I am applying logs to two very skewed variables and then doing the correlation.

Before logs the correlation is 0.49 and after logs it is 0.9. I thought the logs only change the scale. How is this possible?

Here below the graphs for each of them. Perhaps I haven’t applied the right transformation?

**Answer**

There are multiple different types of correlation. The most common one is Pearson’s correlation coefficient, which measures the amount of *linear* dependence between two vectors. That is, it essentially lays a straight line through the scatterplot and calculates its slope. This will of course change if you take logs!

If you are interested in a measure of correlation that is invariant under monotone transformations like the logarithm, use Kendall’s rank correlation or Spearman’s rank correlation. These only work on *ranks*, which do not change under monotone transformations.

Here is an example – note how the Pearson correlation changes after logging, while the Kendall and the Spearman ones don’t:

```
> set.seed(1)
> foo <- exp(rnorm(100))
> bar <- exp(rnorm(100))
>
> cor(foo,bar,method="pearson")
[1] -0.08337386
> cor(log(foo),log(bar),method="pearson")
[1] -0.0009943199
>
> cor(foo,bar,method="kendall")
[1] 0.02707071
> cor(log(foo),log(bar),method="kendall")
[1] 0.02707071
>
> cor(foo,bar,method="spearman")
[1] 0.03871587
> cor(log(foo),log(bar),method="spearman")
[1] 0.03871587
```

The following earlier question discusses Kendall’s and Spearman’s correlation: Kendall Tau or Spearman’s rho?

**Attribution***Source : Link , Question Author : DroppingOff , Answer Author : Stephan Kolassa*