Introduction

In this brief chapter, we introduce yet another data generation process called the two box model. We will see how the sample average difference is distributed through Monte Carlo simulation and analytical methods.

The two box model is an extension of the polling box model (explained in detail in Chapter 10) and provides further practice with inferential methods. Although the rapidly expanding list of box models may seem daunting, do not despair. The same basic principles about variability of sample statistics and understanding the sampling distribution underlie all data generation processes.

Our approach in presenting the various box models is meant to illustrate the point that a properly configured box model can represent a wide variety of chance processes. We are also slowly building toward the box model that underlies regression analysis in an inferential setting.

Section 12.2 introduces the two box model, and Section 12.3 offers a Monte Carlo simulation to explore the sampling distribution of the same average difference. Section 12.4 presents a real-world application of the two box model.

Two Boxes

The two box model is essentially two polling box models combined. Instead of estimating a parameter or testing a hypothesis about a single population – for instance, the average wage of California residents – we are interested in a comparison of two populations (e.g., the difference in the average wages of California and Nevada residents).