## The Annals of Statistics

### Interval Estimation for the Unbalanced Case of the One-Way Random Effects Model

#### Abstract

Interval estimation of variance components is studied for the unbalanced one-way random effects model. An easily calculated function, $W$, of the harmonic mean of the class sizes and of the sample variance of the class means is found to be important. The exact distribution of $W$ is found and is shown to be excellently approximated by a chi-square distribution. The random variable $W$ is used to construct interval estimates for (i) the between classes variance component and (ii) the ratio of the variance components and thus for the intraclass correlation and heritability. For most one-way unbalanced designs use of these approximate interval estimators will work very well.

#### Article information

Source
Ann. Statist., Volume 6, Number 3 (1978), 582-587.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344202

Digital Object Identifier
doi:10.1214/aos/1176344202

Mathematical Reviews number (MathSciNet)
MR484702

Zentralblatt MATH identifier
0386.62057

JSTOR