If the cost of a Type I error is high, a bigger value should be chosen for the _____.

Question

If the cost of a Type I error is high, a bigger value should be chosen for the  _____.

BlackTom AI · Accepted Answer

When assessing hypothesis tests, the cost of a Type I error (false positive) can guide how conservative we want to be. 
Option 1: critical value – Increasing the critical value makes it harder to reject the null, which would actually decrease Type I errors. However, the question asks for a quantity that should be made bigger, and while the critical value can be influenced by alpha, it’s not itself a directly adjustable parameter in the phrasing of this question.
Option 2: test statistic – The test statistic is determined by the data and the chosen test; it’s not typically described as something you set to be bigger to address Type I error costs. Its magnitude depends on the sample and calculation, not on a deliberate choice to increase it.
Option 3: confidence coefficient – The confidence coefficient is the probability that the confidence interval (or the test decision framework) correctly reflects the parameter, equal to 1 − alpha. A higher confidence coefficient corresponds to a smaller alpha, which reduces the risk of a Type I error. Therefore, if the cost of Type I error is high, we opt for a larger confidence coefficient.
Option 4: level of significance – The level of significance is alpha, the probability of a Type I error. A higher level of significance increases the chance of a Type I error, which is contrary to the aim of reducing such errors when costs are high. Hence, this should not be increased.
Thus, among the options, the quantity that should be chosen bigger to mitigate costly Type I errors is the confidence coefficient, since raising it implies lowering alpha and tightening the test against false positives.

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If the cost of a Type I error is high, a bigger value should be chosen for the _____.

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