The sample size for running Pearson's r varies according to authors.  According to David(1938) a sample size equal or superior to 25 suffices. 

I recommend Bonett and Wright (2000), Sample size requirements for estimating ¨Pearson, Kendall and Spearman correlations, Psychometrika, 65(1), 23-2_

Technically one can calculate a correlation coefficient from n=2. This would be absolutely correct, although of little use: the coefficient would always be plus or minus 1 (excpet for the unlikely case that both y-values were exactly identical), and the CI would always be (-1, +1).

From n=3 one can already calculate meaningful CIs.

With increasing sample size the correlation coefficient will "collect" more information - the information about the linear correelation provided by the data.

There is no problem having a small sample size. The assumptions about the scale of the varibles, their linear correlation and homogeneous, normal errors must be reasonable. The only difficult thing is to see or recognize possibly relevant deviations from these assumptions with small samples. But this does not invalidate the test, because the test remains valid under these assumptions. If our data tells us that some of these assumptions are really unreasonable or unacceptable, then we learned something, and we should use this knowledge in future analyses of such data.

It's like walking in a dark room. You go foreward step by step, not knowing if the direction is wrong, until you hit a wall. Then you will have to change the direction. Data (observations) will add some small candle-lights here and there, and a smart person may use this little light to find a better way through the room. But this way will neccesarily contain dark parts again (otherwise one would be caught by the candle-lights like mosquitos and never find a way through the room). And: many small lights can be a decent guide. The problem we trap into is to see and "p0.05" as possible light sources at all. But that's not the fault of the tests (deemed invalid or whatever) but our fault to paint black-and-white pictures of a world coming in colors and grayscales and to interpret p-values "out of context".

As Jochen says, it is technically possible to calculate confidence intervals with very small samples, but those CIs will include a very wide range of values because the standard errors will be quite large. I suppose one could get a correlation so large that it would be significant with an N of six, but it would still include almost the full range from zero to one.

A couple years ago, Ray Koopman and I published an article describing an SPSS macro that computes the confidence interval for rho.  (The CORRELATIONS procedure in SPSS does not include CIs in the output, and only bootstrap CIs for rho are available using "built-in" SPSS procedures.)  The output from our macro includes a column for notes, where one might see one of the following notes:

We explained the thinking behind those notes as follows:

"Computation of the p-value entails using a t-distribution with degrees of freedom equal to n-2; and the standard error of Zr (which is used in computing the CI for rho) has SQRT(n-3) in the denominator. Thus computation of the p-value requires n ≥ 3 and computation of the CI for rho requires n ≥ 4. The warning about the normal approximation being poor for n < 10 is based on Kirk’s (2007) discussion of CIs for rho."

Kirk, R. E. (2007). Statistics: An introduction. Wadsworth Publishing Company.

HTH.

http://www.tqmp.org/Content/vol10-1/p029/p029.pdf

https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/spss/my-spss-page/rhoci

Thank you gents those answers were very useful (and indeed 'illuminating') and I appreciate the efforts and contributions made.

Barry, I have read somewhere that the recommended minimum for Pearson´s r is 30 cases. It was either Discovering Statistics Using SPSS by Andy Field or one source in Czech. I do not remember the reasoning, though.

The sample size for running Pearson's r varies according to authors.  According to David(1938) a sample size equal or superior to 25 suffices. 

I recommend Bonett and Wright (2000), Sample size requirements for estimating ¨Pearson, Kendall and Spearman correlations, Psychometrika, 65(1), 23-2_

I know this is a bit out-dated, but I didn't see anybody on this page mention the statistical power of that correlation. Going to lower sample sizes, reduces our power for determining the correlation at a given alpha (usually 0.05). I found a decent tool that shows how correlation and power interact. 

So in short, correlation can be run at the low values suggested, but they are done so at the sacrifice of statistical power (something often ignored)

I wouldn’t trust any correlation without at least 50 or 60 observations, with 80-100 being around where I feel comfortable. From my experience with pilot data and analyzing subsets of datasets or presenting data on an ongoing study, correlations with 20-40 subjects can be markedly different than when you have 80-100, I’ve even seen correlations between two tasks going from -.70 to +.40 when the observations were doubled.

it’s also important to identify outliers, even with larger sample sizes an outlier or two can have a large effect on the magnitude of the correlation, since this is least squares after all.

http://www.sample-size.net/correlation-sample-size/

http://www.sample-size.net/correlation-sample-size/

the right statistical sample size are not less than 30 participants@