Abstract
For fixed-effect models one can always, according to the Gauss-Markov Theorem, uniquely determine independent variables called source identifiers, each corresponding to a source of variation. When linearly combined, source identifiers can generate all possible expected values for the response variable. The co-effect method uses regression of the response variable on source identifiers. Corresponding regression coefficients are, by definition, unbiased estimates of co-effects, and satisfy the same restrictions as those imposed on main effects and interaction effects in standard analysis of variance. with balanced data, co-effect analysis gives results identical to those of the standard method; with unbalanced data, however, results can be significantly different
.
An example is given where predicted genetic interaction can be easily observed using the co-effect method (Р≈10-14) while Yates' weighted-squares-of-means method does not detect any interaction effects (P>O.l)
.
Keywords
Unbalanced data, analysis of variance, interaction, co-effects, genetic experiment
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Plante, Andre
(1992).
"CO-EFFECT ANALYSIS OF VARIANCE: A NEW METHOD FOR UNBALANCED DATA,"
Conference on Applied Statistics in Agriculture.
https://doi.org/10.4148/2475-7772.1391
CO-EFFECT ANALYSIS OF VARIANCE: A NEW METHOD FOR UNBALANCED DATA
For fixed-effect models one can always, according to the Gauss-Markov Theorem, uniquely determine independent variables called source identifiers, each corresponding to a source of variation. When linearly combined, source identifiers can generate all possible expected values for the response variable. The co-effect method uses regression of the response variable on source identifiers. Corresponding regression coefficients are, by definition, unbiased estimates of co-effects, and satisfy the same restrictions as those imposed on main effects and interaction effects in standard analysis of variance. with balanced data, co-effect analysis gives results identical to those of the standard method; with unbalanced data, however, results can be significantly different
.
An example is given where predicted genetic interaction can be easily observed using the co-effect method (Р≈10-14) while Yates' weighted-squares-of-means method does not detect any interaction effects (P>O.l)
.
