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Some Notes on Power Analysis
What is Power Analysis?
Power Analysis is a procedue that determines if the proposed sample size is large enough to allow a fair test for the proposed statistical hypothesis.
The purpose of research projects is to search for evidence that some feature (a parameter) of a population of interest is different from the hypothesized value.

Some Common Power Analysis Terminology

Type I Error (a)
Type I error is defined as the probability of rejecting the null hypothesis when the null hypothesis is the true hypothesis.

Type II Error (b)
Type II Error is defined as the probability of not rejecting the null hypothesis when the alternate is the true hypothesis.

Power [1]
Power is defined as the probability of rejecting the null hypothesis when the alternate hypothesis is true. Power is the compliment of Type II Error (1-b).

Effect Size[1] [2] [3]
Effect size is defined as the measure of difference in some distribution feature of one or more variables of interest from two or more groups.

For some general notes on power analysis click here

For a list of common statistical/clinical terms with their definitions click here

Dr. Inkyung Jung from University of Texas Health Science Center at San Antonio has provided a great set of notes for power and sample size calculation. CLICK HERE to view these notes.

Power Analysis by model types with examples

The links provided below are some of the notes found in Dr. Karl Wuensch's website from the Department of Psychology at East Carolina University

  1. Power analysis for one and two sample designs
  2. Sample Size estimation for common designs to acheive sufficient power
  3. Power Analysis for t Tests using GPower (one sample, two samples, Pearson r)
  4. Power Analysis for One-Way Independent Samples ANOVA using GPOWER
  5. Power Analysis for One-Way Repeated Measures ANOVA
  6. Power Analysis for an ANCOV
  7. Power Analysis for a Correlation Coefficient (bivariate or multiple) using the R2 program by Steiger and Foulad

Check out Statistic Lessons, by DR. Karl Wuensch, for notes on other statistical topics.

Softwares for Power Analysis

If you are not familiar with the capabilities of the power analysis softwares given below, then read A Review of Statistical Power Analysis Software by Len Thomas and Charles J. Krebs.

NCSS (Number Cruncher Statistical System) - A comprehensive and accurate, easy to learn, statistical system for Windows users. They also list a Windows program for Power Analysis and Sample Size (PASS) determination for a wide range of statistical tests. For more information on NCSS visit

PASS (Power Analysis and Sample Size) - PASS lets you solve for power, sample size, effect size, and alpha level with charts, graphs, numeric tables and text summaries. PASS is a standalone system and is compatible with other statistical softwares. Although it is integrated with NCSS, you do not have to own NCSS to run it. For more information on PASS visit

Power and Precision - This program provides a clear interface, and various tools to assist the user in developing an understanding of power analysis. It calculates power, effect size, sample size, etc, with graphs and provides explanation with neat reports.


nQuery Advisor - This software, which is used for sample size and power calculations, contains extensive table entries and many other convenient features. For more information on nQuery Advisor, click here

SamplePower - SamplePower, available from SPSS, arrives at sample sizes for a variety of common data analysis situations. You can learn more about it at

GPower - This software calculates a sample size for a given effect size, alpha level, and power value. You can download this free program from

UnifyPow - UnifyPow is another free power analysis program that uses SAS. You can find example programs and workshop notes at the UnifyPow web site at

StudySize - StudySize is a program for statistical power and sample size calculation. It includes the most common tests, point estimates and confidence intervals. Any parameter may be calculated (not only power or sample size) and can be presented as a single value or in a table or graph grouped by the values of two other parameters. For more information on StudySize go to

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