When running a correlation analysis the main question is data quality and not sample size. There are many issues connected with data quality. Some of them are questions like – Is the data representative? Does the data span the region of interest? Has the data been gathered in such a manner that the various “independent” variables are in fact independent?
The last question plays a crucial role in correlation analysis and it is one that often brings to a halt analysis efforts involving “lots of data”. For example, if you have two variables X1 and X2 that you wish to correlate with a given response and your measurements were such that every time you increased X1 you increased X2 and every time you decreased X1 you decreased X2 you will have “lots of data” and the confounding of X1 and X2 will be such that you cannot separate their effects. In such a case, four data points from a two level factorial design coupled with two replicates on the centerpoint will provide more information than all of the data points gathered in the manner first described.
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