How We’re Fooled By Statistics
1tSqSMOyNFE • 2013-11-23
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which is most effective for helping
people learn punishment or reward we
consider the case of Israeli fighter
pilot training because instructors there
found that negative feedback was far
superior to positive feedback if a Cadet
performed a particularly poor maneuver
they would reprimand him but they
noticed that on follow-up attempts his
performance invariably improved in
contrast if they praised a Cadet for
executing a skillful maneuver his
performance on subsequent attempts
typically declined so naturally They
concluded that positive feedback is
ineffective or even detrimental whereas
negative feedback is what works the
problem is this seems to contradict a
body of research that shows positive
feedback is actually more effective than
negative feedback for example in studies
involving teachers it was found that if
a teacher increases the ratio of
positive feedback to negative feedback
that actually increases the percentage
of time students spend on task in
another study rugby players were given a
video feedback session following a game
except half of them were shown their
highlights and they were praised for
what they had done and the other half
were shown their biggest blunders their
mistakes and they were scolded for doing
things incorrectly now a week later at
the next game it was the players who had
received the positive reinforcement who
performed the best and in fact the
difference was not just psychological
blood tests revealed that the players
who received positive feedback actually
had higher levels of testosterone than
players who had received the negative
feedback I think that's quite remarkable
that even a week post feedback you could
still see a physiological difference
between the two types of feedback wow
well so why didn't this work for the
Israeli fighter pilots well maybe there
are cultural differences and In some
cultures negative feedback works better
or maybe it's task dependent perhaps
some skills like learning to fly a
fighter jet require more negative
feedback or maybe the feedback had
nothing to do with the performance of
the fighter pilots at all maybe they
would have performed in the same way
regardless of the feedback they received
go with me on this imagine you have a
hundred students taking a test which
consists of a hundred true or false
questions on a subject they know nothing
about now assuming they all answer
randomly we know that the resulting
distribution of scores will have an
average of around 50 but just by chance
some students will have scored
significantly better or worse than the
average man if you select the top 10
students whose scores were all above 50
and gave them a second very similar test
you would find that the average of their
scores would drop back to around 50
similarly if you selected the bottom 10
students their score on a subsequent
test would rise to 50 this is just
regression to the mean regression to the
mean is the reason why if you have a
really good round of golf today your
round tomorrow will not be as
good yes that is because random chance
plays a role in virtually everything
that we do so the outcome comes of
events are influenced by both our skill
and a little bit of luck so if you have
especially good luck on one day chances
are your level of luck will not be as
good the next day now that sounds a
little bit like the gamblers fallacy
which states that past events influence
future probabilities for example if you
flip a coin and it comes up Tails a
couple times the gambler's fallacy is to
expect the probability of heads to
increase for the next flip in reality it
doesn't it's still 50/50 the idea with a
Gam fallacy is that probabilities change
so that overall things even out in the
long run that's the idea with regression
to the mean it's not that things are
evening out it's just that extreme
events are becoming diluted by the
average events which happen much more
commonly now with these students they
were completely guessing on every
question but even when you know
something about the subject there's
still going to be that element of chance
and so regression to the mean always
occurs just to a lesser extent this is
really important to consider in research
imagine you're triing a new drug to help
prevent heart disease so from a sample
of patients you select those in the
bottom 10% of heart health indicators
people with high blood pressure high
cholesterol that sort of thing now after
a month of being on the drug you test
them again to find that their scores
have improved well great the drug is
working right well maybe not see the
trouble is that although blood pressure
and cholesterol are more stable than say
your score on a random true or false
test there's still some inherent
variability caused by say your level of
stress on the day or your recent diet or
even the uncertainties introduced by the
measuring apparatus so the people who
ended up in the bottom 10% on the first
test likely had these factors all count
against them they were particularly
unlucky but you should not expect them
to be as unlucky when you test them a
second time so their scores should
improve just based on random chance that
is why it is so important that clinical
trials use control groups drawn from
exactly the same population so that you
can see whether the drug improv scor is
more than random chance alone would or
what about assessing the impact of speed
cameras when they're first installed
they're normally put in locations that
have had a high volume of accidents in
the previous year or two makes sense now
those accidents are likely due at least
in part to bad Road design but also due
at least in part to bad luck and so you
shouldn't be surprised that after a
speed camera is installed the number of
accidents goes down it would go down
anyway simply due to regression to the
mean meanwhile somewhere else that
previously had a small number of
accidents will likely have more so the
overall accident rate may not change and
yet we will feel as though our
investment in Road Safety has paid off
but perhaps what's most troubling about
regression to the mean is how it
influences our perception of feedback
for example with the fighter pilots
after they execute a maneuver
particularly poorly chances are the next
attempt is going to be better regardless
of the feedback they receive similarly
after an especially successful display
chances are the next attempt is not
going to be as good and that has nothing
to do with the feedback and everything
to do with the statistical nature of our
universe but we are hardwired to see
patterns and causality everywhere which
is why the instructors felt that
positive feedback was detrimental and
negative feedback is what works and this
is really unfortunate because that is
the exact opposite of what
well-controlled psychological studies
show you know I think it's really
unfortunate that if you give negative
feedback chances are you'll be rewarded
they will do better and if you give
positive feedback chances are you'll be
disappointed because it's difficult to
maintain that level of
luck but that's the way our world is so
think about that next time before you
tell someone off if you stay positive it
may just work out for the best in the
long
run this video was inspired by the book
Thinking Fast and Slow by Nobel prize
winning Economist Daniel Conan so that
was the first time I heard of the
Israeli fighter pilot training and
really started thinking about regression
to the mean it was pretty awesome and I
downloaded this book from audible so I
was listening to it on my travels I'm
currently at the perimeter Institute
which you can see has some beautiful
blackboards now if you want to listen to
this book you can download it for free
by going to audible.com/veritasium or
you can listen to any other book of your
choice for a one-month free trial so
thanks to Audible for supporting me
thanks to Perimeter Institute for
putting me up in this amazing location
and I will see you next time with some
theoretical physics ideas so stay tuned
for that
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file updated 2026-02-13 13:08:49 UTC
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