When the degradation of a product is not linear over time, a Box-Cox transformation can make the relationship linear. You can also perform a Box-Cox transformation on your response data when the residuals are not normally distributed or they do not have constant variance. When you transform your data, Minitab transforms the response data and uses it in the analysis. Under most conditions, it is not necessary to correct for nonnormality unless the data are highly skewed. When you use a Box-Cox transformation, all response data must be positive (>0). Check your model carefully before using the Box-Cox transformation.
- Box-Cox Transformation
- Select the lambda value that Minitab uses to transform the data:
- No transformation: Use your original response data.
- Optimal λ: This option is not available if the batch is a random factor. Use the optimal lambda, which should produce the best fitting transformation. Minitab rounds the optimal lambda to 0.5 or the nearest integer.
- λ = 0 (natural log): Use the natural log of your data.
- λ = 0.5 (square root): Use the square root of your data.
- λ: Use a specified value for lambda. Other common transformations are square (λ = 2), inverse square root (λ = – 0.5), and inverse (λ = – 1). Usually, you should not use a value outside the range of -2 and 2.