How to calculate Lambda?

Hi everybody,

I want to calculate Z value of a one-variable dataset by using LMS method and I will use the formula attached as a jpeg. I can't figure out how to calculate the Lambda value in the formula.

Can anyone please help with how to calculate Lambda value for a one-variable dataset? (I mean, I have about 500 height data of a sort of people and I want to get the Lambda value for the height variable.)

Any help and/or source suggest is welcome!



Well-Known Member
I don't have either of those, but this is on
"Go to Transform – Prepare Data for Modelling <select> Automatic from the drop down list. In the Fields tab you can specify which variables to transform by moving them to the Inputs box. In the Settings tab click on Rescale Fields. Tick the box before ‘Rescale a continuous target with a Box-Cox transformation to reduce skew’. Click Run. This will create a new column with the transformed variable."
It may work for you.
Thank you for your help. I applied the recommended procedure and I got a new variable but what I want is a single Lambda value for the height variable and the value is something like 0.17 or so.

In Youtube, I got this video and it needs two variables to get the Lambda value but I have only one variable.

I could not find any source to learn how to calculate it. Googling "how to calculate lambda" turns many irrelevant results. I think I am missing a major point!


Well-Known Member
Probably a different lambda.
I don't know what you mean by the "height variable". Your formula looks very like the Box-Cox formula (which changes the data to normal) and then standardizes things. Lambda is a power.
If it is a variant of Box-Cox, there is no formula for lambda. Essentially you need to try out various values and see which result is most normal. Many programs do this searching for you. Perhaps the SPSS printout included the value of lambda.
When you next google lambda, try including the words Box-Cox.
I have a data set of about 500 measured body height values of the school children. I want to create a percentile chart. I can do this by using Z values for the critical percentages, such as 1.65 for 90% and 1.96 for 95%, etc. But as far as I read, a transformation of a Z score may be suitable if the distribution of the dataset is slightly different than the perfect distribution (but it's still in normal ranges for skewness and kurtosis). The Z value, then, is calculated by using the LMS (Lambda, Sigma, Mu) formula. What I want to understand is how to get the Lambda value from my dataset to use it in the formula.

Hope I am able to explain what I need.

By the way, thank you for your efforts and contribution.


Well-Known Member
1575929109310.png When you did the SPSS Box-Cox did you get a window like this? If you did then the value of lambda is in the small window.