# STATISTICA Power Analysis and Interval Estimation

Using STATISTICA Power Analysis and Interval Estimation 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 and Interval Estimation will help you find the ideal sample size and enrich your research with a variety of tools for estimating confidence intervals.

• Power Calculation
• Sample Size Calculation
• Interval Estimation
• Probability Distributions
• List of Tests
• Example Application

Details

Some of the advantages of STATISTICA Power Analysis and Interval Estimation are:

• Precise and fast computational routines, which maintain their accuracy across a broad range of parameters
• Presentation-quality, automatically-scaled graphs of power vs. sample size, power vs. effect size, and power vs. alpha
• Protocol statements describing calculations in a form that can be transferred directly to a text document

## Power Calculation

Power Calculation allows you to calculate statistical power for a given analysis type (see List of Tests below), and to produce graphs of power as a function of various quantities that affect power in practice, such as effect size, type I error rate, and sample size.

## Sample Size Calculation

Sample Size Calculation allows you to calculate, for a given analysis type (see List of Tests below), the sample size required to attain a given level of power, and to generate plots of required sample size as a function of required power, type I error rate, and effect size.

## Interval Estimation

Interval Estimation allows you to calculate, for a given analysis type (see List of Tests below), specialized confidence intervals not generally available in general-purpose statistical packages. These confidence intervals are distinguished in some cases by the fact that they refer to standardized effects, and in others by the fact that they are exact confidence intervals in situations where only approximate techniques have generally been available.

STATISTICA Power Analysis and Interval Estimation 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.

## Probability Distributions

Probability Distributions allows you to perform a variety of calculations on probability distributions that are of special value in performing power and sample size calculations.

The routines are distinguished by their high level of accuracy, and the wide range of parameter values for which they will perform calculations. The noncentral distributions are also distinguished by the ability to calculate a noncentrality parameter that places a given observation at a given percentage point in the noncentral distribution. The ability to perform this calculation is essential to the technique of “noncentrality interval estimation”  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.

## List of Tests

STATISTICA Power Analysis and Interval Estimation calculates power as a function of sample size, effect size, and Type I error rate for the tests listed below:

• 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

## 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, and (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. 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. Turning to our own study, suppose we examine the relationship between power and effect size for a sample size of 31. The first graph 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. With STATISTICA Power Analysis and Interval Estimation, this entire analysis runs in just a minute or two.

System Requirements

STATISTICA Power Analysis is compatible with Windows XP, Windows Vista, and Windows 7.

## Minimum System Requirements

• Operating System: Windows XP or above
• RAM: 256 MB
• Processor Speed: 500 MHz

## Recommended System Requirements

• Operating System: Windows XP or above
• RAM: 1 GB
• Processor Speed: 2.0 GHz

Native 64-bit versions and highly optimized multiprocessor versions are available. 