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For a 3-class classification problem the theoretical chance level is 33.33%. What should be the minimum accuracy (in percentage) to be above chance level f0r a significance intervals of 5% and 1%. And how to calculate it ?

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  • $\begingroup$ This is a question of statistical power, & determining it is the subject of a power analysis. If you were to specify the power that you want to be able to achieve, & the N that you will have, the minimum detectible accuracy can be determined. W/o this info, this question cannot be answered. $\endgroup$ Jul 20 '13 at 3:40
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I'm presuming this is homework or self learning. Here are some hints:

  1. Although you might express the answer as a percentage, it will depend on the sample size.

  2. To work through the problem, start with a concrete example with real numbers. For example, if the true proportion of success is 0.33 (as in your null hypothesis you are looking for evidence against) and you have six trials, what is the exact chance of getting 4, 5 or 6 successes? For which of these values is the chance of getting that many successes by chance 0.05 or less, and for which is it 0.01 and less?

  3. Once you've worked out how to do this using the binomial distribution, find ways to generalise these to cases where n is different to 6.

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