## Box-Cox lamba and exponentiation

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kiwiana
Posts: 9
Joined: Mon Dec 24, 2007 4:15 am
Location: South Korea

### Box-Cox lamba and exponentiation

Hi Forum,

My variable, 'NetUse, is heavily positively skewed (N=491).

Therefore, I am attempting to apply the Box-Cox transformation to 'normalise' the data.

I'm a newbie so I have had trouble understanding and using the syntax recommended to estimate lambda in SPSS:

http://pareonline.net/pdf/v15n12.pdf (pages 8-9).

So, I went the easier route and used the online statistical tool to estimate Lambda instead:

http://www.wessa.net/rwasp_boxcoxnorm.wasp

After anchoring the variable at one, this provided an estimation of Lambda of -0.18.

I then tried to use this Lambda value (the exponent, -0.18) to transform my dataset in SPSS.

In SPSS I went to: Transform-->Compute variable-->
And, used the following numeric expression:

NetUse **-0.18

However, the output (NetUseNORMAL) seemed to provide inverse values from what I had. I.e., the cases with low NetUse had high NetUseNORMAL.

I'm no mathematician, but I'm assuming the negative fractional logarithm has some type of inverse relationship on the data.

Do I need to do some type of reversing or mirroring to correct the problem?

If so, how do I go about it?

Regards,

Matthew (M. Ed)
kiwiana
Posts: 9
Joined: Mon Dec 24, 2007 4:15 am
Location: South Korea

### Re: Box-Cox lamba and exponentiation

I found the answer for those who may be interested.

Osborne (2010) explains that the raw variable needs to be reflected prior to running the negative fractional exponent:

Inverse transformation. To take the inverse of a
number (x) is to compute 1/x. What this does is
essentially make very small numbers (e.g., 0.00001) very
large, and very large numbers very small, thus reversing
the order of your scores (this is also technically a class of
transformations, as inverse square root and inverse of
other powers are all discussed in the literature).
Therefore one must be careful to reflect, or reverse the
distribution prior to (or after) applying an inverse
transformation. To reflect, one multiplies a variable by
-1, and then adds a constant to the distribution to bring
the minimum value back above 1.00 (again, as numbers
between 0.00 and 1.00 have different effects from this
transformation than those at 1.00 and above, the
recommendation is to anchor at 1.00).

See link to his article: http://pareonline.net/pdf/v15n12.pdf