SAMPLE SIZE CALCULATION PROGRAMS
Vanderbilt University
http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/PowerSampleSize
PS: Power and Sample Size Calculation
Get PS (5.2 MB) version 2.1.31, 2004
Release Notes
by William D. Dupont and Walton D. Plummer, Jr.
PS is an interactive program for performing power and sample size calculations. It can be used
for studies with dichotomous, continuous, or survival response measures. The alternative
hypothesis of interest may be specified either in terms of differing response rates, means, or
survival times, or in terms of relative risks or odds ratios. Studies with dichotomous or continuous
outcomes may involve either a matched or independent study design. The program can
determine the sample size needed to detect a specified alternative hypothesis with the required
power, the power with which a specific alternative hypothesis can be detected with a given
sample size, or the specific alternative hypotheses that can be detected with a given power and
sample size.
The PS program can produce graphs to explore the relationships between power, sample size
and detectable alternative hypotheses. It is often helpful to hold one of these variables constant
and plot the other two against each other. The program can generate graphs of sample size
versus power for a specific alternative hypothesis, sample size versus detectable alternative
hypotheses for a specified power, or power versus detectable alternative hypotheses for a
specified sample size. Linear or logarithmic axes may be used for either axes. Multiple curves
can be plotted on a single graphic.
Downloading the Software
The PS program is freely available on the Internet. To obtain this software on your computer click
PS (5.2 MB). Instruct your browser to download the file to a folder on your computer. A file called
pssetup.exe will be downloaded to this location. Run pssetup.exe to extract the needed files and
install the program.
The program runs on the Microsoft Windows operating systems (Windows 95 and later). We have
not tested the PS program with Microsoft Vista, though we have had a few reports that it does
work. Sometimes, the help functionality does not work under Vista. There is some additional
software that can be downloaded from Microsoft that will help. See
http://support.microsoft.com/kb/917607 for details.
To run the PS program after it has been installed, click the Start button, select Programs and then
click PS. Click the Overview button for an introduction to the program and instruction on its use.
PS is a self-documented program with extensive interactive help.
We are interested in feedback. If you have any questions or comments about our software please
send email to dale.plummer@vanderbilt.edu. It will be appreciated.
Study Designs That Can Be Evaluated By This Program
Survival Studies: Evaluation of independent cohorts using the log-rank test. The approach of
Schoenfeld and Richter3 is used. The ratio of number of patients in the cohorts being
compared may be specified by the user.
Continuous Response Measures in Two Groups: Paired and independent t tests. The
approach of Dupont and Plummer1 is used for paired and independent samples. The ratio
of number of patients in the samples being compared may be specified by the user. This
method produces results that are in close agreement with those of Pearson and Hartley. 4
Linear Regression: Tests of slopes, comparisons of slopes and intercepts from independent
regressions. The methods of Dupont and Plummer2 is used. They may be used to design
studies in which we wish to detect a regression slope of a given magnitude. They may
also be used when we wish to determine whether the slopes or intercepts of two
independent regression lines differ by a given amount. The values of the independent (x)
variable(s) of the regression line(s) may either be specified by the investigator or
determined observationally when the study is performed. In the latter case, the
investigator must estimate the standard deviation(s) of the independent variable(s).
Independent Case-Control Studies: Corrected and uncorrected chi-square contingency table
tests, Fisher's exact test. The method of Schlesselman5 is used for studies with
independent case and control groups that will be analyzed using an uncorrected chisquare test; the method of Casagrande et al.6 is used for independent studies that will be
analyzed using continuity corrected chi-square statistics or Fisher's exact test. When the
case and control sample sizes are unequal, PS uses the generalization of Casagrande's
method proposed by Fleiss.7 The alternative hypotheses may be specified in terms of
odds ratios or exposure prevalence rates.
Matched Case-Control Studies: McNemar's Test. The method of Dupont8 is used for studies
with paired or matched cases and controls. The alternative hypotheses may be specified
in terms of odds ratios or exposure prevalence rates.
Cohort Studies With Dichotomous Outcomes: Independent contingency table tests, McNemar's
test. The methods of Schlesselman,5 Casagrande,6 Fleiss7 and Dupont8 are available.
The alternative hypotheses may be specified in terms of relative risks or outcome
probabilities.
References
Dupont WD, Plummer WD, Jr: Power and Sample Size Calculations: A Review and Computer
Program. Controlled Clinical Trials 11:116-128, 1990
Dupont WD, Plummer WD, Jr: Power and Sample Size Calculations for Studies Involving
Linear Regression. Controlled Clinical Trials 19:589-601, 1998
Schoenfeld DA, Richter JR: Nomograms for calculating the number of patients needed for a
clinical trial with survival as an endpoint. Biometrics 38:163-170, 1982
Pearson ES, Hartley HO: Biometrika Tables for Statisticians Vol. I 3rd Ed. Cambridge:
Cambridge University Press, 1970
Schlesselman JJ: Case-Control Studies: Design, Conduct, Analysis. New York: Oxford
University Press, 1982
Casagrande JT, Pike MC, Smith PG: An improved approximate formula for calculating sample
sizes for comparing two binomial distributions. Biometrics 34:483-486, 1978
Fleiss JL: Statistical Methods for Rates and Proportions. 2nd Ed. New York: John Wiley &
Sons, 1981
Dupont WD: Power calculations for matched case-control studies. Biometrics 44:1157-1168,
1988
National Statistical Service : Australia
http://www.nss.gov.au/nss/home.NSF/pages/Sample+Size+Calculator+Description?OpenDocum
ent
http://www.nss.gov.au/nss/home.nsf/NSS/0A4A642C712719DCCA2571AB00243DC6?opendocu
ment
Sample Size Calculator
What does it do?
