How do you find a correlation error?
In other words, the probable error (P.E.) is the value which is added or subtracted from the coefficient of correlation (r) to get the upper limit and the lower limit respectively, within which the value of the correlation expectedly lies.
What do you mean by probable error?
In statistics, probable error defines the half-range of an interval about a central point for the distribution, such that half of the values from the distribution will lie within the interval and half outside.
How to calculate the standard error of the correlation coefficient?
If you wanted to, you could also create a function like the following to include the standard error of the correlation coefficient. For convenience, here’s the equation: r = the correlation estimate and n – 2 = degrees of freedom, both of which are readily available in the output above.
Why are there two formulas for standard error?
To try to explain why there are two different formulas for the standard error which are circulating, I found that it depends on how you compute it. In my first simulation, I used Pearson formula to compute the correlation, but one can also use the least square regression coefficient.
Is the latter method has the standard error?
I can confirm that the latter method has the standard error proposed in the question: These are two estimators of the correlation which do not have the same variance. That try to reconcile the two formulas did not work, because I forgot to normalize the regression coefficient.
What should the N be for a correlation?
The N should be at least 30 (IIRC), and the marginal distributions (i.e., the univariate distributions of the two variables being correlated) should be normal. For example, I’m not sure that this will be accurate if the correlation were composed of two vectors of 1 s and 0 s. However, higher N should allow you to compensate for minor non-normality.