Recent reviews (e. g., button et al. 2013) suggests that neuroscience research papers have a median power (1 )=0.18, given =0.05. being a skeptic, your prior belief is that only 1 0% of research studies examine “real” effects; you consider the rest to have true effect sizes of effectively zero. given this information, answer the following questions:

a. before examining a neuroscience paper, what probability describes your prior belief about whether it will report a real effect (denoted by ( what probability describes your prior belief that no effect exists (denoted by ( ∅

b. let “sig.” denote a significant result within a given study. given the information above, report the values of the two probabilities: (sig.| ∅) and (sig.| ). additionally, identify each of these probabilities by name.

c. given the four probabilities reported above, what is the value of ( also, describe in english what this probability tells us.

d. using bayes’ rule, calculate your posterior belief that the published significant result describes a true effect. interpret the resulting value in english, and compare it to your prior belief.

e. suppose that you re-read the same study and realize that it is guilty of p-hacking, to the extent that its effective rate of false positives is actually closer to =0.40. assuming the power of the study is still the same (0.18), re-calculate your posterior belief that this published significant result describes a true effect. what does this result tell you about the dangers of p-hacking (or running multiple comparisons, or using any other method that inflates your type i error rate)?