Becoming a Better Informed Citizen
[Applause]
okay
i want you to imagine something that’s
not quite that nice which is you go to
the doctor for regular checkup and it
turns out there’s something wrong
something serious potentially fatal and
you need treatment
luckily the hospital has two doctors on
staff with two different treatments to
offer you
and you’re allowed to choose which one
you want
and as you can see on board you see the
survival rate of those two treatments
and you’re allowed to choose obviously
most of you now think why would i ever
choose to put dr b
although with dr a thank you now what do
you normally do
when you have a serious medical problem
you find a cycling opinion
so you go to a different hospital that
also has two different treatments
and they split up the data a little bit
differently because they split it up
into severe cases in normal cases
now you might think well don’t i need to
know which case i am to make a good
choice and the answer is actually no
because if you look
you will see that dr b’s treatment has a
higher percentage in both categories
right meaning that in this hospital you
would prefer dr b
so to repeat in the first hospital you’d
prefer
dr a and the second hospital
you’d prefer to be the problem being
they’re the same doctors
this is dr a in the first hospital and
in the second hospital
and you can see i can either split his
two cases the normal sphere what’s up
or i can just add them up and get a 80
rate
and the second doctor the same thing the
problem being that although he’s better
both categories independently
overall his percentage is worse
now i hope that those of you who heard
there’s talks about statistics and
started dozing off that this grabbed
your attention enough to listen to me
for another 10 minutes
and what you’ve just experienced is
called simpsons paradox
which means that depending how i split
up data presented to you i can get
two opposite decisions from you
now becoming better informed citizen is
the name of my talk
and i want to introduce you to the
concept of statistical literacy
i teach mathematics which means that the
question that i hear most
often is when will we ever use this in
real life
admittedly it’s been a while since i had
to differentiate something outside of
work
however i’ve come to believe that the
single most important
topic in mathematics that i teach school
is actually
statistics because you will encounter it
no matter what you do
it will be in the news it will be in
medical
issues maybe you can go into research
and you have to deal with it
i mean even if you do psychology you
actually have to do courses in
statistics to
analyze all the data that’s given to you
so there’s no way around it
but as we’ve just seen there are quite
some problems you might encounter
now i’ll go to another example of the
simpsons paradox
which is a topic that’s often in the
news
the pay gap between men and women here i
present to you three companies
and show you the average income between
men and women in those three companies
and the question is which company is the
fairest in regards to pay
so i’ll give you a minute to look at
that but most people will probably think
well
technically none of them are fair
because fair would be if it’s the same
for both but in the first one women are
too then the second one’s a little bit
better but it’s still below and the
third one well compensates the first two
but it’s also not fair that they
actually get more
the problem is let’s have a closer look
so i’ve
split up the work of workers in that
company
into managing positions office workers
and support staff
and here you can see how many of those
are male how many of those are female
and how much they get paid each
the problem here is well it’s not
actually a problem everybody gets paid
the same on their level
but because there are fewer female
managers and office staff
the overall average goes down something
that the one number of average doesn’t
actually tell you
let’s have a look at company b company b
also has fewer women in the positions
but their pay is actually higher than
their male counterparts
but average is still lower bit weird
and now company c where you have
more women in the categories which is
good but they actually get paid less
but the average is higher meaning it
actually looks good
if you present that let’s say in the
news so
the problem is if you just compare the
averages
you don’t see any of that nuance and you
might completely have the wrong
discussion because the discussion could
be in a company
why there are fewer women in leadership
positions or why do people actually get
paid differently for the same
job but you have the right conversation
you actually need to analyze the data
appropriately and we have this tendency
to go for one number one number only
and that’s not always very productive
now i’m pretty sure there are a couple
of people in the audience who think well
this guy’s teaching mathematics and she
just says average that’s not very
good and you’re right because we’re
getting to the idea
that there are actually different kinds
of averages the problem is when we speak
normally in english
every day we don’t actually say we don’t
talk about the average we talk about the
mean
thing that most people are familiar with
you add everything up and then you
divide it evenly that’s the mean
prop the problem being mathematically
there are more
averages now on the board you have three
classes and their grades it’s the ib
system meaning that seven is the best
grade and
one is the worst grade now which class
did best
on average the problem is
if i take the mean i get one result
another average i can use is so called
median which means that you bring the
numbers in order and then you say the
middle one
and the last one called the modes which
simply says which number actually occurs
most often
the first class has these averages
the second one these and third one these
as you might notice each class did best
