Among air pollution paper I read recently, it seems to me that Spearman correlation is used more often to test the correlation between air pollutants, PM2.5 constituents, and meteorological factors. However, I have following concerns about this choice:
1) As air pollutants are often continuous variable, shouldn't Pearson correlation be preferred?
2) If Pearson is not preferred, why?
2) Doesn't Spearman correlation often give more conservative results?
I am not a big specialist in statistics, but try to answer:
1. No, Spearman CC is ok for continuous variables.
2. Because your variables could have another distribution type, but not normal. Spearman is good option, if you do not know, which type of probability distribution do you have. In ecology it is typical situation.
3. One would have more reliable, more robust (to outliers for example) results using Spearman CC, I would say.
Dear Yi Lu
Pearson's correlation coefficient is when you have a parametric distribution, outliers is not a problem and you have linearity. In other words if the population covariance or standard deviation is not known or the distribution is heavily non-gaussian, or non-linearities expected you have to use Spearman's correlation coefficient. The Spearmann correlates the rank of the values rather than by using product of moments as Pearson's(see wikipedia or google).
For example, if the logarithm of PM2.5 is taken, or with ozone, temperature, the distribution is often closer to gaussian , and if there is linear correlation and no outliers, then the Pearson's correlation is fine. However for other combination (precipitation and pollutants) , non-linear and possible outliers the Spearman's is likely better. I would compute both Pearson's and Spearman's and try to explain if there are big differences between the two. Always better to do a scatter plot to evaluate linearity and monotonicity before deciding.
Here is a guide to when use Spearman's and when to use Pearson:
form https://statistics.laerd.com/statistical-guides/spearmans-rank-order-correlation-statistical-guide.php
"A monotonic relationship is not strictly an assumption of Spearman's correlation. That is, you can run a Spearman's correlation on a non-monotonic relationship to determine if there is a monotonic component to the association. However, you would normally pick a measure of association, such as Spearman's correlation, that fits the pattern of the observed data. That is, if a scatterplot shows that the relationship between your two variables looks monotonic you would run a Spearman's correlation because this will then measure the strength and direction of this monotonic relationship. On the other hand if, for example, the relationship appears linear (assessed via scatterplot) you would run a Pearson's correlation because this will measure the strength and direction of any linear relationship. You will not always be able to visually check whether you have a monotonic relationship, so in this case, you might run a Spearman's correlation anyway."
check also wikipedia
https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient
Cheers
Dear Yi Lu
Pearson correlation used for continuous variables and normally distributed data, and Spearman correlation used for an ordinal data or non-normally distributed data.
Good Luck
Hello everyone,
Thank you for your suggestions and I really learned a lot for all of your answers. As suggested, I ran both Pearson and Spearman correlation to compare the results. Overall the results are very similar from the 19 variables I ran correlation. Also, Spearman is not always more conservative based on this result since Pearson sometimes report strong correlation when it's not in the Spearman. Maybe related to the shape of relationship?
Is Spearman rank correlation a weaker test than Pearson for ratio measurement scale?
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