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Variations of the correlation coefficient can be calculated for different purposes. Here are some examples
===Adjusted correlation coefficient
The sample correlation coefficient ''r'' is not an unbiased estimate of ''ρ''. The adjusted correlation coefficient ''r<sub>adj</sub>'' is a relatively unbiased estimate of ''ρ''. The formula<ref name="RealCorBasic"/> for ''r<sub>adj</sub>'' is:
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Note that ''r<sub>adj</sub>'' ≈ ''r'' for large values of n.
For data that follows a [[bivariate normal distribution]], the expectation ''E(r)'' for the sample correlation coefficient ''r'' of a normal bivariate is<ref>{{Cite journal | first = H. | last = Hotelling | year = 1953 | title = New Light on the Correlation Coefficient and its Transforms | journal = Journal of the Royal Statistical Society. Series B (Methodological) | volume = 15 | issue = 2 | pages = 193–232 | jstor = 2983768}}</ref>
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