Using STATISTICA Power Analysis in planning and analyzing your research, you can always be confident that you are using your
resources most efficiently. Nothing is more disappointing than realizing that your research findings lack precision because your
sample size was too small. On the other hand, using a sample size that is too large could be a significant waste of time and
resources. STATISTICA Power Analysis will help you find the ideal sample size and enrich your research with a variety of
tools for estimating confidence intervals and conducting comprehensive power analysis.
Still not convinced? Read on for a detailed technical description of STATISTICA Power Analysis...
STATISTICA Power Analysis is a comprehensive, general purpose tool for helping you plan your research studies so that the
sample size is appropriate for the objectives of the study. It also provides a wide variety of tools for analyzing all aspects of
statistical power and sample size calculation.
STATISTICA Power Analysis is compatible with Windows 2000 and Windows XP.
Why is STATISTICA Power Analysis the most modern and powerful program of its kind?
Because no other power analysis application program matches the full range of capabilities available in STATISTICA Power
Analysis.
Because STATISTICA Power Analysis is by far the fastest and easiest to use.
Because STATISTICA Power Analysis is the only program of its type available on the market that goes beyond standard tests
of "zero effect," and implements modern methods using interval estimation technology. The program can compute exact
confidence intervals on effect sizes and use these to construct exact confidence intervals on sample size and power.
Because STATISTICA Power Analysis offers computational routines of unparalleled accuracy and power. The computational
routines are extremely precise, and maintain their accuracy across a much broader range of parameters than those in other power
analysis applications.
Note the screen shots above, which show how STATISTICA Power Analysis can handle demanding noncentral distribution
calculations. One power analysis program refuses to perform the calculations for the noncentral F example, returning a
"Limit Check Failure" error message. Another program returns, without comment, completely erroneous results for the
noncentral t example.
Because at the touch of a button, the program produces presentation-quality, automatically-scaled graphs of power vs.
sample size, power vs. effect size, and power vs. alpha. Menus for altering the range of these graphs are immediately available,
so that the user can "hone in" on regions of interest, and produce several graphs in rapid succession. The program
produces protocol statements, describing the calculations in a form that can be transferred directly to your final report,
research paper, grant proposal, etc.
Sample Size Calculation. STATISTICA Power Analysis calculates sample size as a function of Type I error rate and
effect size in all the tests listed below.
STATISTICA Power Analysis calculates power as a function of sample size, effect size, and Type I error rate for the:
1-sample t-test
2-sample independent sample t-test
2-sample dependent sample t-test
Planned contrasts
1-way ANOVA (fixed and random effects)
2-way ANOVA
Chi-square test on a single variance
F-test on 2 variances
Z-test (or chi-square test) on a single proportion
Z-test on 2 independent proportions
Mcnemar's test on 2 dependent proportions
F-test of significance in multiple regression
t-test for significance of a single correlation
Z-test for comparing 2 independent correlations
Log-rank test in survival analysis
Test of equal exponential survival, with accrual period
Test of equal exponential survival, with accrual period and dropouts
Chi-square test of significance in structural equation modeling
Tests of "close fit" in structural equation modeling confirmatory factor analysis
Confidence Interval Estimation. Modern statistical practice has placed renewed emphasis on confidence interval estimation,
both in planning studies and evaluating their meaning. STATISTICA Power Analysis is unique among programs of its type in
that it calculates confidence intervals for a number of important statistical quantities such as standardized effect size (in
t-tests and ANOVA), the correlation coefficient, the squared multiple correlation, the sample proportion, and the difference
between proportions (either independent or dependent samples). These capabilities, in turn, may be used to construct confidence
intervals on quantities such as power and sample size, allowing the user to utilize the data from one study to construct an exact
confidence interval on the sample size required for another study.
