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This question already has an answer here:

I'm having a problem with choosing between Pearson and Spearman correlation. I'd like to understand clearly why I should use one or the other. I have read the questions already asked here about this subject, but I am still confused, plsease if someone can help:

The kind of data I'll correlate: I will have an abundance index (of mushrooms) that I'll correlate (test the relationship) with some environmental and biogeographical data, such as: altitude, plant species, soil PH, etc. The aim of doing this is to find positive or negative relationships, to explore if these factors determine the distribution of the mushrooms, and explain how they do this.


I dont know if I should the " Answer option" here, I'm not familiar with the use of the "forum"?. Thank you all for your valuable information and details, I have clearer idea now!

According to the answers if I have ranks so Spearman is most suitable. For plants species, I'll use also an abundance index which i'll correlate with the abundance index of mushrooms. For the other factors(variables) I'll use numerical data PH will vary between (0 and 14), for altitude there will me also " numbers in meter". For some other varibales I might have " ranks" ! so I can use Spearman as it will explore the relationships whatever these are?

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marked as duplicate by gung, John, ttnphns, kjetil b halvorsen, Haitao Du Nov 18 '16 at 16:26

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Pearson's correlation measures linear relationships whereas Spearman's measures any monotone relation. It sounds like you're interested in any relationship whatsoever so Spearman's correlation seems a bit more appropriate. $\endgroup$ – dsaxton Nov 18 '16 at 14:57
  • $\begingroup$ Have a look at this answer: stats.stackexchange.com/a/8073/133561 $\endgroup$ – blazej Nov 18 '16 at 14:59
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    $\begingroup$ i would recommend plotting the data first to get a sense of what type of relationship exists between your abundance index and the other variables. $\endgroup$ – Ashe Nov 18 '16 at 15:01
  • $\begingroup$ Just to add to the options, why not also consider Kendall's tau? $\endgroup$ – mdewey Nov 18 '16 at 15:13
  • $\begingroup$ Can you please enlight me about Kendall test? $\endgroup$ – Souhila Nov 18 '16 at 15:17
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If you have a normal distribution of the abundence index of mushrooms (highly likely with this being biological data) and of your biogeographical data, one would typically use Pearson's correlation coefficient.

However, a lot of situations we may be work with data that either isn't normally distributed, or indeed isn't even continuous but ordinal, for example. Imagine if your data, instead of containing an abundance index rather contained merely the 'rank' of that sample (1 being the most abundant measurement you made, and n being the least abundant). Obviously these values would be uniformly rather than normally distributed. In this situation it would be invalid to use a Pearson, and instead you should use Spearman's.

In a simplistic manner, you can think of Spearman's as asking "does Y go up when X goes up, every time?". If so, the Spearman coefficient is 1. However, it does not tell you about whether y increases by a consistent amount; only if that is true, would Pearson's coefficient also equal 1.

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    $\begingroup$ Normality isn't needed to use Pearson's correlation to estimate the linear relationship. Bivariate normality is only needed to fully describe the association. See: stats.stackexchange.com/questions/3730/… $\endgroup$ – Ashe Nov 18 '16 at 15:00
  • $\begingroup$ Thank you all for your valuable information and details, I have clearer idea now.According to the answers if I have ranks so Spearman is most suitable. For plants species, I'll use also an abundance index which i'll correlate with the abundance index of mushrooms. For the other factors(variables) I'll use numerical data PH will vary between (0 and 14), for altitude there will me also " numbers in meter". For some other varibales I might have " ranks" ! so I can use Spearman as it will explore the relationships whatever these are? $\endgroup$ – Souhila Nov 18 '16 at 15:39
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If your only interest is finding out whether they are positively or negatively correlated then both Spearman and Pearson will point out the direction (assuming the relation is significant).

If you are interested in measuring the dimension of the correlation, then you should check How to choose between Pearson and Spearman correlation? to see which one fits your data better, depending on the relation with altitude and soil. Bear in mind that correlation can be measured in numerical variables. I don't think "plant species" is numerical, if that's the case you shouldn't use neither Spearman nor Pearson.

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