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 Navigation: STATISTICS WITH PRISM 9 > Correlation Key concepts: Correlation

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 variables (often X and Y), and is not appropriate if one of the variables is manipulated or controlled as part of the experiment (X values often fit this description: for example, specific concentrations used in a dose-response experiment are controlled values).

Values of the two variables 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; as the value of one variable goes up, the value of the other variable goes down) to 1 (perfect positive relationship; as the value of one variable goes up so does the value of the other). A correlation coefficient of zero means that there is no correlation at all between the values of the two variables.

Correlation analysis also reports a P value that can be used to test the null hypothesis that the data were sampled from a population where there is no correlation between the two variables (in other words, the null hypothesis is that r=0).

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 values from both variables are sampled from populations with a Gaussian distribution. Spearman correction does not make this assumption.

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