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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.

To input multiple values, seperate them by a comma.

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- Solve For
- The unknown you are interested in solving for.
- N (Arm \(i\))
- The sample size, for arm \(i\), used to test the hypothesis.
- Ratio
- 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). - Alpha
- The \(\alpha\) (Type I error rate) level of the hypothesis test.
- Power
- 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.
- Margin
- 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
- Hypothesis
- 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).

No calculation has been generated yet.

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