Spatial analysis and efficiency of systematic designs in intercropping experiments.
In studies involving intercropping plant populations, the main interest is to locate the position of the maximum response or to study the response pattern. Such studies normally require many plant population levels. Thus, designs such as spacing systematic designs that minimise experimental land area are desired. Randomised block designs may not perform well as they allow few population levels which may not span the maximum or enable exploration of other features of the response surface. However, lack of complete randomisation in systematic designs may imply spatial variability (largescale and small-scale variations i.e. trend and spatial dependence) in observations. There is no correct statistical method laid out for data analysis from such designs. Given that spacing systematic designs are not well explored in literature, the main thrusts of this study are two fold; namely, to explore the use of spatial modelling techniques in analysing and modelling data from systematic designs, and to evaluate the efficiency of systematic designs used in intercropping experiments. Three classes of models for trend and error modelling are explored/introduced. These include spatial linear mixed models, semi-parametric mixed models and beta-hat models incorporating spatial variability. The reliability and precision of these methods are demonstrated. Relative efficiency of systematic designs to completely randomised design are evaluated. The analysis of data from systematic designs is shown be easily implemented. Measures of efficiency that include <pp directed measures (A and E criteria), D1 and DB efficiencies for regression parameters, and power are used. Systematic designs are shown to be efficient; on average 72% for A and E- efficiencies and 93% for D1 and DB efficiencies. Overall, these results suggest that systematic designs are suitable and reliable for intercropping plant population studies.