Basic Statistical Analysis Using the R Statistical Package

• Section 3: Power and sample size calculations
• 3.1 Comparing means between groups
• 3.2 Comparing proportions between groups

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:

Two-sample t test power calculation

NOTE: n is number in *each* group

Two-sample t test power calculation