Transcript Power Analysis

ADVANCED STATISTICS
POWER ANALYSIS & SAMPLE SIZE
Osama A Samarkandi, PhD-RN, NIAC
BSc, GMD, BSN, MSN
OBJECTIVES
Normal Distribution Function, and Curve,
 Standard Deviation (σ), and Quality,
 Introduction to power analysis,
 Effect size, Degree of freedom, and Sample
size calculations,
 G-Power application,
 Type of test required.
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NORMAL DISTRIBUTION
STANDARD DEVIATION & QUALITY
zσ Percentage within CI Percentage outside CI Fraction outside CI
1σ 68.2689492%
31.7310508%
1 / 3.1514872
2σ 95.4499736%
4.5500264%
1 / 21.977895
3σ 99.7300204%
0.2699796%
1 / 370.398
4σ 99.993666%
0.006334%
1 / 15,787
5σ 99.9999426697%
0.0000573303%
1 / 1,744,278
6σ 99.9999998027%
0.0000001973%
1 / 506,797,346
7σ 99.9999999997440% 0.000000000256%
1 / 390,682,215,445
WHAT IS POWER ANALYSIS
Power analysis is a method of reducing the
 risk of Type II errors and for estimating their
occurrence
 Power, by definition, is the ability to find a
statistically significant difference when the null
hypothesis is in fact false (UWM).
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WHAT IS POWER ANALYSIS
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The power of a study is determined by three
factors:
 Sample
size,
 Alpha level (degree of freedom), and
 Effect size.
WHAT IS POWER ANALYSIS
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The significance criterion; Other things being equal, the
more stringent this criterion, the lower the power.
The sample size, N. As sample size increases, power
increases.
The population effect size, gamma (γ). Gamma is a
measure of how wrong the null hypothesis is, that is,
how strong the effect of the independent variable is on
the dependent variable in the population.
Power, or 1-β . This is the probability of rejecting
the null hypothesis.
SAMPLE SIZE
 
n  
 d Diff



2
SAMPLE SIZE
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How much data do you need? That is, how
many subjects should you include in your
research.
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The answer to this question is very simple -- the
more data the better. The more data you have,
the more likely you are to reach a correct
decision and the less error there will be in your
estimates of parameters of interest
SAMPLE SIZE … CONT,
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Before you can answer the question “how many subjects do I
need,” you will have to answer several other questions, such
as:
How much power do I want?
What is the likely size (in the population) of the effect I am
trying to detect, or, what is smallest effect size that I would
consider of importance?
What criterion of statistical significance will I employ?
What test statistic will I employ?
What is the standard deviation (in the population) of the
criterion variable?
For correlated samples designs, what is the correlation (in
the population) between groups?
EFFECT SIZE
 
2

2
f 
2
1 
2
SSbetween
 
SStotal
2
2
n
EFFECT SIZE
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Power analysis builds on the concept of an
effect size, which expresses the strength of
relationships among research variables.
G-POWER
G-POWER
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There are several different sorts of power analyses
A Priori Power Analysis. This is an important part of planning research.
You determine how many cases you will need to have a good chance of
detecting an effect of a specified size with the desired amount of power.
A Posteriori Power Analysis. Also know as “post hoc” power analysis.
Here you find how much power you would have if you had a specified
number of cases. Is it “a posteriori” only in the sense that you provide
the number of number of cases, as if you had already conducted the
research.
Retrospective Power Analysis. Also known as “observed power.” There
are several types, but basically this involves answering the following
question: “If I were to repeat this research, using the same methods
and the same number of cases, and if the size of the effect in the
population was exactly the same as it was in the present sample, what
would be the probability that I would obtain significant results?”
TYPE OF TEST REQUIRED
REFERENCES
Faul, F., Erdfelder, E., Buchner, A., & Lang, A.-G.
(2009). Statistical power analyses using G*Power
3.1: Tests for correlation and regression analyses.
Behavior Research Methods, 41, 1149-1160.
 Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A.
(2007). G*Power 3: A flexible statistical power
analysis program for the social, behavioral, and
biomedical sciences. Behavior Research Methods,
39, 175-191.
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REFERENCES
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www.StatPages.net - This site provides links to a number of online power
calculators.
Power analysis for ANOVA designs - an interactive site that computes that
calculates power or sample size needed to attain a given power for one
effect in a factorial ANOVA design. This particular program can be found
elsewhere on the web.
PASS 2008 - a commercial site that allows you to download a 30 day trial
version of their program. This is the software that I use. I don't think it's
perfect, but I haven't come across anything that I think is better. Unlike
many programs, PASS allows users to compute power for repeated
measures designs.
SPSS makes a program called SamplePower. I have only take a cursory look
at it, and was disappointed that it didn't include repeated measures
designs. However, one nice feature of the software is that it will output a
complete report on your computer screen which you can then cut and paste
into another document.
Thank you !