#### Abstract

Four types of covariates are used to account for spatial variability in data from a field experiment for evaluating 620 soybean varieties for iron chlorosis. The covariates are calculated as the average of 4 and of 14 neighboring residuals and of 4 and of 14 neighboring observations. The residual mean square from the analysis of covariance was smaller' when residuals were used in calculation of the covariates than when observations were used. Moreover, use of 14 neighbors resulted in smaller residual mean squares than did use of 4 neighbors. Differences among 4 covariate types were small and not practically important. Expected values for the covariate regression coefficients were derived based on an errors in variables model. The expected values depend only on the measurement error of the covariate and are unrelated to the strength of the spatial variability. The coefficients estimated from the analysis of covariance are generally greater than the expected values.

#### Keywords

Field-plot experiments, Nearest-neighbor analysis, spatial statistics.

#### Creative Commons License

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

#### Recommended Citation

Hinz, Paul N. and Lagus, John P.
(1991).
"EVALUATION OF FOUR COVARIATE TYPES USED FOR ADJUSTMENT OF SPATIAL VARIABILITY,"
*Conference on Applied Statistics in Agriculture*.
https://doi.org/10.4148/2475-7772.1422

EVALUATION OF FOUR COVARIATE TYPES USED FOR ADJUSTMENT OF SPATIAL VARIABILITY

Four types of covariates are used to account for spatial variability in data from a field experiment for evaluating 620 soybean varieties for iron chlorosis. The covariates are calculated as the average of 4 and of 14 neighboring residuals and of 4 and of 14 neighboring observations. The residual mean square from the analysis of covariance was smaller' when residuals were used in calculation of the covariates than when observations were used. Moreover, use of 14 neighbors resulted in smaller residual mean squares than did use of 4 neighbors. Differences among 4 covariate types were small and not practically important. Expected values for the covariate regression coefficients were derived based on an errors in variables model. The expected values depend only on the measurement error of the covariate and are unrelated to the strength of the spatial variability. The coefficients estimated from the analysis of covariance are generally greater than the expected values.