SDA: Survey Documentation and Analysis
Using Stata to Calculate Sample Size and Power
A. Required Sample Size (for a given alpha and power)
1. For a single measurement (a proportion) in one sample
Command syntax:
sampsi proportion-H0 proportion-H1 , alpha(a) power(p) onesample
Example:
. sampsi .50 .60, alpha(.05) power(.90) onesample
Result:
Estimated sample size for one-sample comparison of proportion
to hypothesized value
Test Ho: p = 0.5000, where p is the proportion in the population
Assumptions:
alpha = 0.0500 (two-sided)
power = 0.9000
alternative p = 0.6000
Estimated required sample size:
n = 259
2. For a single measurement (a mean) in one sample
Command syntax:
sampsi mean-H0 mean-H1 , sd(x) alpha(a) power(p) onesample
Example:
. sampsi 40 45, sd(15) alpha(.05) power(.90) onesample
Result:
Estimated sample size for one-sample comparison of mean
to hypothesized value
Test Ho: m = 40, where m is the mean in the population
Assumptions:
alpha = 0.0500 (two-sided)
power = 0.9000
alternative m = 45
sd = 15
Estimated required sample size:
n = 95
B. Power of a Comparison For Given Sample Sizes and Alpha
1. For two proportions:
Command:
sampsi proportion-1 proportion-2, n1(x) n2(y) alpha(a)
Example:
. sampsi .25 .40, n1(300) n2(200) alpha(.05)
Result:
Estimated power for two-sample comparison of proportions
Test Ho: p1 = p2, where p1 is the proportion in population 1
and p2 is the proportion in population 2
Assumptions:
alpha = 0.0500 (two-sided)
p1 = 0.2500
p2 = 0.4000
sample size n1 = 300
n2 = 200
n2/n1 = 0.67
Estimated power:
power = 0.9301
2. For two means:
Command:
sampsi mean-1 mean-2, sd1(s) sd2(t) n1(x) n2(y) alpha(a)
Example:
sampsi 20 17, sd1(10) sd2(12) n1(200) n2(100) alpha(.05)
Result:
Estimated power for two-sample comparison of means
Test Ho: m1 = m2, where m1 is the mean in population 1
and m2 is the mean in population 2
Assumptions:
alpha = 0.0500 (two-sided)
m1 = 20
m2 = 17
sd1 = 10
sd2 = 12
sample size n1 = 200
n2 = 100
n2/n1 = 0.50
Estimated power:
power = 0.5769
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