Journal of Official Statistics, Vol.3, No.4, 1987. pp. 389401

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On the Design of Interpenetration Experiments for Categorical Data Items

The variance of the ANOVA estimator of the variance component for a balanced one-way random model which has a categorical response variable is derived, without making any distributional assumptions for the random effect. The tightest possible bounds for this variance are determined from the Markov-Krein Theorem by assuming knowledge of only the first two or three moments and the range of possible values of the random effect. The bounds are shown to be useful for planning the survey design, including the sample size requirements, of an interpenetration experiment to estimate the correlated component of response variance for a categorical item in a sample survey. Examples illustrate that the resulting required sample sizes may deviate greatly from that which would be appropriate for estimating the correlated component for a continuous response variable assumed to meet the normality assumptions of the classical variance components model.

Variance component; interpenetration; interviewer variance; survey non-sampling error; Markov-Krein Theorem.

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