About
The Pearson product-moment correlation coefficient is a correlation coefficient formulas that can be applied when both variables are continuous.
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Syntax
<MATH> \begin{array}{rrc} \text{little r} & = & \frac{\text{degree to which X and Y vary together}}{\text{degree to which X and Y vary independently}} \\ & = & \frac{\href{Covariance}{Covariance} \text{ of X and Y}}{\href{Variance}{Variance}\text{ of X and Y}} \end{array} </MATH>
The correlation is the standardized Covariance as standard deviation is the standardized variance. (Standardized to get the value in the range).
Formula
The raw score formula and the Z score formula gives the same result.
Raw score
<MATH> r = \frac{\displaystyle \sum_{i=1}^{N}{\href{cross_product}{\text{Cross Product of X & Y}}}}{\displaystyle \sqrt{ \sum_{i=1}^{N}{(\href{deviation_score}{\text{Deviation score of X}})^2} . \sum_{i=1}^{N}{(\href{deviation_score}{\text{Deviation score of Y}})^2} } } </MATH>
where:
- N is the number of observations in the sample
- N the denominator is:
- N: for descriptive statistics
- of N-1 : for inferential statistics
Z-score
<MATH> r = \frac{\displaystyle \sum_{i=0}^{N}{ (\href{z_score}{\text{Z Score of X }})( \href{z_score}{\text{Z Score of Y}}) } } {N} </MATH>
where:
- N is the number of observation in the sample
- N the denominator is:
- N: for descriptive statistics
- of N-1 : for inferential statistics