Behavioral eco-lect3: Judgement under risk and uncertainty part 2…
Behavioral eco-lect3: Judgement under risk and uncertainty part 2
Regression of the mean
‘Field experts’ typically would say that punishment works better than reward.
They claim that when someone is given a compliment, performance the next time goes down. However, when one is critical, performance next time goes up.
There is a longstanding debate on what works best as a teaching mechanism: punishment or reward.
The mistake here is failing to see ‘regression to the mean’. A bad performance can just be bad luck, and a good performance ‘good luck’. This luck is likely to adjust the more repetitions one takes.
(Failing to note) Regression to the mean: over repeated tests, the tendency of an unlikely outcome tends to return to ‘normal’ over repeated tests.
Base rate neglect: failing to take the base rate of an event into account
Example 1 slide 11/34
Example 2 slide 12/34
Some probability calculation (1)
P(B|A)xP(A) = P(A|B)xP(B)
P(B|A) = (P(A│B)xP(B)) / (P(A))
In similar spirit, when outcomes are dependent on each other, we have:
P(A&B) = P(A|B)xP(B)
P(A&B) = P(B|A)*P(A)
that also holds that:
P(A) = P(A|B)XP(B) + P(A|-B)XP(-B)
When outcomes are independent on each other, we know that
P(A&B) = P(A) x P(B)
Some probability calculation (2)
P(A) = P(A|B)xP(B) + P(A|-B)xP(-B)
P(B | A) = PAB x P(B) / P(A|B) x P(B) + P(A|−B)xP(−B)
Recall from previous slide:
P(B|A) = (P(A│B)xP(B))/(P(A))
Some probability calculation (3)
P(A|B) = chance of being tested positive, while having cancer
P(A|-B) = chance being tested positive, while not having cancer
A = testing positive
P(B|A) = chance of having cancer, while being tested positive (this is what we are trying to calculate)
B = having cancer
P(B | A) = PABx P(B) / P(A|B)xP(B) + P(A|−B) x P(−B)