1. Power Analysis Have you done yours today? G. F. Barbato

2. What is power?

The notion of Statistical Power is really a very simple concept derived from the central ideas of logic. 3. Tests on means are actually test of a hypothesis give that the statement to be tested is the null hypothesis (H 0 ). 4. We then can create an alternate hypothesis (H A ), that is essentially a statement contradicting the null hypothesis.

5. Hypothesis testing

This then leads us to two possible tests

• 1.Reject H 0 , or 6. 2.Fail to reject H 0.

We then accept a certain probability (thelevel) such that: H 0 : 0 , or H A :> 0 . 7. The power of a test is the probability of rejecting H 0when H Ais true!

8. The Basic Idea

Expected distribution of means of samples of 5 housefly wing lengths from normal populations.The center curve represents the null hypothesis H0=45.5, curves to the side are alternate hypotheses.Vertical lines delimit the 5% rejection regions fro the null hypothesis (2.5% shaded in each tail).

9. Increase in Type II error

This illustrates the increase in probability of Type II error a the alternative hypothesis approaches the null hypothesis, i.e., as 1approaches 0 .

10. The Power curve!

By graphing the incremental graphs in the prior slide, we can see that the power drops off sharply as the alternative hypothesis approaches the null (which we can intuitively grasp).

11. To put it simply

The basic equation to determine power is:

Useand OC curves to determine the necessary number of observations to obtain the desired power!

12. Improving the power of a test

To improve the power of a test, holding all else constant, we MUST increase sample size. 13. However, power can also be changed by changing the nature of the test.

• Use non-parametric tests whose power curves are less affected by assumptions of anova. 14. Use a one-tailed test. 15. More complex designs.

16. How to calculate power

One of the best places to go is the series of power calculators at the Iowa Stat WebSite. 17. http://www.stat.uiowa.edu/%7Erlenth/Power/index.html This site will allow you to estimate the power for a variety of models and means testing (with both equal and unequal variances).

18. Now that youve tested the H 2 O

These sites have a comprehensive list of resources that will help you to automatically calculate statistical power given nearly any experimental design.Even better, it will help to design experiments for you (e.g., randomized blocks, treatment placement, etc.) 19. For direct calculation of sample size, try here: http://home.clara.net/sisa/sampshlp.htm or, for multiple comparisons, here: http://www.stat.ohio-state.edu/~jch/ssinput.html