### 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