2 Introduction to modeling, simulation, and hypothesis testing

In this unit, you will explore ideas of randomness. Randomness permeates, and is, in fact, fundamental to statistics. You will learn how to use TinkerPlots™ to model several random processes and generate outcomes from those models. By generating data from different models, you will gain experience in considering the variation in outcomes that is produced by these random processes. This consideration will help you understand and overcome many misleading human intuitions about randomness.

First, you will be introduced to the Monte Carlo simulation process and you will learn how to carry out a Monte Carlo simulation using TinkerPlots™. This process allows you to quickly generate multiple data sets from a model in order to carry out hypothetical experiments. For example, we could ask the question: How likely is it to rain three out of the five days on my vacation given a particular forecast? By modeling the forecast and repeatedly generating data for the five days of vacation, we can then answer this question.

Then, you will explore how to use Monte Carlo simulation to evaluate statistical hypotheses. In addition to evaluating hypotheses, you will learn about common misconceptions regarding model evaluation (e.g., we can never say a model produced the data, only that it produces results compatible with the data), and how to use probabilistic language when providing an “answer” to a research question.

Outline and goals of Unit 2

The following schematic outlines the course readings and in-class activities for Unit 2.

Unit outline
2.1     📖   Modeling and simulation
2.2     🔨   Pet factories
2.3     📖   Monte Carlo simulation
2.4     🔨   Building Monte Carlo simulations
2.5     📖   Regularity in randomness
2.6     🔨   Montana political parties
2.7     📖   Introduction to statistical hypothesis testing
2.8     🔨   Monday breakups
2.9     📖   Null hypotheses
2.10     📖   A closer look at statistical hypothesis testing
2.11     🔨   A preference for 7?
2.12     📖   Quantifying results: p-values
2.13     🔨   Facial prototyping
2.14     📖   Drawing conclusions and ‘statistical significance’
2.15     🔨   Gender and congress
2.16     🔨   Review activity: Racial disparities in police stops
2.17     📖   Unit 2 summary

As you progress through the unit, remember that the modeling process is a creative process that can often be very challenging. At times, this might lead to frustration as you are learning and practicing some of the material. But, as Mosteller et al. (1973) remind us, it is also a profitable experience since, “modeling is not only a technique of statistics…it is a method of study which can be applied in many other fields as well” (p. xii).5