Solved – Log transformation not making data normal

data transformationdistributionsmixed modelnonparametricregression

I have a data set with positive skewness when I log tranform it tends to be negatively skewed. Is there any other transformation that I can use or any statistical method works?
Thanks!!!

Best Answer

The log is considered part of a whole continuum of power transformations...

Power  result
  -1   1/y
 -.5   1/sqrt(y)
   0   log y
  .5   sqrt(y)
   1   y
   2   y^2

(The $0$ case is confusing because we all know that $y^0=1$. But it works out if you look at the limit of $(y^p-1)/p$ as $p$ approaches zero.)

Anyway, note that $\sqrt y$ corresponds to $p=\frac12$ which is between the identity and the log -- so that might give you pretty good results.

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

Related Solutions

Solved – Interpretation of log transformed negatively skewed dependent variable

Solved – Log-linear transformation

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