# Tag Info

### Analogy of Pearson correlation for 3 variables

It is indeed something. To find out, we need to examine what we know about correlation itself. The correlation matrix of a vector-valued random variable $\mathbf{X}=(X_1,X_2,\ldots,X_p)$ is the ...
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### Completing a $3 \times 3$ correlation matrix — $2$ coefficients of the $3$ given

We already know $\gamma$ is bounded between $[-1,1]$ The correlation matrix should be positive semidefinite and hence its principal minors should be nonnegative Thus, \begin{align*} 1(1-\gamma^2)-0.6(...
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### 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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### Is it possible to have Pearson correlation coefficient values $< -1$ or values $> 1$?

The formulas you're using have long been known to be numerically unstable. If the squared means are large compared to the variances and/or products-of-means are large compared to the covariances, then ...
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### 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. ...
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### Difference between Pearson's r ~= 0 and p > 0.05

The p-values and Pearson's correlation coefficient $r$ measure different things. $r$ measures the strength of the correlation. The p-value, on the other hand, measures how likely you would be to ...
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### If the Pearson r is .1, is there a weak relationship between the two variables?

Let me again post the same quote from the web: I once asked a chemist who was calibrating a laboratory instrument to a standard what value of the correlation coefficient she was looking for. ...
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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") [1] 0.9745586 cor(x,y, meth = "s") [1] 1
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### 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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### Can I use Pearson correlation for discrete variables?

Sure! set.seed(2022) N <- 100 x1 <- rpois(N, 5) # Poisson(5) x2 <- rpois(N, 7) # Poisson(7) cor(x1, x2) At no point does the Pearson correlation make ...
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