### 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 language | English |
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Pages (from-to) | 465-483 |

Number of pages | 19 |

Journal | Communications in Statistics - Simulation and Computation |

Volume | 16 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 1987 |

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### Keywords

- categorical data
- goodness of fit
- sparse tables

### ASJC Scopus subject areas

- Statistics and Probability
- Modelling and Simulation

### Cite this

*Communications in Statistics - Simulation and Computation*,

*16*(2), 465-483. https://doi.org/10.1080/03610918708812600

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

Research output: Contribution to journal › Article

*Communications in Statistics - Simulation and Computation*, vol. 16, no. 2, pp. 465-483. https://doi.org/10.1080/03610918708812600

}

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 -