1. Psychology 202b Advanced Psychological Statistics, II February 17, 2011

2. Overview The Box-Cox procedure for selecting an optimal transformation. Sequential regression: –Conceptual discussion –Efficient execution

3. Maximum likelihood estimation A simple example with the mean (in R). A somewhat more complex example with regression (in R). Selecting the optimal transformation to normality by maximum likelihood: the Box- Cox method.

4. The Box-Cox family of transformations The transformations we have considered fit a family of power transformations: t(Y) = Y. When =1/2, the transformation is the square root. When =0, the transformation is the natural log. When = -1, the transformation is the reciprocal.

5. The Box-Cox method The Box-Cox method uses maximum likelihood to estimate the value of that will produce the distribution of residuals that is as close as possible to Normal. Often the same transformation will improve other assumptions as well.

6. The Box-Cox Method

7. The Box-Cox method Illustration in R.