one of these days i'll work up some better graphics .... :)meanwhile, thanks to Sokal/Rohlf and Biometry...
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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