The sample size calculator on the next page allows you to calculate the required sample size,
standard error, RSE, and a confidence interval (95% or 99%) for a proportion estimate, using just
one of these criteria as an input. For example, if you know the minimum standard error you
require to ensure the precision of your estimate, you can find out the sample size required to
achieve that; if you know the likely size of the responding sample you can estimate the standard
error of your estimate, and a confidence interval for it.
The Statistical Clearing House recommends that you set the level of precision that will meet
needs of the users of your data. The level of precision should be set in conjunction with the users
of the data. You should not set the accuracy levels too high, as you will incur higher costs and
place additional burden on the community. You should also not set the accuracy levels too low,
as your data will not be approriate for your users.
Depending on the intended uses of the information, precision may not be the only concern.
Consideration also needs to be be given to cost, turnaround and respondent burden. When
deciding whether to increase precision, returns to scale must be considered. A small increase in
precision that incurs a large cost may not be justified.
The sample size calculator assumes simple random sampling. The results generated here are
intended only as rough guidelines and should only be used as such - they are by no means the
definitive "rule" about the size of a sample.
How do I use it?
Simply follow the steps outlined below.
Select the confidence level you want to work at.
If you are sampling from a finite population (one that isn't very large), enter the size of the
population here.
If you already roughly know the proportion you're estimating, or want to check the RSE of an
existing estimate, fill in the proportion. If left blank it will be assumed to be 0.5.
You must fill in one of Confidence Interval Range, Standard Error, Relative Standard Error or
Sample Size. Make sure the bullet point corresponding to the one you wish to specify is
selected.
Press Calculate to perform the calculation, or Clear to start again.
What do the categories mean?
Confidence Level
This is the chance that the true value will be inside the confidence interval calculated. You can
select 95% or 99%.
Population Size
This option allows you to specify the size of the population of interest. This option can be left
blank, in which case it will be assumed to be very large (typically, populations of size more than
100,000 are considered very large).
Proportion
This option allows you to specify the estimated proportion, if it is approximately known. This
assists in calculating the estimate standard errors which are appropriate for your situation. The
proportion may be sourced from previous cycles of the survey or by a educated guess.
Confidence Interval +/The Sample Size Calculator allows you to express the precision in terms of "some value plus or
minus an amount". For example, if you want your result to be accurate to within 5% (ie. plus or
minus 5%) then you should specify 0.05 here. Note that the value must be entered as a
proportion, not as a percentage.
Upper and Lower
These are the upper and lower bounds of the confidence interval. You cannot enter them, but
they will be displayed once the calculation is made.
Standard Error
This is the standard error of the estimate. Standard error is a measure of the variation of any
estimate that is produced by sampling a given population. This gives us an idea of the likelihood
that the estimate is near the true value. The standard error is expressed in the same units as the
estimate (in the case of any calculations done with this calculator, it is a proportion). A higher
standard error means the estimate is more variable.
Relative Standard Error (RSE)
This is the Standard Error expressed as a percentage of the estimate itself. For example if the
estimate is 0.5 and the standard error is 0.05, then the RSE will be 10%. RSE is often used in
preference to standard error when comparing the variability of samples of different magnitudes.
The RSE places the Standard Error in the context of the estimate. For example, for an estimate of
0.01, a standard error of 0.1 would be of much greater issue than for an estimate of 0.5. In the
first case, the RSE is 1000%, while in the second case it is much smaller (20%).
Sample Size
This is the sample size required for the standard error or confidence intervals displayed. You can
also specify the sample size to have standard error and the confidence interval calculated for you.
University of Iowa
Lenth, R. V. (2001), ``Some Practical Guidelines for Effective Sample Size Determination,'' The
American Statistician, 55, 187-193.
http://www.stat.uiowa.edu/~rlenth/Power/
Download to run locally
The file piface.jar may be downloaded so that you can run these applications locally. [Note: Some
mail software (that thinks it is smarter than you) renames this file piface.zip. If this happens, simply
rename it piface.jar; do not unzip the file.] You may also want the icon file piface.ico if you put
it on your desktop or a toolbar. You will need to have the Java Runtime Environment (JRE) or the Java
Development Kit (JDK) installed on your system. You probably already have it; but if not, these are
available for free download for several platforms from Sun. If you have JDK or JRE version 1.2 or later,
then you can probably run the application just by double-clicking on piface.jar. Otherwise, you may
run it from the command line in a terminal or DOS window, using a command like
java -jar piface.jar
This will bring up a selector list similar to the one in this web page. A particular dialog can also be run
directly from the command line, if you know its name (can be discovered by browsing piface.jar with
a zip file utility such as WinZip). For example, the two-sample t-test dialog may be run using
java -cp piface.jar rvl.piface.apps.TwoTGUI
Links to other sites
Interactive page - Michael Friendly (ANOVA designs)
Interactive page - David Schoenfeld (clinical trials designs; menu based on study type and measurement
type)
Sample-size calculator for k-stage designs (by James Kepner)
UnifyPow - A SAS module for sample-size analysis by Ralph O'Brien.
SSize - ECHIP sample size calculator for Palm devices (freeware) by Bob Wheeler.
A review of power software for PCs (article, pdf format) by Len Thomas and Charles Krebs (of limited use
now as it was published in 1997).