# Box-Cox

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• #23678

Allegood
Member

Hi All,
Can any of you explain to me in plain english how exactly Box-Cox transforms non-normal data to normal data.
Thanks
Troy

0
#56624

Jürgen De Cock
Participant

Hey Troy,
In simple words the non-normal data is transformed by a simple mathematic calculation (SQRT, *1/2, multiplied by itselves,…)
In practise a lot of data does not get more normal by doing this, but sometimes it works.  1 important thing if it works then do not forget to transform also the specifications etc.
Jürgen

0
#56627

Stefan Szemkus
Participant

Hey there,
basically what you do with box cox transformation is to raise your data by the power of lambda. including the specs. Minitab tries lambdas between -5 and + 5 (for example if lambda is -1 its like data*1/x or if lambda is 1/2 it is the sqrt from your data) to find a minimum standard devia´tion. The lambda that leads to minimum std dev. is choosen.
This only works if the data is not bi-modal and the min. value is at least half of the max. value.
Stefan

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#56981

Alpaslan Terekli
Participant

Box -Cox transformation as known power transformation. When you have a distribution shape leaning one side power transformation is helping to convert shape as normal curve.
x                            x
x         x                x                            x                                      x
1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
sqrt data will be:
x  x
x  x  x  x  x
1  2  3  4  5  6  7
You can find the formulas in following table:

l

Yl

-2

1/Y2

-1

1/Y

-0,5

1/ Ö Y

0

Log(Y)

0,5

Ö Y

1

No Tranformation

2

Y2
Alpaslan

0
#56993

Participant

In Box-cox transformation;
Lambda (l)       Transformation

l= 2 =>                                  Y’ = Y2
= 0.5  =>                              Y’ =  Y1/2
= 0     =>                              Y’ = ln Y
= – 0.5  =>                            Y’ = 1 / (Y1/2)
= – 1 =>                                Y’ = 1 / Y
The response is transformed with different levels of l and so are the limits. The results with least std deviation are preferred, then further assumptions can be made as Cpk, ppm levels by using the appropriate lambda level.

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