AN INTERPRETATION AND EXTENSION OF TUKEY'S ONE DEGREE OF FREEDOM FOR NON-ADDITIVITY
Abstract
An interpretation is given of the test for nonadditivity in a two-factor experiment, in which a sum of squares (with a single degree of freedom) for non-additivity is separated from the sum of squares for interaction and tested against the residual. The interpretation is as follows: The sum of squares for non-additivity is the sum of squares for linear regression of the sample interaction on the product of the sample main effects; or equivalently, the ratio of the sum of squares for non-additivity to the sum of squares for interaction is the coefficient of determination (the square of the coefficient of correlation) between the sample interaction and the product of the sample main effects. This interpretation remains valid for an extension to experiments with three or more factors. This extension involves the separation, from the sum of squares for each interaction of two or more factors, of a sum of squares (with a single degree of freedom) for non-additivity, which is then tested against the residual for that interaction. Several artificial examples and two examples involving actual data are given. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1962
- Accession Number
- AD0277151
Entities
People
- H. Leon Harter
- Mary D. Lum
Organizations
- Air Force Research Laboratory