Randomization Analysis of the General Experiment,
Abstract
General consideration has been given to the expectation of quadratic functions, and in particular of analysis of variance components, of random samples drawn from structured populations of elements called 'responses.' Three general notions have entered: the structure of the population, the structure of the sample, and the scheme for drawing the random sample. A systematic approach to these notions is presented. Theorem 1 gives a general form for the expectation of the product of any two of the responses obtained in the experiment. An analysis of variance component is a quadratic form and can be expressed as a linear combination of products of pairs of responses with various 'inequality sets.' Theorem 1 gives the expectation of each of these products, but the combination of these to give the expectation of the component can lead to some difficult algebra. One class of quadratic forms which always occurs in analyses of variance is the class of 'squares of partial means.' Theorem 2, a specialization of Theorem 1, gives a simple expression for the expectation of the square of any partial mean in the sample. Together the two theorems are of great utility in finding, under general conditions, the expectations of mean squares for a wide class of experimental situations. The report concludes with a number of examples for experiments with a balanced but not necessarily complete observation structure. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1970
- Accession Number
- AD0717721
Entities
People
- Robert F. White
Organizations
- Iowa State University