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

Choose Statistics __image\arrow5.gif Power and Sample Size __image\arrow5.gif Normal Mean. 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.

Standard Deviations

For a one-sample test, Sigma1 is required. For a paired test, the standard deviation of the difference between samples is required, so the Sigma(X2 - X1) field becomes active in place of Sigma1.

Null Hypothesis

For a one-sample test, Mean is required. For a two-sample test, Mean1 is required. Both have a default value of 0.

Alternative Hypothesis

For a one-sample test, Alt Mean is required; for a two-sample test, Mean2 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

Enter the name for the object in which to save the results of the analysis.

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 Normal 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 ro return the exact value of N, with no rounding.

Results Page

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In the Normal 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. Click the Fill Down button to copy the last selected digit down the list.