Sample Size for Normality Tests in PASS

PASS includes procedures for power analysis and sample size calculations for eight different tests of normality. The normality calculation procedures are easy-to-use and validated for accuracy. For more details about normality tests in PASS, we recommend you download and install the free trial of the software.

Jump to:


The Normality Calculation procedures in PASS allow you to study the power and sample size of eight statistical tests of normality:

  1. Anderson-Darling
  2. Kolmogorov-Smirnov
  3. Kurtosis
  4. Martinez-Iglewicz
  5. Omnibus
  6. Range
  7. Shapiro-Wilk
  8. Skewness

Since there are no formulas that allow the calculation of power directly, simulation is used. This gives you the ability to compare the adequacy of each test under a wide variety of situations, using any of several different simulation distributions.

The reason there are so many different normality tests is that there are many different forms of normality. Thode (2002) presents that following recommendations concerning which tests to use for each situation.

  • Normal vs. Long-Tailed Symmetric Alternative Distributions
    The Shapiro-Wilk and the kurtosis tests have been found to be best for normality testing against long-tailed symmetric alternatives.
  • Normal vs. Short-Tailed Symmetric Alternative Distributions
    The Shapiro-Wilk and the range tests have been found to be best for normality testing against short-tailed symmetric alternatives.
  • Normal vs. Asymmetric Alternative Distributions
    The Shapiro-Wilk and the skewness tests have been found to be best for normality testing against asymmetric alternatives.

In the Normality Tests procedure in PASS, you may solve for either power or sample size. In a typical scenario where the goal is to estimate the sample size, the user enters power, alpha, the desired test, and specifies the simulation distribution. The procedure is run and the output shows a summary of the entries as well as the sample size estimate(s). A summary statement is given, as well as references to the articles from which the formulas for the result were obtained. For many of the parameters (e.g., power, alpha, and sample size), multiple values may be entered in a single run. When this is done, estimates are made for every combination of entered values. A numeric summary of these results is produced along with easy-to-read sample size or power curve graphs.

PASS Normality Tests Power Curve

Technical Details

This page provides only a brief description of the tools that are available in PASS for power and sample size analysis for normality tests. If you would like to examine the formulas and technical details, we recommend you download and install the free trial of the software, open the Normality Tests procedure, and click on the help button in the top right corner to view the complete documentation. There you will find summaries, formulas, references, discussions, technical details, examples, and validation against published articles.

An Example Setup and Output

When the PASS software is first opened, the user is presented with the PASS Home window. From this window the desired procedure is selected from the menus, the category tree on the left, or with a procedure search. The procedure opens and the desired entries are made. When you click the Calculate button on the normality calculator the results are produced. You can easily navigate to any part of the output with the navigation pane on the left.

PASS Home Window

PASS Home Window Showing Normality Test Procedures

Procedure Window for Testing Normality

PASS Procedure Window for Power Analysis of Normality Tests

PASS Output Window

PASS Output Window from Power Analysis for Normality Tests

Start Your Free 30 Day Trial Now Buy Now

"I had been using [another statistical software package] for over 15 years until recently when I noticed it would not run ANOVAs correctly. After researching numerous options I switched to NCSS and PASS and couldn't be happier. Your product is accurate, fast, easy to use, and very inexpensive. And thanks to the software’s flexibility in reporting and graphing, it has made my consulting business easier as well. Thank you!"

Ken Hansen, M.S., Mechanical Engineer and Applied Statistician

I am a very satisfied user of NCSS. For years I used SPSS in my consulting work, but the cost got to be exorbitant. When I started using NCSS, I found it easy and intuitive to use and extremely accurate in its results. It is not only my statistical analysis program of choice but I have recommended it to many of my clients as well. When I've had questions and called NCSS, I have always gotten expert help and advice and never had a problem go unsolved. Keep up the good work.

Denis Stadther, Denis Stadther Consulting