Summary: Power Calculation for 2-way ANOVA

[Theresa Foti]

>Does anyone have a reference explaining how to do power calculations
>(beta error/sample size estimation) for 2-way ANOVA designs? Thanks >for
any help!
>
>Theresa Foti, Ph.D.
>Motion Analysis Laboratory
>Shriners Hospitals for Children
>Greenville, SC 29605
>tfoti@infoave.net


Biomch-L members,

Thanks to everyone who generously replied to my request above concerning
references on how to do power calculations for 2-way ANOVA designs! I
should have specified that I needed information for repeated measures
designs because the references and web sites I looked at did not include
this. It seems that this information is hard to find and most statistical
packages do not do power analysis for repeated measures designs.

Several textbooks were recommended:

1. Jacob Cohen (1988) Statistical Power Analysis for the Behavioral
Sciences, 2nd ed., Lawrence Erbaum Assoc. Publishers.

This is a great reference and is a whole textbook devoted to power
analysis, but I did not find any information about how to do 2-way ANOVA
with repeated measures designs. Someone tell me where to find it if it is
in there.

2. Maxwell & Delaney (1990) Designing Experiments and Analyzing Data,
pp. 269-271, p. 751

3. D.C. Montgomery (1984) Design and Analysis of Experiments, 2nd ed.,
NY, John Wiley and Sons.

4. Keppel, G. (1982) Design and Analysis: A Researcher's Handbook,
Englewood Cliffs, NJ, Prentic Hall, ch. 4, p. 67

#2-#4: These had formulas to do 2-way ANOVA power calculations, but not
for repeated measures designs.

5. Jerrold H. Zar, Biostatistical Analysis, 3rd ed., Prentic Hall,
1996, ISBN 0-13-084542-6

I was only able to find the 1st edition in the library which did not have
any information on how to do power calculations at all.

6. Geoffrey Norman & David Streiner (1994) Biostatistics: The Bare
Essentials, St. Louis, Mosby.

7. B.J. Winer (1962) Statistical principles in Experimental Design,
McGraw-Hill, NY.

#6&#7: I did not have a chance to look at these two.

Several web sites were also suggested:

1. http://www.sportsci.org/resource/stats/index.html

(info page)

2. http://www.psychologie.uni-trier.de:8000/projects/gpower.html

(a share-ware program which can be downloaded)

3. http://www.math.yorku.ca/SCS/Demos/power/

(a power calculator web page)

4. http://www.statsol.ie/index.html

("nQuery Advisor" statistical package web page with an on-line demo version)

#1-#3: These did not have 2-way ANOVA rep. meas. power analysis as far as I
could tell.
#4: I did not check this one out.

Some software was recommended:

NQuery Advisor. A program called "PASS" v 6.0 written by Jerry Hintze,
NCSS. The GLM procedure of SPSS also does 2-way ANOVA power analysis
(Steve McCaw graciously ran my data through it, but I'm not sure if it is
possible to specify repeated measures). Possibly the newest version of
SigmaStat. A freeware power analysis program called gpower for the mac.

Here are the replies:
************************************************** ****************
Theresa:

Try D.C. Montgomery (1984). Design and Analysis of Experiments (2nd ed.),
New York: John Wiley & Sons.

Peter
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Peter F. Vint, Ph.D.
Department of Exercise and Sport Science
256 HHP Building, PO Box 26169
University of North Carolina at Greensboro
Greensboro, NC 27402-6169
Phone: (336) 334-3031
Fax: (336) 334-3031
E-mail: pfvint@uncg.edu
URL: http://www.uncg.edu/~pfvint
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
************************************************** ****************
You may want to have a look at Keppel, G. (1982). Design and analysis: A
researcher's Handbook. Englewood Cliffs, NJ: Prentice-Hall. Chapter 4 (pp.
67) is related to this question.

Best wishes,

-- Ben Bardy

-----------------------------------------------------
Benoit G. Bardy

UMR CNRS "Mouvement & Perception"
Faculty of Sport Sciences
University of the Mediterranean
CP 910, 163 ave. de Luminy
F-13288 MARSEILLE cedex 09 (FRANCE)

voice : +33 4 91 17 22 76
lab : +33 4 91 17 22 83
fax : +33 4 91 17 22 52
e-mail : mailto:bardy@laps.univ-mrs.fr
home page : http://www.laps.univ-mrs.fr/umr/personnel/bardy

************************************************** ****************
Hi Theresa:

How are you?

