Chapter 5: Analysing the Data |

## PowerThere are several interrelated issues to consider when we think about setting up a research design to evaluate a statistical hypothesis. LetÕs depict a hypothesis testing situation graphically using two normal distributions Š one to represent the sampling distribution for the null hypothesis and the other to represent the sampling distribution for the alternative hypothesis. We use normal distributions because of the In general terms, suppose we evaluate the specific hypothesis that µ has one value (µ Ho) or another value (µ H1) using a sample of size N:
There are four factors that interact when we consider setting significance levels and power: 1. 2. 3. 4. Once we know any three of these quantities, the fourth one is automatically determined. LetÕs examine the ways these factors can be varied to increase or decrease the power of a statistical test. 1. One way to increase power is to Note how the size of the power area is expanded when is relaxed. 2. Another way to increase power is to This happens because the variance of a sampling distribution gets 3. Yet another way to increase power is to look only for The larger effect size pulls the two distributions apart, thus lessening their overlap; consequently, differences are easier to detect. An interesting consideration here is if you need to be able to detect a fairly small effect size, you would need to either alter (by relaxing it) or N (by increasing it) or both in order to keep from losing power. The most common way of increasing power in an experiment or survey is to increase sample size. By doing this you are more likely to pick up a real difference if one is really there. 4. Finally, power can be increased if a directional hypothesis can be stated (based on previous research findings or deductions from theory). |

© Copyright 2000 University of New England, Armidale, NSW, 2351. All rights reserved Maintained by Dr Ian Price |