20
votes
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:
...
- 3,493
17
votes
Accepted
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), ...
- 103k
16
votes
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 ...
- 316k
15
votes
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. ...
- 118k
13
votes
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 ...
- 471
12
votes
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 ...
- 121
12
votes
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 ...
- 2,290
12
votes
Accepted
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 ...
- 1,090
12
votes
Accepted
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 ...
- 58.4k
11
votes
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}{\...
- 231
11
votes
Question about running Spearman's correlation instead of Pearson's
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 ...
- 29.3k
9
votes
Accepted
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 ...
9
votes
Accepted
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) ...
- 8,355
9
votes
Accepted
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.
...
- 312
9
votes
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 ...
- 74.7k
8
votes
Accepted
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")
[1] 0.9745586
cor(x,y, meth = "s")
[1] 1
- 55.2k
8
votes
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:
...
- 37.7k
8
votes
Accepted
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 ...
- 3,929
8
votes
Accepted
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 ...
- 4,682
7
votes
Accepted
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 ...
- 86.9k
7
votes
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, ...
- 3,590
7
votes
Accepted
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....
- 86.9k
6
votes
Accepted
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 ...
- 110k
6
votes
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:
...
- 8,769
6
votes
Question about Spearman's correlation
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 ...
- 2,212
6
votes
Question about running Spearman's correlation instead of Pearson's
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 ...
- 8,769
5
votes
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 ...
- 81
5
votes
Accepted
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 ...
- 57k
5
votes
Difference between Cox regression and logistic regression; question about correlation assessment
1) A logistic regression calculates the probability of an event happening based on the factors you feed into your model, and it uses a logit transform to give you those probabilities. (I will assume ...
- 381
5
votes
Accepted
How can I interpret a moderately negative correlation?
A couple of caveats before moving on to the actual question you asked -
First, with 19 tests (really, more than one test) you should be adjusting for multiple comparisons. If you perform 20 ...
- 37.7k
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