Probability Testing

You almost certainly engage in decision making every day. Usually, you choose an option because you believe that it will have a more pleasing outcome than the other choice(s). If you knew your likelihood of succeeding or failing, you would have an even easier time making a decision. Each decision you make is influenced by probability.

As you would expect, psychologists like to keep the probability of coming to false conclusions in research as low as possible, though you know that it is almost impossible to make a decision that is entirely free of error. But what are the implications of making different types of errors? Are all errors equally dangerous, or do some have more critical importance than others? Consider the four possible decisions a jury could reach in a murder trial when the sentence is the death penalty. If the jury's verdict is correct, either an innocent defendant goes free or a guilty defendant is convicted. However, what about when the jury makes an error, and a guilty defendant goes free or an innocent man is convicted? How do we calculate the probability of each of these types of errors?

Probability tests might help you make decisions of low importance, such as purchasing goods, but they can also play a role in making critically important decisions. For example, scientists often use probability to evaluate the safety of drugs for human use. This Discussion presents an exercise in probability in the context of a research study for a new drug to treat depression.

To prepare for this Discussion, review the textbook sections on probability and Type I and Type II errors.

Scenario:

Imagine that a pharmaceutical company is testing a new medication to treat major depression in people whose symptoms have not been helped by existing medications. You are part of a panel of professionals who must decide if the drug should be considered safe for human trials. The null hypothesis is that the drug is considered to be safe. The alternative hypothesis is that the drug is considered to be unsafe.

1. Keeping in mind that errors are interpreted in relation to the hypotheses, interpret the results of the study if a Type I error had been made. Next, interpret the results of the study if a Type II error was made. That is, explain what Type I and Type II errors would look like in this scenario.

2. Based on your interpretation of Type I and Type II errors, which do you think would be worse to make in this study and why?

3. Discuss what would be better to use - an alpha of .05 or an alpha of .01 in this study. Explain and provide a rationale for your choice.