ANOVA or MANOVA for Correlated Traits in Agricultural Experiments
ANOVA or MANOVA for Correlated Traits in Agricultural Experiments
Iftikhar ud Din* and Yousaf Hayat
ABSTRACT
In most of agricultural experiments, analysis of variance (ANOVA) is the widely used statistical methods for assessing the differences among the means of more than two treatments by considering single trait independently. In reality these traits are not independent and appropriate techniques for analyzing multiple traits simultaneously, is the multivariate analysis of variance (MANOVA). This study deals with the illustration of MANOVA using simulated data, related to agricultural trials. The appropriate design, methods of analysis, interpretation and conclusion are carried out on simulated data. For illustration three factors are considered in a factorial arrangement in completely randomized design (CRD). For the two levels of each irrigation, varieties, and five types of nitrogen sources, all combination of their levels are considered to measure two linear related responses yield and plant height. Data on two parameters (say plant height and yield) are simulated with varying magnitude (low, moderate, and high) of correlation coefficient between the two response variables. The comparative analysis of MANOVA and ANOVA reveals that even a small amount of correlation between the dependent variables creates huge change on the status of main effect and interaction of the three independent variables. The results reveal that when linear relation between traits is low to moderate the effect of some of the main effect and interaction for one of the traits found in ANOVA are contrary to that found in corresponding MANOVA. Further it was observed that for highly correlated traits, the status of some of the effects found in separate ANOVAs for both the traits are totally altered by the MANOVA model.
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