### Abstract

Confidence intervals for the intraclass correlation coefficient (p) are used to determine the optimal allocation of experimental material in one-way random effects models. Designs that produce narrow intervals are preferred since they provide greater precision to estimate ρ. Assuming the total cost and the relative cost of the two stages of sampling are fixed, the authors investigate the number of classes and the number of individuals per class required to minimize the expected length of confidence intervals. We obtain results using asymptotic theory and compare these results to those obtained using exact calculations. The best design depends on the unknown value of p. Minimizing the maximum expected length of confidence intervals guards against worst-case scenarios. A good overall recommendation based on asymptotic results is to choose a design having classes of size 2 + √4 + 3r, where r is the relative cost of sampling at the class-level compared to the individual-level. If r = 0, then the overall cost is the sample size and the recommendation reduces to a design having classes of size 4.

Original language | English (US) |
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Pages (from-to) | 2009-2023 |

Number of pages | 15 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 34 |

Issue number | 9-10 |

DOIs | |

State | Published - 2005 |

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### Keywords

- Expected length
- Optimal allocation
- Variance components

### ASJC Scopus subject areas

- Statistics and Probability
- Safety, Risk, Reliability and Quality

### Cite this

*Communications in Statistics - Theory and Methods*,

*34*(9-10), 2009-2023. https://doi.org/10.1080/03610920500203372