# Accession Number:

## AD0706093

# Title:

## A REPRESENTATION OF THE JOINT DISTRIBUTION OF RESPONSES TO N DICHOTOMOUS ITEMS,

# Descriptive Note:

# Corporate Author:

## COLUMBIA UNIV NEW YORK TEACHERS COLL

# Personal Author(s):

# Report Date:

## 1959-01-01

# Pagination or Media Count:

## 27.0

# Abstract:

Consider a specified set of n dichotomous items with a joint probability distribution given by p. Let p1 denote the joint distribution of the n items when they are independent with the same marginal probabilities as under p. Suppose one represents p p1.f. An explicit expression is obtained for the correction factor f in terms of the n marginal probabilities and 2 to the nth power-n-1 correlation parameters. Certain formal models of dependence, suggested by this expression for f, are defined and discussed. It is pointed out that under certain conditions, the probability distribution of the total score throws some light on which model of dependence is appropriate in a given case. A generalization of this approach to the case when the items are not necessarily dichotomous is also described. Author

# Descriptors:

# Subject Categories:

- Psychology
- Statistics and Probability