Scaling a simplex

A least-squares solution for scaling the variables of a Guttman simplex is developed. The procedure yields a ratio scale, two varieties of interval scale, and orders the variables. A measure of the goodness of fit of the scale to the data is suggested. An example of the application of the method is given. The problem of non-positive correlations is discussed.I am indebted to Professor Lloyd Humphreys for suggesting this problem. Mr. Joseph Levin independently has arrived at the results of the first section of the paper. The final version of this paper was prepared while the author was a U. S. Public Health Service Fellow at the Center for Advanced Study in the Behavioral Sciences.