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.

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.

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.