### Abstract

A simple adjustment to the Pearson chi-square test has been proposed for comparing proportions estimated from clustered binary observations. However, the assumptions needed to assure the validity of this test have not yet been thoroughly addressed. These assumptions will hold for experimental comparisons, but could be violated for some observational comparisons. In this paper we investigate the conditions under which the adjusted chi-square statistic is valid and examine its performance when these assumptions are violated. We also introduce some alternative test statistics that do not require these assumptions. The test statistics considered are then compared through simulation and an example presented based on real data. The simulation study shows that the adjusted chi-square statistic generally produces empirical type I errors close to nominal under the assumption of a common intracluster correlation coefficient. Even if the intracluster correlations are different, the adjusted chi-square statistic performs well when the groups have equal numbers of clusters.

Original language | English (US) |
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Pages (from-to) | 2149-2161 |

Number of pages | 13 |

Journal | Statistics in Medicine |

Volume | 20 |

Issue number | 14 |

DOIs | |

State | Published - Jul 30 2001 |

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### ASJC Scopus subject areas

- Epidemiology

### Cite this

*Statistics in Medicine*,

*20*(14), 2149-2161. https://doi.org/10.1002/sim.857

**Evaluation of an adjusted chi-square statistic as applied to observational studies involving clustered binary data.** / Jung, Sin Ho; Ahn, Chul; Donner, Allan.

Research output: Contribution to journal › Article

*Statistics in Medicine*, vol. 20, no. 14, pp. 2149-2161. https://doi.org/10.1002/sim.857

}

TY - JOUR

T1 - Evaluation of an adjusted chi-square statistic as applied to observational studies involving clustered binary data

AU - Jung, Sin Ho

AU - Ahn, Chul

AU - Donner, Allan

PY - 2001/7/30

Y1 - 2001/7/30

N2 - A simple adjustment to the Pearson chi-square test has been proposed for comparing proportions estimated from clustered binary observations. However, the assumptions needed to assure the validity of this test have not yet been thoroughly addressed. These assumptions will hold for experimental comparisons, but could be violated for some observational comparisons. In this paper we investigate the conditions under which the adjusted chi-square statistic is valid and examine its performance when these assumptions are violated. We also introduce some alternative test statistics that do not require these assumptions. The test statistics considered are then compared through simulation and an example presented based on real data. The simulation study shows that the adjusted chi-square statistic generally produces empirical type I errors close to nominal under the assumption of a common intracluster correlation coefficient. Even if the intracluster correlations are different, the adjusted chi-square statistic performs well when the groups have equal numbers of clusters.

AB - A simple adjustment to the Pearson chi-square test has been proposed for comparing proportions estimated from clustered binary observations. However, the assumptions needed to assure the validity of this test have not yet been thoroughly addressed. These assumptions will hold for experimental comparisons, but could be violated for some observational comparisons. In this paper we investigate the conditions under which the adjusted chi-square statistic is valid and examine its performance when these assumptions are violated. We also introduce some alternative test statistics that do not require these assumptions. The test statistics considered are then compared through simulation and an example presented based on real data. The simulation study shows that the adjusted chi-square statistic generally produces empirical type I errors close to nominal under the assumption of a common intracluster correlation coefficient. Even if the intracluster correlations are different, the adjusted chi-square statistic performs well when the groups have equal numbers of clusters.

UR - http://www.scopus.com/inward/record.url?scp=0035974295&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035974295&partnerID=8YFLogxK

U2 - 10.1002/sim.857

DO - 10.1002/sim.857

M3 - Article

C2 - 11439427

AN - SCOPUS:0035974295

VL - 20

SP - 2149

EP - 2161

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 14

ER -