Finally, it is assume that the spread of measurements is approximately the same at all levels of the two variables. If this is not the case it is again possible to calculate a correlation that is different from the actual correlation in the population. The coefficient of determination As we have already seen, the correlation coefficient is not an equi-interval scale rather it is an ordinal scale. That makes such procedures as comparing one correlation coefficient with another quite difficult. This is called the coefficient of determination and indicates the percentage of variation in one variable that can be accounted for, or determined by variations in the other variable.
Hypothesis testing The correlation coefficient is an estimate of the true population correlation.
On the basis of this test of significance we can make conclusions about whether the observed correlation is real or not. Other correlational measures The Pearson correlation coefficient is used where the data are primarily distributed along more or less interval or ratio scales of measurement. In some cases we may ask subjects to rank items along two dimensions and we may wish to correlate these rankings. Or it may be that the researcher decides to rank the data because of extreme data values. To calculate a Spearman's correlation is quite simple in that once all the data have been ranked then the Pearson's correlation formula is simply applied to the ranked data.