### Abstract

This article proposes a new parameter, the group or class dominance probability, to measure the relative importance of random effects in one-way random effects models. This parameter is the probability the group random effect is larger in absolute size than the individual (or error) random effect. The new parameter compares the middle part of the distributions of the two sources of variation, and pays little attention to the tails of the distributions. This is in contrast to the traditional approach of comparing the variances of the random effects, which can be heavily influenced by the tails of the distributions. We suggest parametric and nonparametric estimators of the group dominance probability, and demonstrate the applicability of the ideas using data on blood pressure measurements.

Original language | English (US) |
---|---|

Pages (from-to) | 217-222 |

Number of pages | 6 |

Journal | American Statistician |

Volume | 59 |

Issue number | 3 |

DOIs | |

State | Published - Aug 2005 |

### Fingerprint

### Keywords

- Bootstrap confidence interval
- Class dominance probability
- Group dominance probability
- One-way random effects model
- Variance component

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*American Statistician*,

*59*(3), 217-222. https://doi.org/10.1198/000313005X55170

**Measuring relative importance of sources of variation without using variance.** / Harris, Ian R.; Burch, Brent D.

Research output: Contribution to journal › Article

*American Statistician*, vol. 59, no. 3, pp. 217-222. https://doi.org/10.1198/000313005X55170

}

TY - JOUR

T1 - Measuring relative importance of sources of variation without using variance

AU - Harris, Ian R.

AU - Burch, Brent D

PY - 2005/8

Y1 - 2005/8

N2 - This article proposes a new parameter, the group or class dominance probability, to measure the relative importance of random effects in one-way random effects models. This parameter is the probability the group random effect is larger in absolute size than the individual (or error) random effect. The new parameter compares the middle part of the distributions of the two sources of variation, and pays little attention to the tails of the distributions. This is in contrast to the traditional approach of comparing the variances of the random effects, which can be heavily influenced by the tails of the distributions. We suggest parametric and nonparametric estimators of the group dominance probability, and demonstrate the applicability of the ideas using data on blood pressure measurements.

AB - This article proposes a new parameter, the group or class dominance probability, to measure the relative importance of random effects in one-way random effects models. This parameter is the probability the group random effect is larger in absolute size than the individual (or error) random effect. The new parameter compares the middle part of the distributions of the two sources of variation, and pays little attention to the tails of the distributions. This is in contrast to the traditional approach of comparing the variances of the random effects, which can be heavily influenced by the tails of the distributions. We suggest parametric and nonparametric estimators of the group dominance probability, and demonstrate the applicability of the ideas using data on blood pressure measurements.

KW - Bootstrap confidence interval

KW - Class dominance probability

KW - Group dominance probability

KW - One-way random effects model

KW - Variance component

UR - http://www.scopus.com/inward/record.url?scp=23844442206&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23844442206&partnerID=8YFLogxK

U2 - 10.1198/000313005X55170

DO - 10.1198/000313005X55170

M3 - Article

VL - 59

SP - 217

EP - 222

JO - American Statistician

JF - American Statistician

SN - 0003-1305

IS - 3

ER -