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Sample Size and Power Calculations |

When you are planning a study or experiment, you often
need to
know how many units to sample to obtain a certain power, or
you may want to know the power you would obtain with a
specific sample size.
The *power* of a hypothesis test is
the probability of rejecting the null hypothesis when the
alternative hypothesis is true.
With an inadequate sample
size, you may not reach valid conclusions with your work;
with an excessive sample size, you may waste valuable
resources. Thus, performing sample size and power
computations is often quite important.

The power and sample size calculations
depend on the planned data analysis strategy.
That is, if the primary hypothesis test is a two-sample
*t*-test, then the power calculations must be based on
that test. Otherwise, if the sample size
calculations and data analyses are not aligned, the results
may not be correct.

Determining sample size requirements ahead of the experiment is a prospective exercise. Then, you proceed to select the appropriate number of sampling units and perform data collection and analysis. However, power and sample size calculations are also useful retrospectively. For a given analysis, you may want to calculate what level of power you achieved or what sample size would have been needed for a given power.

Power and sample size calculations are a function of
the specific
alternative hypothesis of interest, in addition to other parameters.
That is, the
power results will vary depending on which value of the alternative
hypothesis you specify, so sometimes it is useful to do these analyses
for a range of values to see how sensitive the power analysis is to
changes in the alternative hypothesis value.
Often, you produce plots of power versus sample size,
called *power curves*, to see how sample size and power
affect each other.

The Sample Size tasks provide prospective sample size and power
calculations for several types of analyses: *t*-tests, confidence
intervals, and tests of equivalence. Each of these calculations is
available for one-sample, paired-sample, and two-sample study
designs. Power and sample size calculations are also available for
the one-way ANOVA design. Multiple parameter values can be input,
and results and power curves are produced for each combination
of values. Note that retrospective power
computations are also available in a number of the statistical
tasks in the Analyst Application such as the Hypothesis Test,
Regression, and ANOVA tasks.

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