That is, if a Type I error is worse than a Type II error, why would I want to reduce my chances of making a Type II error by raising the significance level in an experiment? I am lost on the logic here, please help!
Statistics: Under what conditions would I want to reduce the chance of making a Type II error?
Sometimes, a Type II error can be critical. If you are dealing with a situation where a wrong decision could cause harm, it is important to minimize Type II error. You wouldn't want to Accept a hypothesis (such as "This medication causes no increase in heart disease") erroneously because you used to low a significance level.
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