Binomial Power and Sample Size

When designing a study, one of the first questions that arises is how large a sample size is necessary. The sample size depends upon the minimum detectable difference of interest, the acceptable probability of rejecting a true null hypothesis (alpha), the desired probability of correctly rejecting a false null hypothesis (power), and the variability within the population(s) under study.

The Binomial Power and Sample Size dialog assists in computing sample sizes for statistics that are asymptotically binomially distributed, such as a proportion. Alternatively, it may be used to calculate power or minimum detectable difference for a sample of a specified size.

From the main menu, choose Statistics __image\arrow5.gif Power and Sample Size __image\arrow5.gif Binomial Proportion. The dialog shown below appears.

Model Page

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In the Normal Power and Sample Size dialog, the Model page has the following options:

Select

Compute

Choose Sample Size (default), Power, or Min. Difference.

Sample Type

Choose a sample type from the dropdown menu. The choices are One Sample, Two Sample, or Paired.

Probabilities

Specify Alpha and Power values, defined as

 Alpha = Pr(reject Null hypothesis if true)

 Power = Pr(reject Null hypothesis if false)

You can select multiple values using the Ctrl key, or you can type in values separated by commas.

Sample Sizes

If computing power or minimum difference, samples sizes are input here.

Null Hypothesis

For a one-sample test, Proportion is required. For a two-sample test, Group1 Proportion is required. Both have a default value of 0.5.

Alternative Hypothesis

For a one-sample test, Alt Proportion is required; for a two-sample test, Group2 Proportion is required.

Test Type If the alternative hypothesis is one of inequality, the test type is two.sided. Other choices are greater and less.

Results

Save As

To save the resulting table as an S-PLUS object, type the name for the object here.

Print Results

Select this to print out the results of the analysis in the designated output window.

Options Page

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In the Binomial Power and Sample Size dialog, the Options page has the following options:

Computational Options

Expand Input

Select Expand Input to expand the input into a table where all combinations of input are used. For example, if you input two different powers and three alternative means, the resulting table has six rows. If this option is not selected, the above example produces a table with three rows.

Recompute Power

By default, sample sizes are rounded up to the next integer value. Select Recompute Power to recompute the power for the rounded sample size value.

Exact Sample Size

Select Exact Sample Size to return the exact value of N, with no rounding.

Continuity Correction

Select this to use a continuity correction in the normal approximation to the distribution of the test statistics.

Results Page

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In the Binomial Power and Sample Size dialog, the Results page has the following options:

Columns

This group allows you to control which columns are printed and in what order.

Options

Number of Digits

The number of digits can be controlled for each column individually.