Post hoc power can be calculated using SPSS. When running procedure GLM,
the options allow you to calculate both power and effect size. They do not
provide many details (nor a reference) regarding specifics of technique.

If you do not have SPSS, but you have the data in a file that is readable
by SPSS, I will run this for you if you email the file and details on the
structure.

************************************************** ****************
Theresa-

Check out:

http://www.psychologie.uni-trier.de:8000/projects/gpower.html

This is a share-ware program (DOS + Mac) that is the best I've seen for
calculating power for all manner of statistical tests. I just downloaded it
this past Friday, so I'm still a neophyte. It looks fairly straightforward,
however. Lots of good reference material & step-by-step instructions on
their web page, too.

Hope this helps!

David

************************************************** ****************
Look on www.sportsci.org they have a list of all you need to know about
stats! Its under research resources and then a new view of stats. Good
luck.

Ross Anderson
Department of PESS
SR2-022 Schrodinger
University of Limerick
Tel - +353 (0) 61 202596
e-Mail - ross.anderson@ul.ie

************************************************** ****************
Hi Theresa,
Michael Orendurff here of the Portland Shrine.
Robin Dorociak and I visited about a year ago with ASB
contingent. I hope things are well.
Anyway about your question, chack out
http://www.sportsci.org/resource/stats/index.html
for a good description of power calculations and
assumptions. No doubt Dr. Will Hopkins, who wrote the
page, will respond to this request. Best of luck.

Sincerely,

Michael

************************************************** ****************
Check out Zar, Biostatistical Analysis, 3rd Ed, Prentice Hall 1996, ISBN
0-13-084542-6. This is the one that everyone else plagarizes from. Also,
I believe the new version of SigmaStat handles that as well.
Good luck!
Cliff Les
----------------------------------------
Clifford M. Les, DVM, PhD
Musculoskeletal Biomechanics Laboratory
178 Building 239, Mail Stop 239-11
NASA Ames Research Center
Moffett Field, CA 94035-1000
Voice (650) 604-0983 Fax 604-3954

There are three types of mathematicians:
those who can count,
and those who can't. -Keith Devlin
************************************************** ****************
Theresa,

You may want to have a look at Statistical Power Analysis for the Behavioral
Science by Jacob Cohen, ISBN 0-8058-0283-5.


Bing Yu, Ph.D.
Assistant Professor
Division of Physical Therapy
The University of North Carolina at Chapel Hill
************************************************** ****************
Hello,

This was laid out nicely in the classic paper:

ES Pearson and HO Hartley, "Charts for the Power function for Analysis
of Variance Tests, Derived from the Non Central F Distrubution," Biometrika,
38:112-130, 1951.

Doug
************************************************** ****************
Theresa:

Yes, I have a reference and do them all the time:

Jacob Cohen. (1988). Statistical Power Analysis for the Behavioral Sciences
(2nd Ed.). Lawrence Erlbaum Associates, Publishers.

They publishers still sell the book because it is an industry classic. If
you need further help. Please feel free to contact me.

David Gabriel.
************************************************** ****************
Theresa:

Try the textbook by Jerrold H. Zar entitled "Biostatistical Analysis", 2nd
edition, Prentice Hall Inc., Englewood Cliffs, New Jersey, 1984. Its
helped me through many statistical problems including the one you are
asking about. Good luck.

Braden
************************************************** ****************
Dr. Foti:

I would suggest you take a look at the following book -

Biostatistics: The Bare Essentials by Geoffrey Norman and David Streiner,
St. Louis: Mosby, 1994.

Each chapter covers the power calculation for progressively more
complicated designs, and I think there's a chapter on two-way or multi-way
ANOVA. If not, then there is some allusion to two-way ANOVA at the end of
the one-way ANOVA chapter. This is a very easy reading book. If it
doesn't answer your questions, then I think it will at least get you started.

Kind Regards,

--
----------------------------
Anthony J. Petrella
University of Pittsburgh
petrella@sprite.me.pitt.edu
----------------------------
************************************************** ****************
Theresa -

Check Maxwell and Delaney's Designing Experiments and Analyzing Data (1990)
- a common text for folks in research and design - pp. 269-270 do
explaining - and there's a table in p. 751 that has a Pearson-Hartley
Power Chart.

Good Luck!

