## Mathematics Department Journal Articles

#### Title

The Importance of Teaching Power in Statistical Hypothesis Teaching

#### Document Type

Article

Published in the International Journal for Mathematics Teaching and Learning, December 21, 2012.

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#### Keywords

statistical power; statistics education; hypothesis testing

#### Publisher

Centre for Innovation in Mathematics Teaching

#### Publication Source

International Journal for Mathematics Teaching and Learning

#### Abstract

In this paper, we discuss the importance of teaching power considerations in statistical hypothesis testing. Statistical power analysis determines the ability of a study to detect a meaningful effect size, where the effect size is the difference between the hypothesized value of the population parameter under the null hypothesis and the true value when the null hypothesis turns out to be false. Although power is an important concept, since not rejecting a false hypothesis may result in serious consequences, it is a topic not often covered in any depth in a basic statistics class and it is often ignored by practitioners. Considerations of power help to determine appropriate sample sizes for studies and also force one to consider different effect sizes. These are important concepts but difficult for beginning statistics students to understand. We illustrate how one can provide a simple classroom demonstration; using applets provided by Visual Statistics 2.0, of how to calculate power and at the same time convince students of the importance of power considerations. Specifically, for beginning students, we focus on a common statistical hypothesis testing example, a test of hypothesis of means concerning one sample. For this case, we examine the power of the test at varying levels of significance, sample sizes, standard deviations and effect sizes, all factors which are important to the results of a testing situation. We then illustrate how students, depending on time and resources, can reproduce these power calculations themselves using several statistical software packages. The use of statistical software will also be very helpful to the students who upon graduation become the practitioners. Finally, examples of power analyses are provided for more advanced problems such as analysis of variance and regression analysis, which might be used in a second semester statistics course.

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