# 15.9: Power of Within-Subjects Designs Demo

• • Contributed by David Lane
• Associate Professor (Psychology, Statistics, and Management) at Rice University

Learning Objectives

• State the relationship between the correlation and power
• State the relationship between variance and power
• State the relationship between the difference in population means and power
• State the effect of using a one-tailed test on power

## Instructions

This simulation demonstrates the effect of the correlation between measures in a one-way within-subjects ANOVA with two levels. This test is equivalent to a correlated t test. The default values for this demonstration are for an experiment with $$10$$ subjects each measured under two conditions. The population difference for the two conditions is $$1.85$$ and the variance in each of the conditions is $$4.0$$. The graph shows the power of the test as a function of the population correlation between the two scores for the $$0.10$$, $$0.05$$, and $$0.01$$ significance levels. The power of an independent-groups $$t$$ test (which assumes the correlation is $$0$$) is shown by the $$x's$$.

Experiment with different combinations of the parameters. Is the correlation an important factor in power?

## Illustrated Instructions

Video Demo

The video begins by changing the population variance to $$8$$ and increases the sample size to $$25$$ and then reduces it to $$5$$. Notice the impact that these changes have on the relationship between power and population correlation. The video concludes by changing the mean difference to $$4$$.

## Contributor

• Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University.