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

Abstract

Consider a specified set of n dichotomous items with a joint probability distribution given by p. Let p(1) denote the joint distribution of the n items when they are independent with the same marginal probabilities as under p. Suppose one represents p + p(1).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)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1959
Accession Number
AD0706093

Entities

People

  • Raj Raghu Bahadur

Organizations

  • Columbia University

Tags

DTIC Thesaurus Topics

  • Classification
  • Computing-Related Activities
  • Data Science
  • Information Science
  • Interdisciplinary Science
  • Mathematical Analysis
  • Mathematics
  • Probability
  • Probability Distributions
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Psychometric Testing or Psychological Assessment.