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Sample Size and Power Calculations |

Sample size and power calculations are available for one-sample and
two-sample paired and independent designs where the proposed
analysis is hypothesis testing of a mean or means via a *t*-test.
These computations assume equally sized groups.

Suppose you want to compute the power for a one-sample *t*-test.
The alternative hypothesis mean and the standard deviation have
the values 8.6137 and 2.0851, respectively. You are interested
in testing whether the null mean has the value 8, at an alpha level
of 0.05, and you are interested in looking at a range of sample
sizes from 11 to 211. The study for which these statistics
were computed had a sample size of 51.

Figure 12.2 displays the resulting dialog. Note that, unlike the other statistical tasks that require a data set for analysis, performing one of the Sample Size tasks requires only entering information in the appropriate dialog. The data table is not involved.

In this task, you specify whether you want to compute sample size or power, enter values for the test hypothesis and parameters, specify the alpha level (0.05 is the default), specify whether you want a power curve produced, and specify a range of power values or sample sizes depending on whether you are computing sample size or power.

To enter the information for this example, follow these steps:

- Select
**Power**. - Enter 8 as the
**Null mean:**value. - Enter 8.6137 as the
**Alternate mean:** - Enter 2.0851 as the
**Standard deviation:** - Make sure that the
**Alpha:**value is 0.05. - Enter 11 as the value for the
**From:**field in the line for**N:** - Enter 211 and 20 as the values under
**To:**and**By:**, respectively, in the line for**N:** - Select
**Power vs. N**to produce a plot. - Enter 51 as the value for
**N ref line:** - Select
**2-sided**for**Tails**if it is not already selected.

Note that you can enter multiple values in fields such as
for **Alpha:** and **Null mean:**, separated by commas or
blanks, and the
analysis will be performed for all combinations of the entered
values. Here, power will be computed for sample sizes ranging from
11 to 211 in multiples of 20.

Figure 12.3 contains the completed dialog.

Figure 12.4 contains the power computations for the sample sizes ranging from 11 to 211.

The interpretation of a power of 0.540 for *n*=51 is as follows:
suppose the true mean and standard deviation are
8.6137 and 2.0851, and suppose a random sample of 51 observations is
taken. Then the probability that the hypothesis test will reject the
null hypothesis () and conclude (correctly) that the
alternative hypothesis () is true is 0.540.

The requested plot is shown in Figure 12.5 with a reference
line at *n*=51.

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