Statistics for the Social Sciences A General Linear Model Approach

Chapter 5 teaches how data analysts can change the scale of a distribution by performing a linear transformation, which is the process of adding, subtracting, multiplying, or dividing the data by a constant. Adding and subtracting a constant will change the mean of a variable, but not its standard deviation or variance. Multiplying and dividing by a constant will change the mean, the standard deviation, and the variance of a dataset. A table shows students shows how linear transformations change the values of models of central tendency and variability. One special linear transformation is the z-score. All z-score values have a mean of 0 and a standard deviation of 1. Putting datasets on a common scale permits comparisons across different units. But linear transformations, like the z-score transformation, force the data to have the desired mean and standard deviation. Yet, they do not change the shape of the distribution – only its scale. Indeed, all scales are arbitrary, and scientists can use linear transformations to give their data any mean and standard deviation they choose.