Simple statistical methods for scalogram analysis

Simple statistical methods are developed to test whether coefficients of reproducibility, of homogeneity, or of consistency differ significantly from what can be expected if responses to different items are statistically independent. Simple methods are also developed for estimating the variance of coefficients of reproducibility when it is not assumed that responses to different items are independent. These estimates are used to test whether a coefficient differs significantly from any prescribed value, and also to obtain confidence intervals for these coefficients. The rationale for the measurement of reproducibility is also discussed.This research was carried out at the Statistical Research Center, University of Chicago, under sponsorship of the Statistics Branch, Office of Naval Research, and of the Social Science Research Committee, University of Chicago. Reproduction in whole or in part is permitted for any purpose of the United States Government. The author is indebted to Jacob Gewirtz for some very helpful comments.This paper is dedicated to Professor Jacob Marschak on the occasion of his sixtieth birthday, July 23, 1958.