# How one can improve correlation (higher rho values) on non normal distributions?

No matter what class or book I see, the normal distribution is always advocated. I have been trying to find ways to assess relationship between variables for non normal distributions, most of which are exponential. Is there any other method other than spearman correlation to deal with such things?

• Your emphasis on wanting "higher rho values" is troubling... Commented Nov 6, 2012 at 23:12
• Jonathan, why? I can edit the question if necessary. Commented Nov 6, 2012 at 23:34
• It sounds like you're looking at two variables where there might really not be a relationship but trying to discover a relationship anyway. This way lies madness and papers which turn out not to be replicable. Commented Nov 7, 2012 at 0:38
• Thanks for double checking my concerns Jonathan. Appreciated feedback :-) I guess the question is better translated then as alternatives techniques to check on the data like Peter Flom said. I think in the long run its all about reducing noise in the data since intuitively things are supposed to be correlated. Great feedback :-) Commented Nov 7, 2012 at 1:44

There are many ways to assess the relationship between two numerical variables: Loess and various other smoothers, scatterplots, lattice plots, qq plots, just off the top of my head.

If you want a single number summary, then you have to deal with the limitations of single numbers. But you can transform the variables in various ways, as wel..

• Hi Peter, thank you. I have bene using scatterplots and qq plots but I am trying to find resources to learn how to interpret them. Summaries are good because it is easier for someone to infer their meaning. Do you know any book or article that discuss more about these different methods for non-parametric association? Commented Nov 6, 2012 at 23:16
• William S. Cleveland wrote two books on statistical graphics, both of which discuss a wide variety of plots. Splines are discussed a bit in Frank Harrell's book Regression Modeling Strategies. Commented Nov 6, 2012 at 23:19
• Thank you Peter Flom. My last question in this matter which is actually the main question: These references discuss alternative ways for non-parametric hypothesis test for statistical dependence. But do you think it makes sense to seek for higher correlation values, or I can just hope to obtain higher values by chance using different methods to observe this? I would also appreciate any reference for these transformations that you have mentioned that are focused on improving correlation. Thank you very much! Commented Nov 6, 2012 at 23:23
• You shouldn't transform in order to get better correlations, you should transform so that there are fewer outliers and so on. If your goal is a statistical test, then I would go with Spearman, unless there is non-linearity. Commented Nov 7, 2012 at 0:00
• Peter, I thought Spearman would account for non-linearity too? What would you suggest then? Thanks. Commented Nov 7, 2012 at 0:11

Why are you not satisfied with the Spearman's rank correlation?

The "ordinary" correlation is typcially the Pearson product-moment correlation coefficient. It is only suitable for data that have a linear relationship and do not have any outliers.

For data that do not exhibit a linear relationship, or may contain outliers, you can use the Rank Correlation, such as the Spearman's correlation or the Kendall's τ. This does not need a normal distribution. You can find out more about those in the different Wikipedia articles.

• Hi gerrit, thank you for your fast reply. In my current situation I am experiencing rho values that are not too high. I understand that perhaps that is the way the variables are but since I do not have much background in statistics, I was hoping that someone could tell me if there are alternative ways. I wondered if no one ever asked themselves if there is a way to reorganize or transform the data to see higher association. Does this makes sense? I dont mind explain further. Commented Nov 6, 2012 at 23:14
• Well, the Spearman's correlation is an alternative way, as is Kendall's τ. And it will improve the correlation value when the relation is not linear (normality is not related to the problem). So I'm not sure what you're asking otherwise. P.S. I'm also just learning. Commented Nov 6, 2012 at 23:16
• I think from your reference link, non-parametric hypothesis test for statistical dependence is what characterizes my question. I am looking for alternative methods to assess this but hoping for higher rho values. Commented Nov 6, 2012 at 23:21
• Ah, well, reading about those is actually my homework for Thursday \o/. Commented Nov 6, 2012 at 23:27
• Mind giving me references for your homework then? Commented Nov 6, 2012 at 23:31