Spatial Analysis of Gamma Distributed Data with Equal Variances

Data correlated in space present in many areas such as agriculture, ecology, criminal justice, and epidemiology. Observations that are closer together in one-dimensional space, two-dimensional space, or space-time can be more similar and highly correlated with one another than observations that are farther apart. Despite spatial prediction, analysis of spatially correlated data with the purpose of testing for significance of treatment effects is also increasingly prominent. For example, researches might be interested in testing the effect of different fertilizers on the yield or testing the effect of different species on the time to plants flower at different geographical regions in which data are spatially correlated. This dissertation focuses on, through a simulation study, the integration of spatial analysis with the two-sample t-test and one-way ANOVA. The NORTA (Normal To Anything) method, suggested by Cario and Nelson (1997) to simulate multivariate non-Gaussian data with different covariance structures, is used to simulate spatially correlated Gaussian and non-Gaussian data with a spherical spatial structure. Further, a completely randomized design with subsampling is used because it is simple, less expensive and practical, and provides more observations to estimate the empirical semivariogaram. The first part of this dissertation evaluates the type I error rate of the two-sample t-test and one-way ANOVA with a single spatial structure when the treatments have spatially correlated Gaussian data and different variances. This study provides a guidance to decide when a single spatial structure is inappropriate depending on the difference in treatment variances. The second part of this dissertation focuses on the performance of the two-sample t-test and one-way ANOVA when the treatments have spatially correlated gamma data, equal variance and different skewness. First, the generalized linear mixed model (GLMM) and a single spatial structure are fit to these data, and adjustments to type I error rate and covariance estimates are suggested based on the skewness of gamma distribution. Further, the power of each of these tests is evaluated when the adjusted significance level based on the skewness of the gamma distribution is used. Second, the square root transformation is suggested as an alternative to GLMM for spatially correlated gamma data