#### Is the first presenter a student?

No

#### Type of Submission

Paper/Presentation

#### 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,"
*Annual Conference on Applied Statistics in Agriculture*.
http://newprairiepress.org/agstatconference/1992/proceedings/3

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)

.