Monique Butcher PhD ATC
Asst. Professor
Barry University
11300 NE 2nd Ave.
Miami Shores, FL 33161
(305) 899-3064
************************************************** ****************
Hi Teresa,
The reference that I refer to -- and it's pretty
comprehensive -- is Power Analysis for the Behavioral Sciences, by Cohen.
Academic Press. New York, 1969.

Tim

================================================== =====
Timothy S. Hilliard, Ph.D. ph: 617-373-5994
Assistant Professor fax: 617-373-3161
Physical Therapy Department
Northeastern University
Boston, MA 02115
================================================== =====
************************************************** ****************
Theresa,
check Keppel's statistical book.
Nick
************************************************** ****************
From: greg_lange@srhcc.org
Subject: power analysis
To: tfoti@InfoAve.Net

T,

I have this freeware power analysis program I downloaded called gpower
for the mac. It was recommended on biomch-l I believe. It is a great,
straightforward program, that may meet your needs. If no one else replies
with more detailes info,let me know and I'll try to dig up the background
info on the software.

Greg
************************************************** ****************
Hi Theresa,

Are you interested in the reference because you want to cite it or
because you are interested in the formulae involved in the
calculations. If the latter is true, I can mail or fax you the method
for power calculations. Unfortunately, I don't have a published
reference. My source is a program called PASS v 6.0 (written by Jerry
Hintze, NCSS). So I can print and send you the relevant pages from the
online help. I can't electronically copy the pages from the online help
because the equations are in a graphic format that can't be selected to
copy. Also, if you are just interested in doing power analysis on some
data that you already have, I would be happy to run it through the program
and give you the results.

All the best,

Darryl
************************************************** ****************
Have you seen the power calculator on the Web?

http://www.math.yorku.ca/SCS/Demos/power/


Rob Herbert (R.Herbert@cchs.usyd.edu.au)
School of Physiotherapy, University of Sydney
PO Box 170, Lidcombe NSW 1825, Australia
http://www.cchs.usyd.edu.au/Academic/PT/RHerbert/
phone: (612) 93519380; fax: (612) 93519278

************************************************** ****************
Therasa,

There is a lovely little FREE software package which does what you ask.
You can download it at

http://www.psychologie.uni-trier.de:8000/projects/gpower.html

This program is based on the book:

Statistical power analysis for the behavioural sciences. Jacob Cohen.
Academic Press, New York, 1977.

Hope this helps

Phil

-----------
Philip Riches
Rm 1.69
Queen's Bld
University Walk
Bristol
BS8 1TR

Tel +44 117 9289000 x9860
Fax +44 117 9251194
phil.riches@bristol.ac.uk
************************************************** ****************
Check the book by BJ Winer "Statistical principles in experimental
design", McGraw-Hill, NY, 1962.

Mei Wang
Dept. of Orthopaedic Surgery
University of Louisville
Louisville, Kentucky
m0wang01@homer.louisville.edu
************************************************** ****************
Theresa,
I have just purchased nQuery Advisor
(see:http://www.statsol.ie/index.html) to make such calculations (& similar
ones for virtually any research design) easy. They have a demo page, so
that could possibly help you immediately.

************************************************** ***********
Gordon Chalmers, Ph.D.
Dept. of Physical Education, Health and Recreation
Western Washington University, M/S 9067
Bellingham WA
U.S.A.
98226-9067

chalmers@cc.wwu.edu
http://www.wwu.edu/~chalmers
Phone: (360) 650-3113
FAX: (360) 650-7447
************************************************** ****************
Point your browser to www.sportsci.org within which you'll find a pretty
neat (and evolving) on-line statistics text.
Cheers
Rod
--
Mitchell & Whiteley Physiotherapy.
************************************************** ****************
Montgomery, D.C. (1984) Design and Analysis of Experiments. New York:
Wiley.

************************************************** ****************
Dear Theresa,

I can recommend the book of Joseph L. Fleiss ("The design and
analysis of clinical experiments"; John Wiley & Sons; 1986).

I hope this information helps.

Christian Peham

************************************************** ******
* Dr.Christian Peham
* email: Christian.Peham@vu-wien.ac.at
* Clinic for Orthopaedics in Ungulates
* Locomotion Research Group
* University of Veterinary Medicine Vienna
* Phone: +43-1-250 77/5506; Fax: +43-1-250 77/5590
* Josef Baumanngasse 1; A-1210 Wien
* http://www.vu-wien.ac.at/i111
************************************************** ******
************************************************** ****************

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