Exercise 4: Making a Correlation
3. The correlation coefficient
We can calculate a number called the correlation coefficient to tell us how strongly the two variables are related. A common form is the Pearson correlation coefficient which, in technical terms, gives the shared variance expressed as a proportion of the product of the standard deviations of both variables.
Pearson’s correlation coefficient is also known as r. When r has a value of 1, the correlation is perfect and positive. A value of -1 means the correlation is perfect and negative. 0 means no linear relationship at all. N.B. there might be a relationship which is not linear, for example a scatter plot of the variables might look curved. The correlation coefficient comes with a p-value: the probability that the value of the coefficient would be greater or equal to its observed value under the null hypothesis (i.e. that there was no relationship).
To calculate the Pearson correlation coefficient for BODYFAT and ADIPOSITY, go to Analyze > Correlate > Bivariate. Drag the two variables from the left window to the right window. Click OK.