skip to main content skip to footer

A Statistical Test of the Hypothesis That a Correlation Corrected for Attenuation in One Variable Only is 1.00

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Correlation, Error of Measurement, Hypothesis Testing, Statistical Significance


A uniformly most powerful significance test is derived to test the null hypothesis that the population value of the correlation corrected for attenuation is 1, in the case where the correlation is carried out on one variable only. The significance test is easily carried out by computing F from two equations and then consulting a standard table of the F distribution. A numerical example is given. The likelihood ratio statistic for testing the foregoing null hypothesis is found to have a simple relation to the statistic used for the uniformly most powerful significance test. A numerical example shows that when the null hypothesis is true, sample values of the correlation corrected for attenuation will differ from 1.00 much less than might be expected. As shown in the example, when the number of examinees is 101 and the sample value of the parallel forms reliability coefficient for the fallible measure is .90, only five percent of the sample values of the correlation corrected for attenuation will be below .990 or above 1.008.

Read More