Editing Pearson correlation coefficient (section)

===Interpretation of the size of a correlation===
[[File:Pearson correlation and prediction intervals.svg|thumb|200px|right|This figure gives a sense of how the usefulness of a Pearson correlation for predicting values varies with its magnitude. Given jointly normal ''X'', ''Y'' with correlation ''ρ'', <math>1 - \sqrt{1 - \rho^2}</math> (plotted here as a function of ''ρ'') is the factor by which a given [[w:Prediction interval|prediction interval]] for ''Y'' may be reduced given the corresponding value of ''X''. For example, if ''ρ'' = 0.5, then the 95% prediction interval of ''Y''{{pipe}}''X'' will be about 13% smaller than the 95% prediction interval of ''Y''.]]

Several authors have offered guidelines for the interpretation of a correlation coefficient.<ref name="Buda">{{cite book |last1=Buda |first1=Andrzej |last2=Jarynowski |first2=Andrzej |title=Life Time of Correlations and its Applications |date=December 2010 |publisher=Wydawnictwo Niezależne |isbn=9788391527290 |pages=5–21}}</ref><ref name="Cohen88"/> However, all such criteria are in some ways arbitrary.<ref name="Cohen88">{{cite book |last=Cohen |first=J. |year=1988 |title=Statistical Power Analysis for the Behavioral Sciences |edition=2nd}}</ref> The interpretation of a correlation coefficient depends on the context and purposes. A correlation of 0.8 may be very low if one is verifying a physical law using high-quality instruments, but may be regarded as very high in the social sciences, where there may be a greater contribution from complicating factors.