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Statistical Power and Sample Size Calculation

General comments:

There is no one all-inclusive formula for calculating sample size.  Calculating sample size (or statistical power, type 2 error) depends on the following:
  • The size of the difference that has practical meaning to the experimenter.  (The effect size.)
  • The amount of variation.
  • Other considerations, including:  The type of data, the statistical method, the null hypothesis and null distribution.

BASIC CONCEPTS of Power Analysis

Types of Error

Type 1 and Type 2 Error

Effect Size

The size of the difference that is meaningful, that the experimenter wishes to detect.

Wikipedia - Effect Size

Standardized Effect Size

The effect size divided by the standard deviation.


(Root Mean Sum Standardized Effect Size) for ANOVA

Null Distribution

The null distribution is influenced by the type of data, the null hypothesis, the experimental design - including randomization, the statistical method.

The null distribution might loosely be thought of as being the population distribution (which can not be known) if there were no differences between groups in the population

A hypothesis test asks the question ... if there were no differences between groups in the population, what are the chances of seeing the differences that may be present in the sample (experimental) data?

Other Concepts

noncentrality parameter

the number of uncensored observations in the presence of censoring

simulation-based approach


StatSoft - Power Analysis 

NIST - Sample size computations (Univariate)
  1. Sample size for mean
  2. Sample size for standard deviation
  3. Sample size for proportion
  4. Sample size for defect densities

Arsham - Power of a Test and Size of an Effect

Cornell paper on Experimental Power and Design
  • Includes R code for t-test, O-C curves, and for simulation.

A free statistical power analysis program, G*Power 3, is available at:
  • (I have not vetted this software myself, but the odds are good that, if properly used, the results are fine.)

Power Analysis and Sample Size using R

n = both
n = embarrassingly low
n = wasted lab time
n = anemic
n = irresponsible