I'm wondering why 0.05 (alpha) was used in that formula? True positive and false negative rates depends on statistical power (1-beta) and beta, and in case of beta 0.2, rate of "Melatonin is working" in case of negative result is 0.457 (not a 0.1739)
"Melatonin is working" branch (prior P(W) = 0.8) have 2 possibilities True positive, P("W"|W) = 1-b = 0.8 False negative, P("~W"|W) = b = 0.2
"Melatonin is not working" branch (prior P(~W) = 0.2) have 2 possibilities False positive, P("W"|~W) = a = 0.05 True negative, , P("~W"|~W) = 1-a = 0.95
I'm wondering why 0.05 (alpha) was used in that formula? True positive and false negative rates depends on statistical power (1-beta) and beta, and in case of beta 0.2, rate of "Melatonin is working" in case of negative result is 0.457 (not a 0.1739)
"Melatonin is working" branch (prior P(W) = 0.8) have 2 possibilities
True positive, P("W"|W) = 1-b = 0.8
False negative, P("~W"|W) = b = 0.2
"Melatonin is not working" branch (prior P(~W) = 0.2) have 2 possibilities
False positive, P("W"|~W) = a = 0.05
True negative, , P("~W"|~W) = 1-a = 0.95
P(W|"~W") = P("~W"|W) * P(W) / (P("~W"|W) * P(W) + P("~W"|~W)... (read more)