Economic values under inappropriate normal distribution assumptions

Abstract

The objectives of this study were to quantify the errors in economic values (EVs) for traits affected by cost or price thresholds when skewed or kurtotic distributions of varying degree are assumed to be normal and when data with a normal distribution is subject to censoring. EVs were estimated for a continuous trait with dichotomous economic implications because of a price premium or penalty arising from a threshold ranging between −4 and 4 standard deviations from the mean. In order to evaluate the impacts of skewness, positive and negative excess kurtosis, standard skew normal, Pearson and the raised cosine distributions were used, respectively. For the various evaluable levels of skewness and kurtosis, the results showed that EVs can be underestimated or overestimated by more than 100% when price determining thresholds fall within a range from the mean that might be expected in practice. Estimates of EVs were very sensitive to censoring or missing data. In contrast to practical genetic evaluation, economic evaluation is very sensitive to lack of normality and missing data. Although in some special situations, the presence of multiple thresholds may attenuate the combined effect of errors at each threshold point, in practical situations there is a tendency for a few key thresholds to dominate the EV, and there are many situations where errors could be compounded across multiple thresholds. In the development of breeding objectives for non-normal continuous traits influenced by value thresholds, it is necessary to select a transformation that will resolve problems of non-normality or consider alternative methods that are less sensitive to non-normality.