Solved – Transformations not correcting significant skews

data transformation

I am running an experiment which measured using Likert Scales and I have 6 variables out of 24 which either have significant skewness or kurtosis. These are mixed with some positive and some negative values.

I transformed my data using log transformations, Square root transformations, reciprocal transformations and reverse score transformations, but this did not solve the problem.
In fact, all this did was give me a greater number of significantly skewed variables (for example square root transformations left me with 11 variables significantly skewed or suffering from kurtosis).

Is there any other type of data transformations that anyone can recommend that may help, especially when some skews are positive and others are negative? If so, does anyone know the SPSS syntax involved?

Best Answer

A few points

If your variables are individual Likert items on (say) a 7 point scale, then it is arguable whether they should be treated as continuous at all.
This sounds like you are using these variables as independent variables. If so, why do you want them to be normally distributed?
It also sounds like you applied all the transformations willy-nilly to all the variables. This is not right. Positive skew can be corrected (at least sometimes) by logs. Negative skew would be made worse; negative skew could be dealt with (perhaps) by squaring or reciprocal. But, again, applying these transformations to a Likert scale makes relatively little sense, usually.

Related Solutions

Solved – Interpretation of log transformed negatively skewed dependent variable

Your original x and your transformed x are inversely related, so, naturally, any relationship that is positive on one will be negative on the other. One way to see this inverse relationship is

x <- rnorm(100)
x2 <- log(1 + max(x) - x)
plot(x, x2)

(I used a normally distributed X here, but it does not matter for these purposes; you could substitute your variable and its transformation).

Further explanation after reading one of @Beka 's comments above.

x2 is a transformed version of x, using the transformation you used. Then I plotted x vs. x2. When x goes up, x2 goes down. So, any relationship between x and some other variable will be reversed between x2 and that variable.

In other words, your findings do not contradict earlier work.

Solved – Log-linear transformation

1) OLS regression assumes that the residuals are normally distributed, not that the variables are.

2) Skew of 0.7 is pretty minor

3) The idea of "adding 1" to take the log has problems. Why 1? Why not .1? Or .01? Or, for that matter, 100? These would give different results, perhaps substantially so.

4) Often, transformation isn't the right solution to such problems. You could try robust regression, for instance.

Finally, why don't you tell us more about the details of your problem so that we can help more? What are your DV and IVs? What is your N? What are your hypotheses? What are you trying to find out?

Best Answer

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Solved – Interpretation of log transformed negatively skewed dependent variable

Solved – Log-linear transformation

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