| Zusammenfassung |
Many fisheries data are commonly summarized by two statistics: mean and variance (or standard deviation). Because observed values are subject to various errors, which often are large and heterogeneous in fisheries studies, outliers commonly exist in the data. The existence of outliers biases estimation of the mean and variance if traditional estimation methods are used. Instead of assuming that errors in fisheries data follow a normal distribution with a constant variance, we propose that errors associated with observations for a variable may encompass a mixture of different levels of normally distributed errors. Based on concepts from a robust regression method, least median of squares, that is not sensitive to atypical observations in data, we develop a simple algorithm to estimate mean and standard deviation. We compare the proposed robust estimation approach with traditional methods and Tukey's biweight robust approach using simulated and field data. Based on simulations, we found little difference in estimated means and variances between the proposed and traditional methods when there were no outliers defined in simulated data. However, when outliers were defined in simulated data, the errors in estimation of the mean and its standard deviation were much smaller with the proposed method than were those estimated with traditional methods. Means and standard deviations estimated with the proposed method changed little, regardless of whether or not the simulated data were contaminated by atypical values. The proposed approach tended to have smaller estimation errors than did the robust biweight method. We demonstrate how the significance and interpretation of fisheries and ecological relationships may be adversely affected when outliers are present. We suggest using our proposed robust method to identify and down-weight outliers in estimating a mean and its standard deviation. One should justify deletion of the identified outliers using the knowledge about fish biology and environmental conditions independent of the variable assessed. |
