6Assumptions in Nonparametric Correlations
6.1 Introduction
Nonparametric tests are generally used where the data does not follow a normal distribution. Besides the violation of normality, the data type is also an important consideration while choosing an appropriate statistical method. For instance, the data in hand may be based on ordinal or nominal ratings (categorical data) rather than originally measured data observations at a continuous scale (interval or ratio). To deal with such data, the nonparametric counterparts are used. Specifically, for testing the bivariate relationships among variables, several measures are available for correlations and association. The conventional bivariate Pearson's moment correlation requires the data to be measured at interval or ratio scale; however, for categorical data, its extensions are available, which are Spearman's rank‐order correlation, Phi coefficient, and the point‐biserial correlations. These can be considered as special cases to the traditional Pearson's correlation coefficient and sometimes can be regarded as nonparametric measures for correlation and association.
6.2 Spearman Rank‐Order Correlation
It is a nonparametric statistical technique for measuring the relationship between two ordinal variables or rank‐ordinal correlation. If the sample size is greater than or equal to 4, then the Spearman rank‐order correlation is computed as follows:
where
- n is the number of rank pairs and Di is the difference between a ranked ...