transforming variables with pronounced celing effect

[Jean Hanson]

Dear Listers,

I have tried transforming some variables with prounounced celing effects using a variety of transformations in SPSS. I am unable to get anything near a normal distribution. Does anyone have a suggestion?

 

Thank you,

Jean Hanson

[Maguin, Eugene]

Jean,

If your data were on a 1-5 scale, you have large or very large proportions
of '4's and '5's. I think others will agree with me but there is nothing you
can do to make the distribution normal-shaped. You can do transformations to
reduce skew by either pulling the left-hand tail toward the top response
value or pulling the top response value toward the lower response value. An
example of the latter is a fractional power transformation, e.g. square or
cube or fourth power root. Others probably will have different and better
transformations to recommend. I believe that Tukey publised either an
article or book about data transformations.

So, you have to change, or at least reconsider, your statistical model
choice. Maybe a coarse (e.g., two or three categories) categorization
followed by logistic or ordinal regression instead of normal distribution
regression.

Gene Maguin

>>I have tried transforming some variables with prounounced celing effects
using a variety of transformations in SPSS. I am unable to get anything near
a normal distribution. Does anyone have a suggestion?



Thank you,

Jean Hanson

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[Richard Ristow]

At 03:06 PM 3/31/2009, Jean Hanson wrote:

>I have tried transforming some variables with pronounced ceiling
>effects using a variety of transformations in SPSS. I am unable to
>get anything near a normal distribution. Does anyone have a suggestion?

One suggestion is, don't do it.

First, very few statistical procedures assume normal distribution of
the variables. Generally, the linear procedures (ANOVA, regression,
Pearson correlation) assume normal distribution of the error term,
the variance that can't be explained by the model; but even they are
fairly robust against normality violations.

Second, when you transform a variable (or don't), you make a decision
about where, in its measurement range, variation is most meaningful.
If you make a transformation, you then have to argue that a unit
change in the transformed variable is about equally meaningful
anywhere in the range.

Gene Maguin mentioned Tukey. Tukey strongly opposed transforming
variables to make their distributions roughly normal, or otherwise
'pretty'. He'd argue, roughly, that if the scaling mattered so little
that such transformations were proper, you don't really have a scale
variable at all. Recognizing that this is often the case, Tukey
recommended nonparametric methods unless a scale-level interpretation
could be explicitly justified.

In your case, the next step would be to think about the variable's
meaning: what, in the real world, makes most of the distribution
cluster toward one end of the range? How do you assess the relative
importance of a unit change within that cluster, and a unit change
farther out in the distribution's 'tail'?

And, seriously consider an ordinal analysis method.

-Best success to you,
  Richard

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