APPLICATION GENERALITY OF SOME RESULTS FOR ANALYSIS OF VARIANCE,
Abstract
Attention is called to a very general unconditional model for representing the observed outcomes resulting from use of some experimental designs in analysis of variance. Included as special cases are factorial, randomized block, and split-plot designs. The model is of a fixed-effects nature and the interest is in investigating the effects of treatments. The outcomes are allowed to be dependent in an almost arbitrary fashion and each outcome can have a substantially different distribution. In particular, the outcomes can be correlated almost arbitrarily and can have appreciably different variances. In spite of this generality, the sum of squares for error, the sum of squares for treatments, and estimates of contrasts (comparisons) in treatment effects possess the properties that would occur if the observations were independent and the random error terms had the same distribution. This model may help explain why the usual estimates and tests for treatment effects in factorial, randomized block, splitplot, and other designs have been applied so successfully. These estimates and tests are known to be approximately applicable for a broad class of situations when the error terms constitute a random sample. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 07, 1965
- Accession Number
- AD0617770
Entities
People
- John E. Walsh
Organizations
- System Development Corporation