ADVANCED STATISTICS POWER ANALYSIS & SAMPLE SIZE

Osama A Samarkandi, PhD-RN, NIACBSc, 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.

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).

WHAT IS POWER ANALYSIS

The power of a study is determined by three factors: Sample size, Alpha level (degree of freedom), and Effect size.

WHAT IS POWER ANALYSIS

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

2

Diffdn

SAMPLE SIZE

How much data do you need? That is, how many subjects should you include in your research.

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,

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

22

1

f total

between

SSSS

2

n

22

EFFECT SIZE

Power analysis builds on the concept of an effect size, which expresses the strength of relationships among research variables.

G-POWER

G-POWER 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.

REFERENCES

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 !