Understanding Statistical Analysis and Modeling is a text for graduate and advanced undergraduate students in the social, behavioral, or managerial sciences seeking to understand the logic of statistical analysis. Robert Bruhl covers all the basic methods of descriptive and inferential statistics in an accessible manner by way of asking and answering research questions. Concepts are discussed in the context of a specific research project and the book includes probability theory as the basis for understanding statistical inference. Instructions on using SPSS® are included so that readers focus on interpreting statistical analysis rather than calculations. Tables are used, rather than formulas, to describe the various calculations involved with statistical analysis and the exercises in the book are intended to encourage students to formulate and execute their own empirical investigations.

# Part Three: Statistical Inference and Probability

Statistical Inference and Probability

### Why Probability Theory?

While statistical analysis is concerned with actual observations of phenomena, probability analysis is concerned with hypothetical observations of phenomena (said to be events), and both statistical estimation studies and statistical association studies rely on logic based on probability analysis:

• In an estimation study, an investigator is interested in describing the pattern of occurrences of a property of a set of phenomena (said to be a “population”), but for logistical reasons not all the phenomena of interest can be collected for observation. In such cases, the investigator will collect a small subset of the population (said to be a “sample”) and use the pattern of occurrences of the property found in the sample to estimate the pattern of occurrences of ...