>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: 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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