Discuss the difference between a parametric and nonparametri

Discuss the difference between a parametric and nonparametric correlation coefficient? When would you use each? Give an example of each and discuss that briefly.

Solution

One example of parametric Correlation coefficient is Pearson\'s correlation coefficient and that of non-parametric Correlation coefficient is Spearman correlation coefficient. I am gonna use these two correlation coefficient to explain the differences.

Pearson\'s correlation coefficient between two variables is defined as the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a \"product moment\", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.

If the covariance and variances of the two vairables exist, the Pearson\'s correlation coefficient can be extimated. No normal distribution assmption is needed.

The Spearman correlation coefficient is defined as the Pearson correlation coefficient between the ranked variables. If the data has outliers, a few values are far away from others, use Spearman correlation coefficient.

Note that this method should not be used in cases where the data set is truncated; that is, when the Spearman correlation coefficient is desired for the top X records (whether by pre-change rank or post-change rank, or both), the user should use the Pearson correlation coefficient formula

The Pearson correlation coefficient is the most widely used. It measures the strength of the linear relationship between normally distributed variables. When the variables are not normally distributed or the relationship between the variables is not linear, it may be more appropriate to use the Spearman rank correlation method.