fallacies and paradoxes (V)

Monty Hall problem

3 doors, 3 choices
Monty opens door with goat, never with car
so in 2/3 of scenarios, Monty is FORCED to open the door with the second goat, revealing the car’s location
so in 2/3 of scenarios, switching is smarter

Birthday paradox

how likely is it that two people in a group share a birthday?

leads to the multiple comparison problem
very unlikely things are not that unlikely if you have many comparisons

if you have a group of more than 23 people then it is more likely than not that two people share a birthday

Cherry picking

selective and biased extraction of data for analysis

choosing specific data points that support one’s desired conclusions
while ignoring other relevant data that may contradict it

graph showing global warming with an upwards trend
only picking the one short time frame where temperatures fell for a couple months

Simpson’s fallacy

conclusions are different based on wether data is aggregated or not

two different graphs
one shows aggregated data, showing that new treatment is effective
one shows specific data, showing that the treatment group has more children (which are naturally better at recovery) so we don’t know if treatment works

Berkley admission data
aggregated data: women have lower admission
disaggregated data: women applied to more selective departments than men

Gambler’s fallacy

the false belief that the occurrence of an event affects the probability of an independent event occurring in the future

investing, flying, game playing
“I fly so much, something must happen once!”

we are conditioned to look for patterns to rationalise and make life more predictable

Base rate neglect

ignoring the base rate/prior probability in favor of specific data

Steve is shy, he’s either a sales person or librarian.
We think he’s a librarian because librarians are shy.
But way more people are sales persons than librarians, so he's probably a sales person.

Gerrymandering

biased representativeness

how data is grouped can influence the statistics and results

done with election areas or in management of working teams

Will Rogers phenomenon

moving an element from one group to another improves the average of both groups, even though the element doesn’t change

group averages can be misleading when grouping changes

company part of a holding company A makes 100M
this company is bought by another holding company B

A: (100+200+300)/3 = 200 → NOW (200+300)/2 = 250
B: (70+70)/2 = 70 → NOW (70+70+100)/3 = 80

taken a low performer out of the overall higher performing group
an putting it into the overall lower performing group where it becomes a high performer
increases average for both

Berkson’s paradox

involved in generating and maintaining stereotypes

when selecting a sample of the population based on certain criteria creates a false correlation
- correlation that does not exist in real population
- reverse pattern than that in real population

talent vs attractiveness data points
if we only look at top of both groups, there seems to be a negative correlation, more attractiveness less talent
but this is in fact not true

given two independent events, if you only consider outcomes where at least one occurs, they become conditionally dependent

false cause fallacy

mistaking correlation for causality

number of people dying by being tangled in bedsheets
per capita cheese consumption
94% correlation but obviously not caused by one another

confounding variable

a third variable connecting an independent and dependent variable

we can correlate ice cream sales and shark attacks
they are seemingly unrelated
higher temperature is the confounding variable

definition of cognitive biases

a deviation from rationality in judgement

clustering illusion

perceiving patterns/clusters in random data points even when there is none
we tend to see meaning/patterns where there aren’t any

survivorship bias

the false belief that if one person can achieve something difficult, everyone can

if I can become a millionaire, everyone can!
when companies that no longer exist are excluded from analyses of financial performances

denomination effect

people may be less likely to spend larger currency denominations than their equivalent value in smaller denominations

people are less likely to spend equivalent amounts in larger currency denominations than in smaller denominations

subadditivity effect

the false intuition that the sum of probabilities of the parts is bigger than the probability whole

when you ask people to estimate the probability of different natural disasters occurring and sum up the given probabilities they will be more than 100%

appeal to probability

it’s unlikely/likely that X will happen so X will/won’t happen

there’s only a low chance of rain during PFW, so you don’t need your umbrella