## WISE Power Tutorial

**Statistical Power**: Statistical power is the probability of correctly rejecting a false null hypothesis when a specific alternate hypothesis is true.

**Example:** Suppose an educational training company created a program named “ACE” to help students improve their scores on a standardized exam. The company spokesperson boasts that their graduates score higher on a standardized test than the population of individuals who do not participate in their training course. The null hypothesis is that graduates of the ACE program do not score higher than non-graduates. Power analysis allows us to determine how likely it is that a test of statistical significance will support the claims of the training company (i.e., reject the null hypothesis). We also can determine how many cases we need in our sample to attain a specific level of statistical power.

**Purpose of the Tutorial:** This tutorial is designed to provide a conceptual, non-mathematical, overview of the factors that affect power. You will learn how statistical power is influenced by four features of the test situation: the size of the difference between the actual population mean and the null hypothesized mean (μ_{1} – μ_{0}); variability of scores within groups (σ); sample size (n); and alpha error (α). Further, you will use an interactive applet that allows you to manipulate features of the test situation and immediately see the effect on statistical power. The mathematics for power calculations are provided at the end of this tutorial.

**What do I need to know?** You should have an understanding of hypothesis testing concepts and procedures. You may want to complete the WISE Hypothesis Testing Tutorial prior to the power tutorial. The examples in this power tutorial are similar to those used in the hypothesis testing tutorial.

**What do I need?** If you don’t need to turn in your work, you can proceed with the tutorial.

**If your instructor requires you to turn in a paper copy, you have three options.**

- You can record information on-line during the tutorial by following instructions, and at the end you can print out the worksheets with a record of your work.
- You can print out blank worksheets now, so you can record your findings on paper.
- You can print out the entire tutorial, including the questions on the worksheets.

**Instructions:** You will be asked to use the Power applet to simulate sampling data in different situations. You will record data and then interpret your findings in terms of statistical power. Along the way you will be asked questions to test your understanding and you will be given feedback regarding your answers. The end of the tutorial includes some “thought” questions. If you leave the tutorial, you can use the menu on the left to jump to any place in the tutorial when you return.

**Optional review material (one page each):**

- Review Sampling Distribution of the Mean
- Review Central Limit Theorem
- Review
*z*-scores and the Normal Distribution

If we know the mean and standard deviation (i.e., μ and σ) for a normal distribution, then we know everything about the distribution. We can compute the probability of observing an *x* score above or below any specific value. Fortunately, tables and computer programs such as the *p*–*z* converter are available to help us find these values.

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