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Pearson correlation
Explanations > Social Research > Analysis > Pearson correlation Description  Example  Discussion  See also
DescriptionPearson devised a very common way of measuring correlation, often called the Pearson ProductMoment Correlation. It is is used when both variables are at least at interval level and data is parametric. It is calculated by dividing the covariance of the two variables by the product of their standard deviations. r = SUM((x_{i}  xbar)(y  ybar)) / ((n  1) * s_{x}
* s_{y}) r may also be considered as being: r^{2} = explained variation / total variation In other words, it is the proportion of variation that can be explained. A high explained proportion is good, and a value of one is perfect correlation. For example an r of 0.8 explains 64% of the variance. When calculated from a population, Pearson's coefficient is denoted with the Greek letter 'rho' (ρ). When calculated from a sample, it is denoted with 'r'. The Coefficient of Determination is calculated as r^{2}. Example
Hence: Pearson r = sum((x_{i}  xbar)(y  ybar)) / ((n  1) * s_{x} * s_{y}) = 0.854
This is quite high, showing a moderately good correlation between the sets of numbers.
DiscussionPearson is a parametric statistic and assumes: The coefficient of determination, r^{2}, represents the percent of the variance in the dependent variable explained by the dependent variable. Correlation explains a certain amount of variance, but not all. This works on a square law, so a correlation of 0.5 indicates that the independent variable explains 25% of the variance of the dependent variable, and a correlation of 0.9 accounts for 81% of the of the variance. This means that the unexplained variance is indicated by (1r^{2}). This i typically due to random factors. Pearson's Correlation is also known as the Pearson ProductMoment Correlation or Sample Correlation Coefficient. 'r' is also known as 'Pearson's r'. See alsoSpearman correlation, Kendall correlation, Types of reliability 

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