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Why you need to choose sample size before doing a study. It is tempting to analyze your data as you go. Stop when you get statistical significance, and keep going otherwise. This article explains the major problem with this sequential approach (unless you use special analysis techniques).
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What values of alpha and power should I pick? To compute sample size, you must choose a value for alpha (the significance level of the comparison) and power (the chance of finding a "significant" differenence if a difference of a specified size actually exists). While many investigators choose standard values of 0.05 for alpha and 80% for power, this article explains why you should choose values according to the scientific context of the experiment.
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Why it doesn't help to use standard definitions of effect size. Computing sample size requires that you decide how large a difference you are looking for -- how large a difference (association, correlation..) would be scientifically interesting. Some investigators answer this question using the concept of "standard effect sizes". This article explains why this approach is rarely helpful.
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Computing sample size for data to be analyzed with nonparametric tests. Standard methods for computing sample size assume you will assume that your data are sampled from a Gaussian distribution. This article explains how to compute sample size when you plan to analyze the data with nonparametric tests.
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Links to other sites |
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Chapter 2 from VanBelle's Statistical Rules of Thumb This is the only chapter of VanBelle's exellent book, Statistical Rules of Thumb, to be published online. As with the rest of the book, this chapter is eclectic with practical advice (and shortcuts) you won't find anywhere else.
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Sample size and statistical power A great set of "slides" (as a pdf file) giving equations and principles for sample size compuations for many experimental design. By Diane Catellier, Dept. Biostatistics
Univ. North Carolina.
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Power analysis and sample size determination. Concepts and software tools. A terrific article by Roger J. Lewis clearly explaining the principles, and with an extensive bibliography.
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Some practical guidelines for effective sample-Size determination. This is an earlier draft of an article published as Lenth, R. V. (2001),
``Some Practical Guidelines for Effective Sample Size Determination,'' The
American Statistician, 55, 187-193. It explains the principles clearly and concisely. In addition, Lenth points out two mistakes that are commonly made. One is to compute power for a completed study to have the difference you already found. Some programs compute this power, and he explains why this this is not helpful. The second mistake is to classify a difference as "small",
"medium" or "large" based on comparing the difference between means with the
standard deviaiton within groups. The decision about which effects are small
or large must be made in a scientific context, and it is not helpful to compare a difference between means with a standard deviation.
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UCLA's web-based sample size calculators. Calculate power for a specified sample size, or sample size to achieve a specified power for several experimental designs. These calculators assume you know what you are doing, and provide very little explanation.
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What is power analysis? This page, and the next three it links to, present a concise explanation of power analysis and sample size computations.
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List of free on-line power and sample size calculators.
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Power and Precision This is the manual for the program with the same name. Much of the
manual, of course, will be of interest only if you use that program. But the
majority of the manual is general explanations that would be of interest
even if you use other programs. Chapter 2 is an excellent overview of
power and sample size computations. Later chapters go through the analyses one
by one. The information on t tests and comparing two proprtions is the same as
you'll find in lots of places, but this may be the best resource for learning
about sample size determinations in survival analysis, logistic
regression, and analyses of contingency tables (larger than 2x2).
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Recommended books |
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Adequacy of Sample Size in Health Studies
by Stanley Lemeshow, David W. Hosmer, Janelle Klar, Stephen K. Lwanga, and World Health Organization, John Wiley & Sons, February, 1990.
ISBN 0471925179. List price: US$75.00.
Buy from amazon.com for US$75.00
| A clear description of the theory of power and sample size calculations, accompanied by lots of tables. Covers comparing two means and two proportions, and some quality control issues. But nothing about ANOVA, survival analysis, or more advanced stats. |
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How Many Subjects? : Statistical Power Analysis in Research
by Helena Chmura Kraemer, Sage Publications, November, 1987.
ISBN 0803929498. List price: US$36.00.
Buy from amazon.com for US$36.00
| This short book clearly explains general principles. It also applies them, with a bit of math, to different kind of analyses. It includes a good discussion of ANOVA but not survival analysis. |
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Statistical Power Analysis for the Behavioral Sciences
by Jacob Cohen, Lawrence Erlbaum Assoc, 15 January, 1988.
ISBN 0805802835. List price: US$99.95.
Buy from amazon.com for US$99.95
| A comprehensive book about computing power and sample size in many situations, including ANOVA but not survival analysis. About half the book is a discussion of principles; the other half is a set of tables.
Cohen pushes the concept of "effect size". No matter what kind of data you collect, you can reduce the results down to an effect size, and can compute sample size and power based on effect size. This is a helpful concept that unifies statistical methods that are otherwise somewhat distinct. But the concept can be overused. Cohen defines "small" and "large" effects. But effect size is simply the ratio (for a t test) of the difference between means, to the SD you see within groups. I think that deciding whether an effect is "small" or "large" must be based on the kind of data you collect and the decisions you'll make based on the findings. I think the idea that you can define whether a difference is "large" or "small" simply based on numbers (and not based on scientific context) leads to misleading conclusions. |
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Power Analysis for Experimental Research : A Practical Guide for the Biological, Medical and Social Sciences
by R. Barker Bausell and Yu-Fang Li, Cambridge University Press, October, 2002.
ISBN 0521809169. List price: US$65.00.
Buy from amazon.com for US$65.00
This book discusses t tests, ANOVA (including complicated designs) with a good conceptual explanation of the principles of power analysis. Chapter 2 is particularly interesting with a list of eleven strategies to increase the power of an experiment.
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Survival Analysis: A Practical Approach
by Mahesh K. B. Parmar and David Machin, John Wiley & Sons, 21 November, 1995.
ISBN 0471936405. List price: US$140.00.
Buy from amazon.com for US$140.00
| Chapter 10 is the best explanation I've seen on sample size calculations for survival analysis. |
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Modelling Survival Data in Medical Research, Second Edition
by D. Collett and David Collett, Chapman & Hall/CRC, 01 March, 2003.
ISBN 1584883251. List price: US$59.95.
Buy from amazon.com for US$48.56
| Chapter 10 explains sample size computations for studies to be analyzed by survival analysis. |
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