Statistical Distribution Calculators. Besides the wide range of distributions available in all modules of STATISTICA,
the STATISTICA Power Analysis program provides special capabilities that are particularly useful in performing power
calculations. These routines, which include the noncentral t, noncentral F, noncentral chi-square, binomial, exact distribution of
the correlation coefficient, and the exact distribution of the squared multiple correlation coefficient, are characterized by their
ability to solve for an unknown parameter, and for their ability to handle "non-null" cases.
For example, not only can the distribution routine for the Pearson correlation calculate p as a function of r and
N for rho=0, it can also perform the calculation for other values of rho. Moreover, it can solve for the
exact value of rho that places an observed r at a particular percentage point, for any given N.
Example Application. Suppose you are planning a 1-Way ANOVA to study the effect of a drug. Prior to planning the study, you
find that there has been a similar study previously.
This
particular study had 4 groups, with N = 50 subjects per group, and obtained an F-statistic of 15.4. From this information,
as a first step you can (a) gauge the population effect size with an exact confidence interval, (b) use this information to set a
lower bound to appropriate sample size in your study.
Simply enter the data into a convenient dialog, and results are immediately available. See the results at left.
In this case, we discover that a 90% exact confidence interval on the
root-mean-square standardized effect (RmsSE) ranges from about .398 to .686. With effects this strong, it is not surprising that the
90% post hoc confidence interval for power ranges from .989 to almost 1. We can use this information to construct a confidence
interval on the actual N needed to achieve a power goal (in this case, .90). This confidence interval ranges from 12 to 31.
So, based on the information in the study, we are 90% confident that a sample size no greater than 31 would have been adequate to
produce a power of .90.
On the other hand,
Turning to our own study, suppose we examine the relationship between power and effect size for a sample size of 31. The first
graph (at left) shows quite clearly that as long as the effect size for our drug is in the range of the confidence interval for the
previous study, our power will be quite high.
should the actual effect size for our drug be on the order of .25, power will be inadequate. If, on the other hand, we use a sample
size comparable to the previous study (i.e., 50 per group) we discover that power will remain quite reasonable, even for effects on
the order of .28 (see graph at right). With STATISTICA Power Analysis, this entire analysis would take you only a minute or
two.
![[Screen Shot]](images/power_ss.gif)
Using STATISTICA Power Analysis in planning and analyzing your research, you can always be confident that you are using your
resources most efficiently. Nothing is more disappointing than realizing that your research findings lack precision because your
sample size was too small. On the other hand, using a sample size that is too large could be a significant waste of time and
resources. STATISTICA Power Analysis will help you find the ideal sample size and enrich your research with a variety of
tools for estimating confidence intervals and conducting comprehensive power analysis.
![[Dialog of Options]](images/pow_startup.gif)
![[t Calculator]](images/t_calc.gif)
![[F Calculator]](images/fcalc.gif)
![[Results Dialog]](images/pow_example.gif)
Example Application. Suppose you are planning a 1-Way ANOVA to study the effect of a drug. Prior to planning the study, you
find that there has been a similar study previously.
This
particular study had 4 groups, with N = 50 subjects per group, and obtained an F-statistic of 15.4. From this information,
as a first step you can (a) gauge the population effect size with an exact confidence interval, (b) use this information to set a
lower bound to appropriate sample size in your study.
![[First Graph]](images/power1.gif)
![[First Graph]](images/power2.gif)
On the other hand,
Turning to our own study, suppose we examine the relationship between power and effect size for a sample size of 31. The first
graph (at left) shows quite clearly that as long as the effect size for our drug is in the range of the confidence interval for the
previous study, our power will be quite high.
should the actual effect size for our drug be on the order of .25, power will be inadequate. If, on the other hand, we use a sample
size comparable to the previous study (i.e., 50 per group) we discover that power will remain quite reasonable, even for effects on
the order of .28 (see graph at right). With STATISTICA Power Analysis, this entire analysis would take you only a minute or
two.![[StatSoft]](../images/sssmall.gif)
![[StatSoft]](../images/emailed.gif){kind=small}
e-mail: info@statsoft.com