The Effect of Sampling Methods for Linear Regression Estimation of Population Means of Dependent Variables

Abstract

In this paper, we compare an efficient population mean estimator of dependent variable on simple linear regression model in three sampling methods, namely simple random sampling (SRS), ranked set sampling (RSS) and L ranked set sampling (LRSS) when the population mean of the independent variable is known. The independent variable and the dependent variable jointly followed a bivariate t-distribution with the different degree of freedom (df) levels, correlation coefficient (ρ) between ones with the different levels, set size and number of sample units allocated to each set (m) number of cycles (r) and LRSS coefficient (k) with the different levels. The efficiency of population mean estimator of all sampling methods are considered by the average of variance of population mean estimator (AVPME) values. The results indicate that for very low level of df (df=1), for all levels of ρ that less than 1, all levels of m and for low and moderate levels of r (r=5, 10), the RSS method is the most efficient but for high levels of r (r=20), the SRS method is the most efficient. For the other levels of df, for all levels of ρ that less than 1 and for all levels of r, the RSS method is the most efficient when m is in low levels (m=8 and 10), the LRSS method is the most efficient when m is in moderate levels (m=15, 20 and 30) at k=1, for large level of m (m=40) at k=2 and for very large level of m (m=50) at k=3. For very high level of ρ (ρ=1) in all levels of df, m and r, the performance of the three sampling methods are nearly the same. The efficiency of population mean estimator of dependent variable from each sampling methods increase and nearly the similar when m, r and ρ increases.