematics , statistics , test (biology) , rank correlation , sample (material) , parametric statistics , excellence , order (exchange) , econometrics , combinatorics , law , chemistry , finance , chromatography , political science , economics , biology , paleontology
Kendall's rank order test for association between two variables is generalized to the case where the total sample is made up of several subgroups and the data on one or both variables consist of the rank order within each subgroup. The test involves no assumptions concerning scales of measurement, shapes of distributions, or relative level of excellence or amount of variability of the different subgroups. Two empirical examples indicate that the normal approximation to the exact test of significance can be considered adequate for most practical situations. Special consideration is given to the case of tied ranks. If ties occur in but one variable within any given subgroup, only a slight modification in procedure is needed. Extensive ties in both variables within subgroups lead to difficulties in determining the appropriate correction for continuity.