Survey data: association between two non-normally distributed variables — what metric to use

Question

I am looking at survey data that measures satisfaction with provided services . I am interested in exploring the relationship between the time the product is used (measured in days, ranging from 10 to 3000) and satisfaction.

The data:

• ~ 1k responses
• "Satisfaction" has two peaks around 2 and 7
• "Time used" is peaking around 800 ( long right tail)
• Due to the nature of the product, there is no reason to assume that users, who use it for a long time are satisfied with it( = There is no reason to expect that if a user unsatisfied (s)he stops using it)

Questions:

1. What would be an appropriate metric to measure the degree of association between two variables?
2. What could "go wrong"? ( what should I check before using a metric, what are the assumptions that the metric implies)

It looks like Pearson's and Spearman's correlations are both good candidates to start with, although there are several things that concern me

1. Is that an issue that one of the variables is discrete and the other one is (sort of) continuous? (looks like it is not ?)
2. Is that okay to have a bimodal distribution (satisfaction)?
3. I keep seeing somesources saying that pearson's correlation assumes normal distribution, while other sources saying it is okay to have non-normal distributions. What is the source of this confusion? what am I missing?

I would appreciate any comments/suggestions. Thanks.

Answer 1

I did some additional research and clearly Spearman has to be used in my case.

The Spearman correlation coefficient is a good replacement of the Pearson correlation, if one of the following conditions applies to your variable.

1. They're not numerical, but one or both of the variables are ordinal.
2. They are not linearly related, they contain one or more outliers,
3. they don't follow a bivariate normal distribution, or you cannot check this distribution, due to lack of data.

This is a quote from a Coursera class that can be found here. I found it very helpful.