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Navigation: STATISTICS WITH PRISM 9 > Correlation

Key concepts: Correlation

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When two variables vary together, statisticians say that there is a lot of covariation or correlation.

The correlation coefficient, r, quantifies the direction and magnitude of correlation.

Correlation is used when you measured both X and Y variables, and is not appropriate if X is a variable you manipulate.

X and Y are almost always real numbers (not integers, not categories, not counts).

The correlation analysis reports the value of the correlation coefficient. It does not create a regression line. If you want a best-fit line, choose linear regression.

Note that correlation and linear regression are not the same. Review the differences. In particular, note that the correlation analysis does not fit or plot a line.

Correlation computes a correlation coefficient and its confidence interval. Its value ranges from -1 (perfect inverse relationship; ax X goes up, Y goes down) to 1 (perfect positive relationship; as X goes up so does Y). A value of zero means no correlation at all.

Correlation also reports a P value testing the null hypothesis that the data were sampled from a population where there is no correlation between the two variables.

The difference between Pearson and Spearman correlation, is that the confidence interval and P value from Pearson's can only be interpreted if you assume that both X and Y are sampled from populations with a Gaussian distribution. Spearman correction does not make this assumption.

If either X or Y has only two possible values, the results of Pearson correlation are identical to point-biserial correlation.

 

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