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

\[ x_{ij} = p_i + \epsilon_{ij} \]where \(\epsilon_{ij}\) is the random error.

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.

**Note:** This calculator uses large sample theory which approximates a binomial random variable with a normal one.

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.
- Proportions
- The proportions of each group. Seperate each proportion a comma.
- Null Proportion (optional)
- If you are comparing several proportions against a single value, this is the value to compare against. Otherwise, pairwise comparisons between the proportions will be performed.

No calculation has been generated yet.

Proportions: {{ p }}

Null Proportions: {{ p_0 }}

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