Residual Analysis and Data Transformations: Important Tools in Statistical Analysis

Abstract

Analysis of variance (ANOVA) is a commonly used statistical analysis in agricultural experiments. Additivity, variance homogeneity, and normality are often considered prerequisites for ANOVA (Cochran, 1943; Eisenhart, 1947). The interpretation of ANOVA is valid when the random errors are independently distributed according to a normal distribution with zero mean and an unknown but fixed variance (Kempthorne, 1952; Scheffe, 1959; Steel and Torrie, 1980). Failure to meet one or more of these assumptions affects the significance levels and the sensitivity of the F test (Gomez and Gomez, 1984; Kempthorne, 1952; Little and Hills, 1978) Thus, strong deviations from one or more of the assumptions must be checked and corrected before the statistical analysis and interpretation of the results. Discrepancies of many kinds between an assumed model and the data can be detected by studying the error component or residuals (Anscombe and Tukey, 1963; Emerson and Stoto, 1983). The residuals are the deviation bserved and the predicted values to the assumed model. If the asabout the validity of the model are sidual plot (scatter plot between ls and the predicted values) will dom distribution. If the residual unexplained systematic pattern, NOVA model is not appropriate. lots can be used to detect the viassumptions in ANOVA, such as eterogeneity (unequal variance], ated error (nonindependence), and ce of outliers. Thus, it is crucial the residuals before interpreting