Estimation and inference about land equivalent ratio.

Four standardization methods for computing LER [Land Equivalent Ratio] values are examined, namely: (1) monocrop yields as average of each treatment from all replications, (2) monocrop yields as the grand mean, (3) monocrop yields as each treatment from each replication, and (4) monocrop yields as average of all treatments from each replication. These four methods are used for the estimation of vector of LER. The ordinary least square method (OLSE) for estimating parametric LER was also examined. Approximate formulas for bias, variance and mean square error were derived for each of the five methods. To evaluate the approximate formulas and assess the different methods of estimation, a rice-mungbean intercropping simulation experiment was conducted. The experiment involved a randomized complete block design with four replications of nine treatments which included three mono-crop and six intercrop treatments. The study showed that the approximate formulas are good enough for calculating the bias, variance and MSE [Mean Square] of LERs for each of the methods, in sense that average error of bias less than or equal to 0.002, average error of variance less than or equal to 0.0003 and average error of MSE less than or equal to 0.00037. The results also indicate that among the methods for estimating vector of LER, the bias and variance of LERs when Method 2 is used are 17.50% to 82.21% less for bias and 3.82% to 43.78% less for variance than those of the other methods. Thus, this method gives better accuracy and precision in estimating values of vector of LER. Although the OLSE method has the same bias as Method 1 for estimating LER values, OLSE method yields variance value which is 62.67% less than what Method 2 yields, the OLSE method, therefore, is more precise. The distribution of LER data in each method for estimating vector of LER were also examined vis-a-vis the normality assumption underlying the ANOVA. Based on chi-square goodness-of-fit test, LER values from all methods for estimating vector of LER gave evidence of non-normality.