The effects of lack of normality and homogeneity of variance on analysis of variance and clonal heritability in in vitro clonal propagation traits

Abstract

We studied the fulfilment of assumptions of normality and homogeneity of error variance, prior to application of analysis of variance (ANOVA), for in vitro clonal propagation data. We assessed the use of data transformations and mean values for situations when the original data did not satisfy the required assumptions. The purpose of the study was to establish whether the use of original, transformed or mean values had any effect on F values, significance levels and clonal heritability values. The F values, significance levels and values of clonal heritability obtained showed analysis of variance to be reliable, despite deviations with respect to normality and homogeneity of variance and despite the fact that samples sizes were unequal. Original data may be used for ANOVA applied to measured variables such as number of shoots per explant, length of tallest shoot, number of 1-cm segments per explant and also derived variables such as the multiplication coefficient. Frequency data can be used for analysis of variance of categorical-type variables such as apical necrosis and percentage of responsive explant. For shoot colour variables, the distributions were very skewed and the variances were very different, but even though the sample sizes were not identical in all cases, lack of homogeneity of variance did not significantly affect F values, significance levels or clonal heritability values, and thus analysis of variance may be applied to the original data. The use of original and frequency data makes interpretation of the results easier than when transformed data are used and also allows us to calculate variance components more accurately than when using mean values, which do not provide as much information. Clonal heritability values from transformed data and mean values showed differences of less than one hundredth compared with those from original data. Box–Cox-transformed data showed slightly lower heritability values than those corresponding to original data, whereas clonal heritability values from both mean data and angular-transformed data were slightly higher than those obtained using original data. In clonal variability studies with single growth medium, nutritional conditions that encouraged highly unequal growth or characteristics among clones gave rise to data that were unlikely to satisfy the conditions of normality or homogeneity of variance.