Row–column designs: non-additivity makes them hazardous to use
✍ Scribed by J.N. Srivastava; Y.C. Wang
- Book ID
- 104340663
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 271 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0378-3758
No coin nor oath required. For personal study only.
✦ Synopsis
Let there be v treatments, and two nuisance factors (rows and columns) at p and q levels, respectively. The general model is:
where k is the e ect of the kth treatment, ij is the e ect of the (i; j) cell, and "ij's are independent random errors with zero mean and variance 2 , where the (i; j) cell has the kth treatment assigned to it. The nuisance factors are called "additive" if for all (i; j); ij is of the form ( i + ÿ j ), where i and ÿ j are respectively the e ects of the row i and column j. There is no reason to assume that arbitrary nuisance factors arising in nature will be additive. This will be illustrated in the paper through examples of real data. In this paper, we shall systematically study the problem concerning non-additivity in row-column designs. A method for examining non-additivity and identifying the non-additive cells will be developed. Our examples show that the e ect of non-additivity, in the analysis of row-column designs, has misled experimenters in the past.