Data Analysis of Intercropping Experiments by Bivariate Analysis Variance and Comparison of the Means and Drawing Graphs with Skew Axes

Approaches of data analysis in intercropping experiments and evaluation of crop competition are very important in interpreting the results. Intercropping advantages may be influenced by both plant density and relative frequency of the intercrop components as key factors. The fundamental problem in replacement series method (usual method on intercropping experiments) arises from the two-dimensional nature of intercropping. Results based on linear regression model are not independent of plant densities, and varying densities produce different results. Conducting methods such as univariate analysis of variance or comparing the means by using procedures such as the least significant difference (LSD) or Duncan's multiple range test (DMRT) are not appropriate to evaluate data obtained from the interpreting experiments, due to fact that they cannot explain simultaneously the response of agronomic plant to different treatments. On the other hand, bivariate analysis of variance has enough accuracy and sensitivity in this regard because effects of treatments on each plant, as a component of a planting system, are not independent of another plant and are placed under its interaction effect. The effects can be explained with the help of graph drawing in which the angle between two axes depends on the magnitude of the effect and the positive or negative effect of the interaction changes between two states of open angle and closed angle. The variance and covariance calculations, mean comparisons, graph drawing and the determination of significant differences between means were performed by using a program (Skew Axes)*. For practical application of the method of bivariate analysis and Skew Axes program with incorporation of one input data file (yield of sesame and sorghum intercropping ) and showing some figures, correlation and relation between yield of two specific for a specific treatment(density, proportion or interaction of density and proportion), also possibility to analyzed two values obtained from one plot related to a specific treatment simultaneously were presented and discussed.