Test of the Correlation Coefficient in Bivariate Normal Populations Using Ranked Set Sampling

Ranked Set Sampling (RSS) is a statistical method for data collection that leads to more efficient estimators than competitors based on Simple Random Sampling (SRS). We consider testing the correlation coefficient of bivariate normal distribution based on Bivariate RSS (BVRSS). Under one-sided and two-sided alternatives, we show that the new tests based on BVRSS are more powerful than the usual uniformly most powerful tests based on bivariate SRS. Furthermore, the proposed tests for repeated and unrepeated samples are compared.