3.1.3.4 The Spearman Rank Correlation Test This test assumes that the variance of the disturbance term is either increasing or decreasing as Xincreases and that there will be a correlation between the absolute size of the residuals and the size of Xin an OLS regression. The data on Xand the absolute values of the residuals are both ranked, and the rank correlation coefficient is defined as
∑
( )
…[3.02] whereD i is the difference between the rank of Xand the rank of ein observation i. Under the assumption that the population correlation coefficient is 0, the rank correlation coefficient has a normal distribution with 0 mean and variance 1 ( 1) n in large samples. Theappropriate test statistic is therefore
√ and the null hypothesis of homoscedasticity will be rejected at the 5 percent level if its absolute value is greater than 1.96 and at the 1 percent level if its absolute value is greater than 2.58, using two- tailed tests. If there is more than one explanatory variable in the model, the test maybe performed with anyone of them.
