Statistical models for yield, pest abundance and disease incidence of tomato

Analysis of variance (ANOVA) is one of the general linear models used to nearly unimaginable range of problems in many different disciplines and has been a fundamental method used by plant pathologists and other researchers for analysis of continuous data, disease incidence and insect pest abundance data. However, disease incidence and pest abundance data usually violate the assumptions of ANOVA because they are discrete data. Most researchers often transform the data using arcsine for disease incidence, square root for pest abundance and other forms of transformation although most researchers finally do not check if the transformation was effective to correct for the violated assumptions. Hence, the objectives of this dissertation is to (1) to determine the performance of ANOVA on continuous data (tomato fruit weight) including the validity of statistical inferences, (2) to assess the performance of logistic regression and ANOVA on tomato yellow leaf curl disease incidence including the validity of statistical inferences, (3) to evaluate the performance of Poisson regression and ANOVA on pest abundance including the validity of statistical inferences. Tomato fruit weight data was analyzed assuming only normal distribution while tomato yellow leaf curl disease incidence data were analyzed assuming normal (ANOVA), binomial distribution (logistic regression). Whitefly population data were analyzed assuming normal (ANOVA), Poisson, and negative binomial error distribution. On the basis of multiple R Square (higher value) and small residual standard error close to zero, ANOVA model on tomato fruit weight confirmed better goodness of fit to the data. The greater p-value for deviance (p=0.1207) and Pearson (0.0896) statistics showed that logistic regression model performed better compared to ANOVA on tomato yellow leaf curl disease. Also the greater p-value for deviance (0.0077) and Pearson (0.2796) statistics, decreased AIC value (475.22 to 300.11) indicated that negative binomial model was most appropriate compared to Poisson regression models. It was concluded that GLMs could be alternative models for discrete data.