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 Power and Sample Size
Binomial Proportion. The dialog shown below appears.
Model Page
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.
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
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
In the Binomial Power and Sample Size dialog, the Results page has the following options:
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.