A comparison of tests of homogeneity for sparse contingency tables

D. Kraemer, Robert F. Woolson

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Five tests of homogeneity for a 2x(k+l) contingency table are compared using Monte Carlo techniques. For these studies it is assumed that k becomes large in such a way that the contingency table is sparse for 2xk of the cells, but the sample size in two of the cells remains large. The test statistics studied are: the chi-square approximation to the Pearson test statistic, the chi-square approximation to the likelihood ratio statistic, the normal approximation to Zelterman's (1984) ф, the normal approximation to Pearson's chi-square, and the normal approximation to the likelihood ratio statistic. For the range of parameters studied the chi-square approximation to Pearson's statistic performs consistently well with regard to its size and power.

Original languageEnglish
Pages (from-to)465-483
Number of pages19
JournalCommunications in Statistics - Simulation and Computation
Volume16
Issue number2
DOIs
Publication statusPublished - Jan 1 1987

Fingerprint

Test of Homogeneity
Chi-square
Contingency Table
Normal Approximation
Statistics
Likelihood Ratio Statistic
Test Statistic
Approximation
Monte Carlo Techniques
Cell
Statistic
Sample Size
Range of data

Keywords

  • categorical data
  • goodness of fit
  • sparse tables

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation

Cite this

A comparison of tests of homogeneity for sparse contingency tables. / Kraemer, D.; Woolson, Robert F.

In: Communications in Statistics - Simulation and Computation, Vol. 16, No. 2, 01.01.1987, p. 465-483.

Research output: Contribution to journalArticle

@article{e866eeaffcbf44d19677389eb2a3b689,
title = "A comparison of tests of homogeneity for sparse contingency tables",
abstract = "Five tests of homogeneity for a 2x(k+l) contingency table are compared using Monte Carlo techniques. For these studies it is assumed that k becomes large in such a way that the contingency table is sparse for 2xk of the cells, but the sample size in two of the cells remains large. The test statistics studied are: the chi-square approximation to the Pearson test statistic, the chi-square approximation to the likelihood ratio statistic, the normal approximation to Zelterman's (1984) ф, the normal approximation to Pearson's chi-square, and the normal approximation to the likelihood ratio statistic. For the range of parameters studied the chi-square approximation to Pearson's statistic performs consistently well with regard to its size and power.",
keywords = "categorical data, goodness of fit, sparse tables",
author = "D. Kraemer and Woolson, {Robert F.}",
year = "1987",
month = "1",
day = "1",
doi = "10.1080/03610918708812600",
language = "English",
volume = "16",
pages = "465--483",
journal = "Communications in Statistics Part B: Simulation and Computation",
issn = "0361-0918",
publisher = "Taylor and Francis Ltd.",
number = "2",

}

TY - JOUR

T1 - A comparison of tests of homogeneity for sparse contingency tables

AU - Kraemer, D.

AU - Woolson, Robert F.

PY - 1987/1/1

Y1 - 1987/1/1

N2 - Five tests of homogeneity for a 2x(k+l) contingency table are compared using Monte Carlo techniques. For these studies it is assumed that k becomes large in such a way that the contingency table is sparse for 2xk of the cells, but the sample size in two of the cells remains large. The test statistics studied are: the chi-square approximation to the Pearson test statistic, the chi-square approximation to the likelihood ratio statistic, the normal approximation to Zelterman's (1984) ф, the normal approximation to Pearson's chi-square, and the normal approximation to the likelihood ratio statistic. For the range of parameters studied the chi-square approximation to Pearson's statistic performs consistently well with regard to its size and power.

AB - Five tests of homogeneity for a 2x(k+l) contingency table are compared using Monte Carlo techniques. For these studies it is assumed that k becomes large in such a way that the contingency table is sparse for 2xk of the cells, but the sample size in two of the cells remains large. The test statistics studied are: the chi-square approximation to the Pearson test statistic, the chi-square approximation to the likelihood ratio statistic, the normal approximation to Zelterman's (1984) ф, the normal approximation to Pearson's chi-square, and the normal approximation to the likelihood ratio statistic. For the range of parameters studied the chi-square approximation to Pearson's statistic performs consistently well with regard to its size and power.

KW - categorical data

KW - goodness of fit

KW - sparse tables

UR - http://www.scopus.com/inward/record.url?scp=2642585167&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2642585167&partnerID=8YFLogxK

U2 - 10.1080/03610918708812600

DO - 10.1080/03610918708812600

M3 - Article

VL - 16

SP - 465

EP - 483

JO - Communications in Statistics Part B: Simulation and Computation

JF - Communications in Statistics Part B: Simulation and Computation

SN - 0361-0918

IS - 2

ER -