Essentials

22 ESSENTIALS OF STATISTICScome concerned about their distribution only if it seems as though their datacould not possibly be coming from a distribution that looks like the ND.Trimming Your DataWhat can researchers do if they are concerned that their data do not look normal(i.e., like the ND)? If the data look fairly consistent with the ND except for a fewextreme scores, it makes sense to try to find a good reason to drop the outliers(e.g., the respondent didn’t understand the instructions, got drowsy, etc.). If noindependent reason can be found for dropping outliers, sometimes researcherstrim their data, eliminating the highest (or most extreme) 5 or 10% of the scores.This method is especially acceptable if one can anticipate outliers based on previousexperiments (this is particularly common when measuring reaction times)and plan the trimming in advance. Trimming your data leads to some complicationsin applying more advanced statistical analysis to your results, but in recentyears there has been a good deal of progress in developing methods for dealingwith robust statistics (Wilcox, 1998). When the mean, for instance, is calculated fortrimmed data, it is called a trimmed mean; this is a robust statistic in that outliers donot affect it.Data TransformationsIf instead of having a few distinct outliers your data have a strong skew to oneside or the other, you can make your distribution more normal by applying amathematical transformation to all of the scores in your data set. Suppose thatchildren from different economicCAUTIONFor more advanced statistics it is oftenhelpful to be dealing with a normaldistribution. If your distribution containsoutliers, or has a skewness orkurtosis very different from the ND,you may want to either trim your dataor transform your data. However,trimmed data require special robustmethods of data analysis, and statisticalresults on transformed data can bedifficult to interpret.backgrounds are sketching the samecoin from memory and you are measuringthe areas of the circle they aredrawing. The data for five childrencould be 4, 9, 9, 16, and 100 squaredcentimeters. The strong positiveskew of the data can be reduced bytaking the square root of each number;the data would be transformed to2, 3, 3, 4, and 10. In this case you haveswitched from measuring the area ofthe coins to a measure that is propor-