Precision
- controlling
The process
of planning for precision has some obvious parallels to planning for power,
but the two processes are not identical and, in most cases, will lead
to very different estimates for sample size. The program displays an estimate
of the precision for a given sample size and confidence level.
Typically,
the user will enter data for effect size and sample size. The program
immediately displays both power and precision for the given values. Changes
to effect size will affect power (and may have an incidental effect on
precision). Changes to sample size will affect both power and precision.
Changes to alpha will affect power, while changes to the confidence level
will affect precision. Defining the test as one-tailed or two-tailed will
affect both power and precision.
Precision
- Tolerance intervals
The confidence
interval width displayed for t-tests is the median interval width (assuming
the population SD is correct, the confidence interval will be narrower
than the displayed value in half the samples, and wider in half the samples).
The width displayed for exact tests of exact proportions is the expected
value (i.e. the mean width expected over an infinite number of samples).
For other procedures where the program displays a confidence interval,
the width shown is an approximate value (it is the value that would be
computed if the sample proportions or the sample correlation precisely
matched the population values).
For many
applications, especially when the sample size is large, these values will
prove accurate enough for planning purposes. Note, however, that for any
single study the precision will vary somewhat from the displayed value.
For t-tests, on the assumption that the population SD is 10, the sample
SD will typically be smaller or greater than 10, yielding a narrower or
wider confidence interval. Analogous issues exist for tests of proportions
or correlations.
For t-tests
the researcher who requires more definitive information about the confidence
interval may want to compute tolerance intervals, i.e. the likelihood
that the confidence interval will be no wider than some specific value.
In this program the 50% tolerance interval (corresponding to the median
value) is displayed as a matter of course. The 80% (or other user-specified)
tolerance interval is an option enabled from the View menu. For example,
the researcher might report that in 50% of all studies the mean would
be reported with a 95% confidence interval no wider than 9 points, and
in 80% of all studies the mean would be reported with a 95% confidence
interval no wider than 10 points.
Note. The
confidence interval displayed by the program is intended for anticipating
the width of the confidence interval while planning a study, and not for
computing the confidence interval after a study is completed. The computational
algorithm used for t-tests includes an adjustment for the sampling distribution
of the SD that is appropriate for planning but not for analysis. The computational
algorithms used for tests of proportions or a single correlation may be
used for analysis as well.
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