MANE 6313
Week 4, Module H
Student Learning Outcome
Analyze simple comparative experiments and experiments with a single factor.
Module Learning Outcome
Evaluate the Box-Cox Transformation for non-homoskedastic data.
Box-Cox Method
- Power transformation used to stabilize variance
\[
y^*=y^\lambda
\]
- Computational formula
\[
y^{(\lambda)}=\left\{ \begin{array}{cc}\frac{y^\lambda-1}{\lambda\dot{y}^{\lambda-1}} & \lambda\neq 0\\ \dot{y}\ln y & \lambda=0 \end{array}\right.
\]
- Note \(\dot{y}\) is the geometric mean and is computed by using
\[
\dot{y}=\ln^{-1}\left[\frac{\sum\ln y}{n}\right]
\]
Selecting Value of Lambda
- Plot \(\lambda\) versus \(SS_E\left(\lambda\right)\)
- Correspondence between Box-Cox Values and transformations
| lambda | Transformation |
|---|---|
| -2 | \(\frac{1}{x^2}\) |
| -1 | \(\frac{1}{x}\) |
| -0.5 | \(\frac{1}{\sqrt{x}}\) |
| 0 | \(\log(x)\) |
| 1 | \(x\) |
| 2 | \(x^2\) |
Box Cox Transformation
Exact Value of Lambda
Transformed Data
