Minitab Box-Cox Calculated Lambda Value (Why calculated different?)


I have faced an issue about calculating the Lambda value of a given dataset. I used Minitab's (v. 19) Box-Cox Transformation and I got a Lambda value. I calculated the Lambda by following the calculation steps prescribed by Cole (1990) (see below) and I had a different Lambda value.

What I want to ask is, how does Minitab calculate the Lambda for Box-Cox Transformation? And is the formula that Minitab uses different from Cole's method?

Why are the two results different? Excel calculations give L=0,4622 but Minitab returns L=0,57.

You may find the screenshots depicting the calculations attached (sample values are used).

Thanks for any help, in advance.



Well-Known Member
This is how I read it. Finding lambda is essentially trial and error. You have some index of normality and you try various values until you find the one that gives you the most normal distribution according to that index. Minitab does that search by zeroing in on the best value (by systematic trial and error). That is what the graph indicates. This will be the one that gives the closest to normality measured by your index.
This is is a very time consuming thing to do by hand. It looks like Cole has devised a cunning plan to estimate lambda by hand without the hard work. But it is only an estimate of the best value. The graph is very flat at the bottom and there is no real practical difference between the two values. My guess is that both will work, but Minitab is technically more accurate.