Editing Pearson correlation coefficient (section)

===Sample size===
*If the sample size is moderate or large and the population is normal, then, in the case of the bivariate [[normal distribution]], the sample correlation coefficient is the [[maximum likelihood estimate]] of the population correlation coefficient, and is [[asymptotic distribution|asymptotically]] [[bias of an estimator|unbiased]] and [[efficiency (statistics)|efficient]], which roughly means that it is impossible to construct a more accurate estimate than the sample correlation coefficient. 
*If the sample size is large and the population is not normal, then the sample correlation coefficient remains approximately unbiased, but may not be efficient.
*If the sample size is large, then the sample correlation coefficient is a [[consistent estimator]] of the population correlation coefficient as long as the sample means, variances, and covariance are consistent (which is guaranteed when the [[law of large numbers]] can be applied).
*If the sample size is small, then the sample correlation coefficient ''r'' is not an unbiased estimate of ''ρ''.<ref name="RealCorBasic"/> The adjusted correlation coefficient must be used instead: see elsewhere in this article for the definition.
*Correlations can be different for imbalanced [[dichotomous variable|dichotomous]] data when there is variance error in sample.<ref>{{cite journal |last1=Lai |first1=Chun Sing |last2=Tao |first2=Yingshan |last3=Xu |first3=Fangyuan |last4=Ng |first4=Wing W.Y. |last5=Jia |first5=Youwei |last6=Yuan |first6=Haoliang |last7=Huang |first7=Chao |last8=Lai |first8=Loi Lei |last9=Xu |first9=Zhao |last10=Locatelli |first10=Giorgio |title=A robust correlation analysis framework for imbalanced and dichotomous data with uncertainty |journal=Information Sciences |date=January 2019 |volume=470 |pages=58–77 |doi=10.1016/j.ins.2018.08.017 |s2cid=52878443 |url=http://eprints.whiterose.ac.uk/134706/2/ELSEVI_3.pdf }}</ref>