The statistical meaning of Correlation is not that far from the lay use. If you have data from two variables from a sample of people, say age and baseline change measure score, or scores on two different measures, then the correlation between the two variables is how often people with larger values on one variable also have larger values on the other variable: do older people have higher baseline scores than younger people? A correlation can be negative: older people generally having lower scores than younger people. Where there is no relationship between the two variables in the sample data the correlation will be near zero.
Details #
A correlation coefficient is a number derived by crunching two sets of numbers to give an indication of the correlation between the two variables in that sample. It is important to distinguish between the coefficient and its statistical significance. For our purposes all correlation coefficients will take values between -1 for a perfect negative correlation and +1 for a perfect positive correlation and zero will indicate no correlation at all. Even a very small correlation such as .1 may be statistically significant, i.e. very unlikely to have arisen by chance alone, if a sample is large, in hundreds or thousands; such a correlation may be of very little importance. Similarly, even a very strong correlation such as .9 might not be statistically significant in a small sample, e.g. n = 7.
Rank correlations, such as Spearman‘s or Kendall‘s correlation coefficients don’t consider the actual values of the variables only the ranks of the values which avoids some problems computing the statistical significance of a correlation if the distribution of one or both variables is not Gaussian (“Normal“). However, bootstrapping and computing confidence intervals around an observed correlation are arguably making the use of these “non-parametric” correlation coefficients of little real importance.
Try also … #
Bootstrapping
Confidence interval
Gaussian/”Normal” distribution
Parametric versus non-parametric statistics
Statistical testing & hypothesis tests
Kendall correlation coefficient
Ranking
Spearman correlation coefficient
Chapters #
Nothing here yet!
Online applications #
At some point: online form into which you can upload data and get the scattergram for the data and correlation coefficients with the confidence interval around that observed value.
