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# One Sample Test of Means

The one sample test of means compares an unknown mean, $$\mu$$, to a fixed value, $$\mu_0$$.

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.

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## Power Calculation Explanation

Solve For
The unknown you are interested in solving for.
N
The sample size used to test the hypothesis.
Alpha
The $$\alpha$$ (Type I error rate) level of the hypothesis test.
Power
The power (1 - Type II error rate) of the hypothesis test.
Unknown Mean $$\mu$$
The mean of the sample. If you are comparing a difference in means to zero, set this value to the difference.
Null Mean $$\mu_0$$
The mean against which the unknown mean is compared to. If you are comparing a difference in means to zero, set this value to zero.
Standard Deviation
The standard deviation of the sample.
Known Standard Deviation
If the standard deviation is known or estimated (usually it is estimated).
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

## Calculation Results

No calculation has been generated yet.

Hypothesis: {{ hypothesis }}

Known Standard Deviation

Unknown Standard Deviation

N Alpha Power Alt. Mean $$\mu$$ Null Mean $$\mu_0$$ Standard Deviation Margin
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## Power Graph

There are no results to graph yet.

## References

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