Section 3: Power and sample size calculations
This section describes how to calculate necessary sample size or power for a study comparing two groups on either a measurement outcome variable (through the independent sample t-test) or a categorical outcome variable (through the chi-square test of independence).
3.1 Comparing means between groups
The power.t.test( ) function will calculate either the sample size needed to achieve a particular power (if you specify the difference in means, the standard deviation, and the required power) or the power for a particular scenario (if you specify the sample size, difference in means, and standard deviation).
The input for the function is:
- n – the sample size in each group
- delta – the difference between the means of the two populations
- sd – the standard deviation
- power – the desired power, as a proportion (between 0 and 1)
To find the required sample size to achieve a specified power, specify delta, sd, and power. To find the power for a specified scenario, specify n, delta, and sd. R assumes you are testing at the two-tailed p=.05 level; you can over-ride these defaults by including sig.level=xx or 'alternative='one.sided'.
Finding required sample size:
>power.t.test(delta=.25,sd=0.7,power=.80)
Two-sample t test power calculation
n = 124.0381
delta = 0.25
sd = 0.7
sig.level = 0.05
power = 0.8
alternative = two.sided
NOTE: n is number in *each* group
Finding power:
> power.t.test(n=50,delta=.25,sd=0.7)
Two-sample t test power calculation
n = 50
delta = 0.25
sd = 0.7
sig.level = 0.05
power = 0.4239677
alternative = two.sided
NOTE: n is number in *each* group
3.2 Comparing proportions between groups
The power.prop.test( ) function in R calculates required sample size or power for studies comparing two groups on a proportion through the chi-square test. The input for the function is:
- n – sample size in each group
- p1 – the underlying proportion in group 1 (between 0 and 1)
- p2 – the underlying proportion in group 2 (between 0 and 1)
- power – the power of the test
To find the necessary sample size, specify p1, p2, and power. To find the power for a particular situation, specify n, p1, and p2. R assumes you are testing at the two-tailed p=.05 level; you can over-ride these defaults by including sig.level=xx or 'alternative='one.sided'.
Examples:
Finding power:
> power.prop.test(n=100,p1=.2,p2=.1)
Two-sample comparison of proportions power calculation
n = 100
p1 = 0.2
p2 = 0.1
sig.level = 0.05
power = 0.5081911
alternative = two.sided
NOTE: n is number in *each* group
Finding necessary sample size:
> power.prop.test(p1=.2,p2=.1,power=.8)
Two-sample comparison of proportions power calculation
n = 198.9634
p1 = 0.2
p2 = 0.1
sig.level = 0.05
power = 0.8
alternative = two.sided
NOTE: n is number in *each* group