## Make Decisions with Sequential Observations: A Simulation

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Theodore W. Frick

Copyright 2005
(revised June 27, 2012)

This simulation illustrates how to make a specific decision when making sequential observations. It employs a method of reasoning that is based on Bayes Theorem and Abraham Wald's Sequential Probability Ratio Test. These methods have been used in computer adaptive testing for determining mastery or nonmastery of educational objectives (e.g., see Frick, 1992; Welch & Frick, 1993), and more recently in computerized classification testing. These methods have also been used in quality control in manufacturing and other settings where sequential sampling is both practical and a more efficient way to reach a specific decision.

You can play with this simulation to see how decisions can be made with uncertainty, so you'll know the chances that you have made the right decision for a specific case. Feel free to experiment, to see what happens under different assumptions and outcomes of observations. You might be surprised to discover how few observations are needed to reach a decision under some conditions, and how many are needed for others.

Just to make this concrete, let's say you are an algebra teacher and you have a student named Sam. You want to know whether Sam can solve quadratic equations. If he can, then you don't need to teach him quadratic equations, and he could spend his time learning something new. Otherwise, you will need to teach him. So the decision has consequences for both Sam and you his teacher.

As another example, suppose you are a parent, you want to know whether your teenage daughter, Susie, can drive a car safely. If she can, you'll let her drive your car. Othewise, you won't. There are big consequences here. If Susie is not able to drive safely, she could kill or injure herself or others if she has an accident. It's your car and you need to decide if you will let her drive it by herself.

In both examples, you need to make a decision about a specific case and choose between 2 alternatives: whether or not to teach Sam quadratic equations, or to let Susie drive your car.

#### 1. Enter labels for two mutually exclusive alternatives, one of which you need to choose--based on observations you will make.