Introduction

This Chapter describes some of the statistical methods for developing point and interval estimators. Most statistical problems encountered by behavioral ecologists can be solved without the use of these methods so readers who prefer to avoid mathematical discussions may skip this Chapter without compromising their ability to understand the rest of the book. On the other hand, the material may be useful in several ways. First, we believe that study of the methods in this Chapter will increase the reader's understanding of the rationale of statistical analysis. Second, behavioral ecologists do encounter problems frequently that cannot be solved with ‘off the shelf’ methods. The material in this Chapter, once understood, will permit behavioral ecologists to solve many of these problems. Third, in other cases, consultation with a statistician is recommended but readers who have studied this Chapter will be able to ask more relevant questions and may be able to carry out a first attempt on the analysis which the statistician can then review. Finally, many behavioral ecologists are interested in how estimators are derived even if they just use the results. This Chapter will help satisfy the curiosity of these readers.

The first few sections describe notation and some common probability distributions widely used in behavioral ecology. Next we explain ‘expected value’ and describe some of the most useful rules regarding expectation. The next few Sections discuss variance, covariance, and standard errors, defining each term, and discussing a few miscellaneous topics such as why we sometimes use ‘n’ and sometimes ‘n – 1’ in the formulas. Section 2.10 discusses linear transformations, providing a summary of the rules developed earlier regarding the expected value of functions of random variables.