You will transfer them only to make them little smooth, but the formula for correlation will be the same. You can try online calculations also. https://www.easycalculation.com/statistics/correlation.php

Hi Ghose,

After you have log transformed the data to make it normally distributed, you can apply the normal correlation to check the relationship.

You can try a spearman rank correlation coefficient, which transforms data to ranks prior to correlation

You can use Sigmaplot to carry out co-relation tests. Either Pearson or Spearman.

I think Spearman rank co-relation is better suited for your data

Several other data transformation methods exist to achieve normality. You can try them also.

For example, arch-sin, box-cox transformation, rescaling, standard deviation-1 etc. etc.

Once data transformation is done, you should check whether it is fulfilling the criterion of normality by running normality test(s) like Shapiro-Wilk test, Anderson-darling test etc. etc.

If data is normalized, you can apply whatever correlation you want. If it doesn't, then you need to remove the values which are outlier after running an outlier test. 

If you dont want to remove data or cannot justify its removal, you can use non-parametric tests like Spearman's rank-order correlation or Kendall's Tau correlation, which are much less sensitive to outliers.

Also, your data should meet the assumption of homogeneity of variance (or Homoscedasticity). You can run Leven's test to check for this.

The main issue in the analysis of the correlations is not the lack of normality (skewness, asymmetry, ...) it is related to the variability of the residuals that are not explained by the (linear or non-linear) model.

However, the lack of normality is not the main issue, the heterogeneity is not only an assumption, it must be explained (if exists) because it is of main importance (if exists).

Then, if a transformation "smooth" the skewness, you must explain the origin of the skewness, and to propose a model to explain the relationship between independent and dependent variables, and, analyse the residual of the model. Finally, you can explain the behaviour of the correlation.

Therefore, the analysis of a correlation between two variables, must be explained from all those perspectives, not only the coefficient of correlation and some p-values.

You can easily analyse the correlation between two variables by utilizing the software (GraphPad Prism).