# Correlation coefficient for use with nonlinear finite sets

I need to find the correlation between two data sets that are nonlinear and only have values between 0 and 10. Both sets contained the same number of values.

I've tried using Pearson's R and introducing some linearity by adding n+10 to each data point. That however introduces strong correlation where there really shouldn't be any.

I'm completely new to statistics, so here is a layman's explanation of what I'm trying to achieve.

I have a questionnaire that asks customers for an overall score between 0-10. I then ask several more specific questions for things like Price, Service, etc. These questions are also 0-10.

I want to find the degree of correlation between the overall score and the scores for the specific questions. For example, if customers that give a high score for Price also give a high overall score, then I can see that Price is important to the customer. Whereas if their scores for Service do not closely match the overall score, then the quality of Service is not as important to the customer.

A perfect correlation in my data would look like this:

Price: 10, 10, 10, 10

Overall score: 10, 10, 10, 10

Could someone suggest a suitable coefficient to achieve this?

Cheers

• What is a response supposed to represent? E.g., when a customer gives a 10 to price, does that mean they like the price they paid or that they think price is very important in their buying decision? The interpretation should play some role in your choice of assessing associations when the purpose is to determine "importance" to the customer.
– whuber
Commented Feb 29, 2012 at 20:36
• Its that they liked the price they paid. The important of price on their overall satisfaction is actually want I want to calculate, but I don't want to have to directly ask that. Commented Feb 29, 2012 at 22:03
• Does a Distance correlation (en.wikipedia.org/wiki/Distance_correlation) sound like what I may need? I need sets of identical values to return a perfect correlation, and sets of values at the opposing ends of the 0-10 scale, i.e x: 0,0,0 and y: 10,10,10 to return a perfect negative correlation, -1?. I guess two sets of values with a random distance between each point should return low correlation, i.e 0? I apologise for my complete lack of statistical knowledge, it is no doubt making it much more tricky to understand what I'm after :) Commented Feb 29, 2012 at 22:14

For all three of those sets of data, any measure of association will give a reading of 0, because, in each of those three, there is no variation in either X or Y. Measures of association, generally, answer questions like "If X goes up, how much does Y go up?" but in your sets, X doesn't change, so the question is meaningless.

Further, it isn't clear what you mean by a data set that isn't linear.

Perhaps if you described your actual problem in everyday language, someone here could suggest something.

• Thanks, Peter. I have updated my question with a simple explanation. Commented Feb 29, 2012 at 14:51
• I think you may have misinterpreted the (first version of this) question, Peter, because there are plenty of measures of association that will do what the OP is asking for.
– whuber
Commented Feb 29, 2012 at 16:18
• @whuber Maybe I am still confused! If a variable doesn't vary, how can it be associated with anything? Commented Mar 1, 2012 at 0:48
• Because not all association has to be related to variation. The intuition expressed by the O.P. is that when $X$ and $Y$ are both consistently at the high end of established ranges, they are associated. In this sense, even when there's no variation within $X$ or $Y$, one could say they are simultaneously high. It is potentially confusing to call this "correlation," which it's not, but it sounds like a valid concept to me.
– whuber
Commented Mar 1, 2012 at 1:52