Power Analysis for BeginnersPresentation Transcript
Power Analysis Have you done yours today? G. F. Barbato
What is “power”?
The notion of “Statistical Power” is really a very simple concept derived from the central ideas of logic.
Tests on means are actually test of a hypothesis give that the statement to be tested is the null hypothesis (H 0 ).
We then can create an alternate hypothesis (H A ), that is essentially a statement contradicting the null hypothesis.
This then leads us to two possible tests
1. Reject H 0 , or
2. Fail to reject H 0.
We then accept a certain probability (the level) such that: H 0 : ≤ 0 , or H A : > 0 .
The “power” of a test is the probability of rejecting H 0 when H A is true!
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 from the null hypothesis (2.5% shaded in each tail). [Graphic and Data from Biometry (2 nd edition) by Sokal & Rohlf, 1981]
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 1 approaches 0 . [Graphic and Data from Biometry (2 nd edition) by Sokal & Rohlf, 1981]
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…). [Graphic and Data from Biometry (2 nd edition) by Sokal & Rohlf, 1981]
To put it simply
The basic equation to determine power is:
Use and OC curves to determine the necessary number of observations to obtain the desired power!
Improving the power of a test
To improve the power of a test, holding all else constant, we MUST increase sample size.
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.
Use a one-tailed test.
More complex designs.
How to calculate power
One of the best places to go is the series of power ‘calculators’ at the “Iowa Stat” WebSite.
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).
Now that you’ve 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.)
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