# Tag Info

### Is it meaningful to calculate Pearson or Spearman correlation between two Boolean vectors?

I would not advise to use Pearson's correlation coefficient for binary data, see the following counter-example: ...
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### What is the distribution of sample correlation coefficients between two uncorrelated normal variables?

As a general remark, your questions are usually very clear and well illustrated, but often tend to go too much into explaining your subject matter ("Q methodology" or whatever it is), ...

### Correlations - Pearson and Spearman

Pearson correlation depends on the values of the data; Spearman correlation depends only on their (marginal) ranks. Thus, the former is (far) more sensitive to outlying data. What kind of outlying ...

### Pearson or Spearman?

Neither correlation coefficient presupposes normality. Marginal or bivariate normality is completely irrelevant to the choice between them. They do differ in the questions they ask of the data. ...

### How to calculate a confidence interval for Spearman's rank correlation?

Maybe some additional remarks about the comment of @chl The Spearman correlation can be seen as a Pearson correlation of the ranks. Ranks clearly do not follow a normal distribution, with the ...

### Is it meaningful to calculate Pearson or Spearman correlation between two Boolean vectors?

Arne's response above isn't quite right. Correlation is a measure of dependence between variables. The samples A and B are both independent draws, although they are from the same distribution, so we ...

### Correlations between continuous and categorical (nominal) variables

I'm having the same issue now. I didn't see anyone reference this just yet, but I'm researching the Point-Biserial Correlation which is built off the Pearson correlation coefficient. It is mean for a ...
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### Minimum sample size for Spearman's correlation and Kendall's Tau b

For the purposes of a hypothesis test, there are two related approaches to finding an optimal sample size that are viable if you're willing to assume bivariate normality. Power To estimate minimal ...
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### Calculate Spearman and Pearson correlation on variables of different units

Pearson correlation, $\rho_{XY}$, divides through by the product of the units and results in a unitless measure. $$\rho_{XY}=\dfrac{ \text{cov}\left(X,Y\right) }{ \sigma_X\sigma_Y }$$ The covariance ...

### Spearman $\rho$ as a function of Pearson $r$

I think I found the answer. In Pearson's "On further methods of determining correlation" (1907) he derives the expression: $$r=2 \sin \Big(\frac{\pi}{6}\rho\Big),$$ which implies,  \rho= \frac{6}{\...

Pearson's correlation coefficient ($\boldsymbol{r}$) provides a measure of linear association between paired variables. Spearman's correlation coefficient ($\boldsymbol{r_{\bf{S}}}$) provides a ...
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### Does Spearman's $r = 0.38$ indicate agreement?

Correlations, such as Pearson's product moment correlation or Spearman's rank correlation, are not measures of agreement, no matter what their values are (i.e., even if $r = 1.0$). Consider a ...
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### What is the explanation for having a Pearson's correlation coefficient significantly larger than the Spearman's rank correlation coefficient?

This is a simple dataset, where the points come alternating from two linear functions: The pearson correlation detects, there is a general upwards motion in the combined data (red an black together) ...
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### Spearman's rank correlation coefficient

What does each measure? Pearson's correlation coefficient is measure of the strength of a linear relationship between x and y. It is swayed by outliers much like a mean and standard deviation. ...

### Why Spearman's rank correlation ranges from from -1 to 1

See Wikipedia for the definition. Note that Spearman correlation is just the usual Pearson correlation, but calculated using the ranks of the data, not the data itself. So the reason it is always in ...
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### Is Spearman correlation never greater than Pearson correlation?

Simple example in which Spearman correlation is greater than Pearson correlation: x = 1:10; y = x^2 cor(x,y, meth = "p")  0.9745586 cor(x,y, meth = "s")  1

### How much can the Pearson and Spearman correlation coefficients differ in a dataset? (edited)

Sure. We can achieve this result by adding a single extreme data point to an otherwise uncorrelated, and nonmonotonically related, set of data: ...
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### Does zero Spearman's rho imply zero Covariance?

Counterexample: X Y 1 500 2 1 3 2 4 3 5 4 For these values, Pearson's $r \approx -0.70$ Spearman's $\rho = 0$ That single large Y value affects the covariance ...
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### Interpreting the results of different correlation methods

Correlation is not a binary yes/no property, but a continuous feature that can be weak or strong, which is indicated by the value of the correlation coefficient. Testing for "statistical ...
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### Correlation between a continous and integer variable

Although your emotional rating data are coded as integers, are you sure that a difference between scores of 1 and 2 means the same as a difference between scores of 8 and 9 (etc.)? If not, what you ...

### Correlations - Pearson and Spearman

I know that Pearson correlation is sensitive to outliers, unlike Spearman correlation. There is a more striking difference between the two: Pearson assumes a linear relationship between the data, ...
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### What does it mean if the Pearson's correlation is significant but Spearman is not?

To stir the pot a little I suggest that it primarily means that one too many correlation coefficients was estimated. It is better to choose a measure based on statistical principles and stick with it....
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### What can spearman's rank do that regression can't?

Regression can't do everything rank correlation does. If you are talking about simple linear regression on the raw data then Regression makes assumptions that Spearman's does not. Regression results ...

### Calculate Spearman and Pearson correlation on variables of different units

Dave is already correct in his answer. The formula for the correlation is a unitless measure. Here I use R for illustration. If you scale your x and y values and run a correlation on them: ...

As @Harvey Motulsky said, software will handle the ranking. But you will probably get the same results even if you rank the variables yourself first. Here is an example using ...

I think a couple valuable journal articles on this subject are de Winter et al., 2016 and Bishara & Hittner, 2015. I highlight the main points of both below, focusing primarily on Pearson and ...

### Pearson's or Spearman's correlation with non-normal data

I think these figures (of Gross-Error Sensitivity and Asymptotic Variance) and quotation from the below paper will make it a bit clear: "The Kendall correlation measure is more robust and slightly ...
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### Equivalent to Spearman correlation for non-monotonic data

Is there a way to test if my data is monotonic prior to Spearman's rho / Kendall's tau correlation calculations? You could plot the data and look for a non-monotone shape. Also, you could fit a ...