{{ message }}

Two Sample Test of Means (Parallel Design)

The two sample test of means compares the means of two arms of a study, \(\mu_1\) and \(\mu_2\), with equal standard deviations.

The statistical test used for this set of hypotheses can be a \(t\)-test or a \(z\)-test, depending on if the standard deviation is a known value or estimated from the sample.

Power Calculation Parameters

To input multiple values, seperate them by a comma.

{{ this.errors }}

Power Calculation Explanation

Solve For
The unknown you are interested in solving for.
N (Arm \(i\))
The sample size, for arm \(i\), used to test the hypothesis.
The ratio of the sample size in arm 1 to arm 2. The total sample size is minimized for a given power when the ratio is 1 (i.e. the design is balanced).
The \(\alpha\) (Type I error rate) level of the hypothesis test.
The power (1 - Type II error rate) of the hypothesis test.
Mean (Arm 1)
The estimated mean for arm 1 (\(\mu_1\)).
Mean (Arm 2)
The estimated mean for arm 2 (\(\mu_2\)).
Standard Deviation
The pooled standard deviation of the sample.
The margin is a value the effect size needs to exceed to be meaningful. For hypotheses of equivalence, the margin must be greater than 0, or the calculation will not be solvable. For one sided tests, a margin is less than 0 implies a non-inferiority hypothesis. Otherwise, a superiority hypothesis is implied. Read More
There are three types of hypotheses that can be tested: two-sided, one-sided and equivalence. Tests of equivalence must include a margin if the unknown and null means are equal. Read More
Known Standard Deviation
If the standard deviation is known or estimated (usually it is estimated).

Calculation Results

No calculation has been generated yet.

Sign Up to Save Power and Sample Size Calculators!

Hypothesis: {{ hypothesis }}

Known Standard Deviation

Unknown Standard Deviation

N (Arm 1) N (Arm 2) Alpha Power Mean (Arm 1) Mean (Arm 2) Standard Deviation Margin Ratio
{{ val }}

Power Graph

There are no results to graph yet.


  • Chow, S., Shao, J., & Wang, H. (2003), Sample size calculations in clinical research, New York: Marcel Dekker.