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Estimation and Inference About Land Equivalent Ratio
Dissertation Abstract:
For standardization, methods for computing Land Equivalent Ratio (LER) values were examined, namely: 1) monocrop yields as average of each treatment from all replications; 2) monocrop yields as the grain 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 were used to estimate 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 (MSE) were derived for each of the five methods.
To evaluate the approximate formulas and assess different methods of estimation, a rice-mung bean intercropping simulation experiment was conducted. The experiment involved a randomized complete block design with four replications of nine treatments, which included three monocrop and six intercrop treatments.
The study showed that the approximate formulas were good enough for calculating the bias, variance, and MSE for LERs for each of the methods. The average errors of bias, variance, and MSE were 0.002, 0.0003, and 0.00037, respectively.
Results also indicated that among the methods for estimating vector of LER, the bias variances of LERs when Method II was used were 17.50-82.21 percent less for bias and 3.82-43.78 percent less for variance than those of the other methods. Thus, Method II was more accurate and precise in estimating values of vector of LER. Although the OLSE method has the same bias as Method I for estimating LER values, OLSE method yielded variance value which was 62.67 percent less than that of Method II. The OLSE method, therefore, was more precise.
The distribution of LER data in each method for estimating vector of LER was also examined vis-a-vis the normality assumption underlying the analysis of variance (ANOVA). Based on Chi-square goodness-of fit test, LER values from all methods for estimating vector ofLER gave evidence ofnon-nonnality.