Sample Size
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Dr. Michael R. Hyman, NMSU
Relationship Between Sample Size
and Error
2
Determine Size for Probability
Sample—Practical Issues
• Financial
• Statistical
• Managerial (how confident needed)
3
Ways to Determine Sample Size
•
•
•
•
Blind guess
Available budget
Bayesian considerations
Rules of thumb
– Main group
– Subgroups
n > 100
20 < n < 100
• Standards for comparable studies
• Statistical precision
4
Typical Sample Sizes
5
Statistical Precision
Must know:
• Variability of population and individual
stratum
• Acceptable level of sampling error
• Needed level of confidence
• Type of distribution (if non-normal)
6
Online Sampling Calculators
From DSS Research:
• Sample Size
http://www.dssresearch.com/toolkit/sscalc/size.asp
• Sample Error
http://www.dssresearch.com/toolkit/secalc/error.asp
7
Sample Size Formula
zs 

n 
E
2
where:
n = sample size
z = confidence interval in standard error units
s = standard error of the mean
E = acceptable magnitude of error
8
Sample Size Formula:
Example #1
Suppose a survey researcher, studying
expenditures on lipstick, wishes to have a
95% confident level (Z) and a range of
error (E) of less than $2.00. The estimate
of the standard deviation is $29.00.
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Calculation: Example #1
 zs 
n  
E
2
 1.9629.00 


2.00


2
2
 56.84 
2




28
.
42

 2.00 
 808
10
Sample Size Formula:
Example #2
Suppose, in the same example as the one
before, the range of error (E) is acceptable
at $4.00. By how much is sample size is
reduced?
11
Calculation: Example #2
 zs 
 1.9629.00
n    

4.00 
E

2
2
2
56.84
2




14
.
21

 4.00 
 202
12
Calculating Sample Size
99% Confidence


(
2
.
57
)(
29
)
n

2


74.53 


 2 
2
 [37.265]
1389
2
2


(
2
.
57
)(
29
)
n

4


2


74
.
53


 4 
2
 [18.6325]
 347
2
13
Sample Size for a Proportion
2
Z pq
n
E
2
14
Where:
z2pq
n
E2
n = number of items in samples
Z2 = square of confidence interval in standard error units
p = estimated proportion of success
q = (1-p) or estimated the proportion of failures
E2 = square of maximum allowance for error between true
proportion and sample proportion, or zsp squared.
15
Calculating Sample Size
at the 95% Confidence Level
p  .6
q  .4
(1. 96 )2(. 6)(. 4 )
n
( . 035 )2
(3. 8416)(. 24)
001225
. 922

. 001225
 753

16
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