READING 9 PARAMETRIC AND NON- PARAMETRIC TESTS OF INDEPENDENCE

LOS 9.a

Testing the hypothesis that the population correlation coefficient equals zero involves using a t-statistic as the appropriate test statistic, which has degrees of freedom equal to n minus two and is calculated using the formula.

, where r is the sample correlation coeficient.

A non-parametric measure of correlation can be executed when we have access to only ranked data (such as deciles of investment performance). The Spearman rank correlation test evaluates the association between ranked values across multiple time periods. The measure of rank correlation represents.

where

The value n represents the sum of squared differences in rank pairs, where n denotes the number of sample size. The statistic value has a tendency to follow a t-distribution when used with sample data.

sizes greater than 30.

LOS 9.b

A contingency table is utilized to evaluate the assumption concerning the independence between two categorical variables in a sample. A contingency table represents the count of sample items, such as irms that possess both categories simultaneously. The value of this statistic follows a chi-square distribution, which allows us to determine whether there is a significant association between the two categorical variables under study.

The degrees of freedom amount to (r−1)(c−1). Failing to support the hypothesis that two characteristics are independent requires that the test statistic exceed the critical chi-square value at a specified significance level.