At what sample size do correlations stabilize?

• Sample correlations converge to true value ρ, but are inaccurate in small samples.
• From which sample size on do correlations only show minor fluctuations around ρ?
• Monte-Carlo simulations were used to determine the “point of stability” (POS).
• Necessary sample size depends on effect size, tolerable fluctuations, and confidence.
• In typical scenarios n should approach 250 for stable estimates.

Sample correlations converge to the population value with increasing sample size, but the estimates are often inaccurate in small samples. In this report we use Monte-Carlo simulations to determine the critical sample size from which on the magnitude of a correlation can be expected to be stable. The necessary sample size to achieve stable estimates for correlations depends on the effect size, the width of the corridor of stability (i.e., a corridor around the true value where deviations are tolerated), and the requested confidence that the trajectory does not leave this corridor any more. Results indicate that in typical scenarios the sample size should approach 250 for stable estimates.

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