ABSTRACT

Statistical inference is about probabilistic distributions of data, model error, and model parameters. Because statistical thinking is inductive in nature, distributional assumptions are the basis of statistics analysis and inference. When using a statistical procedure, exploratory analysis of the data should be performed to check whether these assumptions are met. Although some statistical procedures are robust against the departure of probabilistic assumptions, understanding these underlying assumptions is an important part of learning statistics. Especially when applying statistics in ecological and environmental studies, an understanding of these assumptions will help us avoid some commonly seen mistakes in applying statistics. A thorough exploratory analysis in terms of statistical assumptions often relies on graphical presentation of data. Graphical presentation of the data often serves as the bridge linking an ecological or environmental problem and an abstract statistical representation of the problem. This book emphasizes graphical procedures for checking important assumptions. In this chapter, three commonly used assumptions are briefly discussed. In the rest of the book, assumptions of each statistical procedure will be discussed in detail with graphical methods for checking the compliance of these assumptions.