#### Is the first presenter a student?

No

#### Type of Submission

Paper/Presentation

#### Abstract

Latin Square (LS) designs have long been advocated for field crop experiments on the grounds that '. . . soil fertility and other variations in two directions are controlled.' As counter-evidence, the published standard analyses of eight LS experiments showed that in only two did the sum of squares for both between-rows and between-columns account for appreciable background variability.

Regarding the background concomitant variability as a continuous surface to which treatment effects are additive, it is suggested that a contributory shortcoming of the standard model is that it admits only a restricted class of surfaces because parameters for warp, or row x column interaction, components are excluded.

It is shown that, at the loss of some orthogonality between background and treatment effects, the deficiency can be remedied by fitting a more general polynomial surface. The principle is exemplified using a backward selection mUltiple regression procedure to analyze LS data in Cochran and Cox (1957). The procedure gave a considerable reduction in the coefficient of variation, from 12.9 to 6.3%, and permitted more sensible inferences than those (null) from the standard analysis.

A note on medieval cultivation practices and experimental design is appended.

#### Keywords

field crop experiments

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

#### Recommended Citation

Cox, C. Philip and Meeker, Jeff B.
(1992).
"A SIMPLE ALTERNATIVE TO THE STANDARD STATISTICAL MODEL FOR THE ANALYSIS OF FIELD EXPERIMENTS WITH LATIN SQUARE DESIGNS,"
*Annual Conference on Applied Statistics in Agriculture*.
http://newprairiepress.org/agstatconference/1992/proceedings/11

A SIMPLE ALTERNATIVE TO THE STANDARD STATISTICAL MODEL FOR THE ANALYSIS OF FIELD EXPERIMENTS WITH LATIN SQUARE DESIGNS

Latin Square (LS) designs have long been advocated for field crop experiments on the grounds that '. . . soil fertility and other variations in two directions are controlled.' As counter-evidence, the published standard analyses of eight LS experiments showed that in only two did the sum of squares for both between-rows and between-columns account for appreciable background variability.

Regarding the background concomitant variability as a continuous surface to which treatment effects are additive, it is suggested that a contributory shortcoming of the standard model is that it admits only a restricted class of surfaces because parameters for warp, or row x column interaction, components are excluded.

It is shown that, at the loss of some orthogonality between background and treatment effects, the deficiency can be remedied by fitting a more general polynomial surface. The principle is exemplified using a backward selection mUltiple regression procedure to analyze LS data in Cochran and Cox (1957). The procedure gave a considerable reduction in the coefficient of variation, from 12.9 to 6.3%, and permitted more sensible inferences than those (null) from the standard analysis.

A note on medieval cultivation practices and experimental design is appended.