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Outline for Class Meeting 4 (Chapter 2, Lohr, 1/30/06)
Sample size estimation
I.
The link between sample size and precision
A. In order to make a sample size determination, you must link desired precision to
sample size. This is done using CLT and expressions for the variance of the
estimators for the design you plan to use.
B. For a SRS design, the linking equation for estimation of means is
P[ y s  yU  e]  1   .
e is sometimes called margin of error, especially when  = .05.
C. The formula above leads to the following method for determination of sample size for
a SRS:
2 2
Step 1. Calculate n0  z S2 .
e
n0
Step 2. Calculate n 
.
1 n0 N
II.
A.
(1)
(2)
(3)
The problem is that you have to come up with a way to estimate S 2 .
Can use
pilot survey
similar surveys
educated guesses
B. Educated guessing methods
(1) If y is a 0/1 variable, S 2  P(1  P) , which reaches its maximum at (.5)(.5) = .25. So
it is common to substitute .25 for S 2 in the expression above. Thus a margin of error
of +/- 3% requires a SRS of size 1100.
(2) If the variable of interest is numerical, simple models can be used.
(3) If the distribution is more complicated, the following ANOVA expression is
sometimes useful:
S 2   Wh [ S h2 ( y h  yU ) 2 ]
h
Example: Suppose I wanted to estimate the mean rent paid by students at SMU to within
$25. How large a sample size is needed?