Correlation

I have river flow rates for two separate rivers.

The data produced this scatter graph for both rivers

https://i.imgur.com/jVnWF3t.png

What is the best type of correlation to use here?

Spearman, Pearson or Kendall?

Why?

Thank you.

I have river flow rates for two separate rivers.

The data produced this scatter graph for both rivers

https://i.imgur.com/jVnWF3t.png

What is the best type of correlation to use here?

Spearman, Pearson or Kendall?

Why?

Thank you.

Reasonable summary of the assumptions, pros & cons at
http://www.statisticssolutions.com/wp-content/uploads/wp-post-to-pdf-enhanced-cache/1/correlation-pearson-kendall-spearman.pdf
What do you think? Is the data normally distributed data etc?

I would be inclined to apply a transform to both variables before attempting any correlation analysis. What are the two variable measuring?

Looking at the graph, I would suggest Pearson's because the data appears to be normaly distributed. Also, no ranking is required, so Spearman and Kendall unsuitable. Would you agree?

Nope. "The data appear to be normally distributed" is meaningless; you should be looking at the distribution of each variable separately, then considering whether each needs some sort of transform (log, perhaps, or square root) that makes the distributions more nearly approximate normal. If this doesn't work, consider a non-parametric approach.

What he said.

I'm not sure whether the OP is answering a book question or trying to do some actual analysis, but the data is certainly not normally distributed.

Nope. "The data appear to be normally distributed" is meaningless; you should be looking at the distribution of each variable separately, then considering whether each needs some sort of transform (log, perhaps, or square root) that makes the distributions more nearly approximate normal. If this doesn't work, consider a non-parametric approach.

How can you tell that by the graph?

Yes I'm trying to do data analysis.

Which correlation is most suitable, Pearson, Spearman or Kendall?

How can you tell that by the graph?

Transform should not be necessary for my task.

That's a very strange thing to say; why do you think a transform "should not" be necessary? If you are doing real-world data analysis, you should be applying standard techniques to your data!

We were not taught this.

They said one of three correlation methods is fine.

But I don't know which one in this situation, Spearman or Kendall?

Ah, so this is an exercise in data analysis that you're doing is it? Have you been told anything about what the data means?

The individual variables are not normally distributed, so you have a choice: either (a) transform the variables so that they do become approximately normal (which would be the standard approach with data that looks like the stufff you have) and then apply the Pearson correlation coefficient or (b) use a rank correlation method, using the scale they're measured on to give you ranks.

If (b) you have a choice again of which rank correlation. Time to look at their applicability. Looking at your plot, which one of these do you think best applies here?

It depends on if you consider those data points in the top right outliers, or not.

An outlier is basically a data point that is very unlikely to be consistent with the probability model that you're using. So for variables like the ones you have, you'd be looking for a point (or two or three) that are well separated from the rest. So here? Nope, not outliers.

So, Spearmans would be best choice?