Problem 3. Colquhoun (2014) claimed that, "if you use p-0.05 to suggest that you have made a discovery, you will be wrong at least 30% of the time." He uses the following example. Suppose you pick a drug at random from 1000 candidate drugs and run a randomized controlled trial to determine whether the drug truly is effective. You perform a hypothesis test that has a significance level of 0.05 and a power of 0.8. Write the null and alternative hypothesis for this hypothesis test, using words only (no math). A B. What is the probability of committing a Type I Error on this single hypothesis test? C. What is the probability of committing a Type II Error on this single hypothesis test? D. If you independently run experiments and hypothesis tests for four drugs, what is the probability of committing at least one Type I Error when performing the four hypothesis tests? 10% of the drugs truly have an effect, and the other 90% are no different from placebo. Find the E. probability that your randomly chosen drug has an effect, given that you rejected the nullhypothesis.

Question

Questions d and e

Problem 3. Colquhoun (2014) claimed that, "if you use p-0.05 to suggest that you have made a
discovery, you will be wrong at least 30% of the time." He uses the following example.
Suppose you pick a drug at random from 1000 candidate drugs and run a randomized controlled trial to
determine whether the drug truly is effective. You perform a hypothesis test that has a significance level
of 0.05 and a power of 0.8.
Write the null and alternative hypothesis for this hypothesis test, using words only (no math).
A
B. What is the probability of committing a Type I Error on this single hypothesis test?
C. What is the probability of committing a Type II Error on this single hypothesis test?
D. If you independently run experiments and hypothesis tests for four drugs, what is the
probability of committing at least one Type I Error when performing the four hypothesis tests?
10% of the drugs truly have an effect, and the other 90% are no different from placebo. Find the
E.
probability that your randomly chosen drug has an effect, given that you rejected the nullhypothesis.

Image Transcription

Problem 3. Colquhoun (2014) claimed that, "if you use p-0.05 to suggest that you have made a discovery, you will be wrong at least 30% of the time." He uses the following example. Suppose you pick a drug at random from 1000 candidate drugs and run a randomized controlled trial to determine whether the drug truly is effective. You perform a hypothesis test that has a significance level of 0.05 and a power of 0.8. Write the null and alternative hypothesis for this hypothesis test, using words only (no math). A B. What is the probability of committing a Type I Error on this single hypothesis test? C. What is the probability of committing a Type II Error on this single hypothesis test? D. If you independently run experiments and hypothesis tests for four drugs, what is the probability of committing at least one Type I Error when performing the four hypothesis tests? 10% of the drugs truly have an effect, and the other 90% are no different from placebo. Find the E. probability that your randomly chosen drug has an effect, given that you rejected the nullhypothesis.

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