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Page 19.1 (C:\DATA\StatPrimer\sampsize.wpd © B. Gerstman 5/15/03
)
n
s
d
=
4
2
2
(19.1)
n
s
d
d
=
4
2
2
(19.2)
n
s
d
p
=
4
2
2
(19.3)
19: Sample Size, Precision, and Power
A study that is insufficiently precise or lacks the power to reject a false null hypothesis is a waste of time and
money. A study that collects too much data is also wasteful.
Therefore, before collecting data, it is essential to
determine the sample size requirements of a study. Before calculating the sample size requirements of a study you
must address some questions. For example:
•
Do you want to learn about a
mean? a mean difference? a proportion? a proportion (risk) ratio? an odds ratio? a
slope?
•
Do you want to
estimate
something with a given precision or do you want to test something with a given
power?
•
What type of sample(s) will you be working with? A single group? Two or more independent groups? Matched
pairs?
Let us first address the problem of estimating a mean or mean difference with given precision.
Sample Size Requirements for Estimating a Mean or Mean Difference
To determine an appropriate sample size you must first declare an acceptable margin of error
d
. Recall that margin of
error
d
is the wiggle room around the point estimate. This is equal to
half
the confidence interval width. When
estimating μ with 95% confidence use
Example:
To obtain a margin of error of 5 for a variable with a standard deviation of 15,
n
= (4)(15
2
)/(5
2
) = 36.
This method is applied to estimating a mean difference based on
paired samples
(μ
d
) by using the standard deviation
of the DELTA variable (
s
d
) in your formula:
With
independent samples
, use the pooled estimate of standard deviation (
s
p
) as your standard deviation estimate:
You should put considerable effort into getting a good estimate of the standard deviation of the variable you are
studying since sample size calculations depend on this fact. Such estimates come from prior studies, pilot studies,
and “Gestalt” (a combination of sources that contribute to knowledge about the variable).
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This note was uploaded on 04/01/2012 for the course ECON 101 taught by Professor Doc during the Spring '11 term at Yale.
 Spring '11
 Doc

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