BoxCox
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 This topic has 4 replies, 5 voices, and was last updated 15 years, 8 months ago by Özkan Kaderli.

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April 7, 2005 at 8:58 am #23678
Hi All,
Can any of you explain to me in plain english how exactly BoxCox transforms nonnormal data to normal data.
Thanks
Troy0April 7, 2005 at 7:30 pm #56624
Jürgen De CockParticipant@JürgenDeCock Include @JürgenDeCock in your post and this person will
be notified via email.Hey Troy,
In simple words the nonnormal 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.
does this answer your question?
Jürgen0April 7, 2005 at 8:31 pm #56627
Stefan SzemkusParticipant@stefan Include @stefan in your post and this person will
be notified via email.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 bimodal and the min. value is at least half of the max. value.
Stefan0May 3, 2006 at 8:13 am #56981
Alpaslan TerekliParticipant@AlpaslanTerekli Include @AlpaslanTerekli in your post and this person will
be notified via email.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
hope helpfull.
Alpaslan
0May 24, 2006 at 9:08 am #56993
Özkan KaderliParticipant@ÖzkanKaderli Include @ÖzkanKaderli in your post and this person will
be notified via email.In Boxcox transformation;
Lambda (l) Transformationl= 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.0 
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