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One-way analysis of variance (ANOVA) is used to compare the means of more than two groups. The model that one-way ANOVA assumes is that if \(x_{ij}\) is observation from the \(j^{th}\) subject from the \(i^{th}\) group, where \(i = 1, \dots, k\) and \(j = 1, \dots n\),

\[ x_{ij} = \mu_i + \epsilon_{ij} \]where \(\epsilon_{ij}\) is the random error. We assume that the random errors are i.i.d normal random variables whose mean is 0 and variance is \(\sigma^2\).

When we compare the means of each treatment group using one-way ANOVA, we can compare them simultaneously, which answers the question 'is one of the means different from the rest', or compare them pairwise. When pairwise comparisons are performed, the type I error rate is increased. This calculator takes that into account by adjusting the type I error of each pairwise test so that the overall type I error is less than the desired alpha.

To input multiple values, seperate them by a comma.

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- Solve For
- The unknown you are interested in solving for.
- Comparison
- If you desire simultaneous or pariwise comparisons of the means.
- 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.
- Means
- The means of each group. Seperate each mean a comma.
- Standard Deviation
- The standard deviation of the sample (\(\sigma^2\) in the above model).
- Known Standard Deviation
- If the standard deviation is known or estimated (usually it is estimated).

No calculation has been generated yet.

Comparison: {{ comparison }}

Means: {{ mu }}

Known Standard Deviation

Unknown Standard Deviation

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