in one category
meaning that if this was either in the
newspaper or you actually discussed this
or the class is discussed with each
other every class has a right to say
on average we were better so
whenever you heard hear somebody saying
on average
the negativity of response would be well
which one
talking a little bit more about averages
because it’s really important because
our brains
really don’t like our brains don’t work
well with averages
because i’m pretty sure each one of you
has often or sometimes at least heard
the
expression the most likely outcome
whether that’s in science
an experiment maybe even politically to
say this will be the most likely outcome
the problem is there’s more to it than
you might think
so i feel the point two times that
average
should be that i actually get one head
and one tail right
what’s the actual probability of that
happening
fifty percent our brain likes that
what if i use 10 coins and flip it you
will still stay well on average it
should be five heads and five tails
right
the problem being that this actually
happening
has only a probability of 25
meaning that in 75 percent something
else than the average happens
and this actually gets worse as i
increase the numbers if i flip it 100
times
you would say it should still be 50 50
but not actually happening
only happens in eight percent of the
cases you might say well that’s a neat
thing but why should i care now
for the experiment you have a country
with ten major cities each city has ten
thousand cabinets
and there’s a disease which occurs in
roughly 1 in 10 000 people
so on average every single city should
have one of these cases right
now assuming that this this disease is
actually random
and there are no factors about it what’s
the chance that every city
has exactly one sick person come up with
a number in your head
and the actual answer is
probably slightly lower than you thought
now why is that important
because it means it’s not one in each
city that means at least one city has
two
and you can be sure that the mayor of
that city won’t like the newspaper
headlines of saying that this city has
twice the average the national average
rate of that disease
maybe even three times if there are
three cases in the city
maybe the citizens demand that time and
resources will be used
to fight off this problem and actually
find out why their city
has this problem in the first place the
problem is
in statistics when you just have random
events
clusters are actually to be expected to
visualize this
i will take a coin and because i want to
avoid embarrassing myself and not ever
being able to flip it here i now have it
here
i want you in your head to decide if
it’s going to be heads or tails
so just think if this head details
it’s tails please stand up if you were
correct
now because every second person on
average should be right our brain
kind of thinks it should be standing
sitting standing sitting standing
sitting
but as you can see that’s far from the
truth and the problem is
should i actually go in one of the
corners maybe the two people standing
next to each other who are both standing
up now
and analyze whether they have the
ability to predict the future or
not there’s another group there in the
middle so looking at these clusters
after the effect and trying to analyze
why
there is a cluster cluster is not
necessarily productive
if you don’t understand that cluster is
actually to be expected
and you need to think about how big of a
cluster will actually be a problem
otherwise limited resources and time and
energy might be diverted in the wrong
place please sit down
now i’ve been talking about percentages
a little bit
and i’ll stick with that for a moment
i have in my kitchen three eggs and two
sausages
which means that i have sixty percent
eggs because it’s three out of five
i feel like a snack and i go to the
kitchen and eat a sausage
now i have 75 percent eggs because it’s
three out of four
what’s a valid conclusion that an
outside observer might have if he sees
mr barakat
enters the kitchen and the potential
eggs goes up from 60 to 75 percent
if the person doesn’t know anything else
that might be a conclusion
they get to and the problem is this is a
silly example but that actually happens
in the real world imagine you have a
city with different
police precincts and one present
initiates a new program which is
actually successful
in reducing overall crime in their area
of the city
what does that mean about the crime rate
in the other precincts
it will go up although the actual number
of crimes
stays the same maybe
your company your department does better
and suddenly everybody else
looks worse although they’re still as
productive as before
of course you could say well relatively
they didn’t improve it you did but
to be honest that’s not what people
think when they see a percentage go up
or down
that’s why i’m actually having this
talking
another problem about percentages is
when percentage or percentages
change because if i say a percentage
goes down by 10 percent
i mean something like this that it goes
from 15 percent to five so it’s reduced
by 10 what do i actually mean
it goes from 50 to 13.5 you might notice
that by 13.5
well 10 percent of 15 is 1.5
so 15 went down by 1.5 that’s a
reduction of 10 percent
both of these are actually valid points
meaning that if somebody actually talks
about the change in a percentage
it’s very important to know which case
they’re talking about i’ll come back to
a medical example
the mortality rate for cancer in some
cases halves if you do chemo
now the expression the cure is sometimes
worse than the disease
has its place and when making the
decision you might be interested in
is this a drop from twenty to ten
percent
or is it a drop from two to one percent
both are half but if you’re only told it
halves
and you have to make a decision you
don’t have necessary all
information to make an informed decision
sometimes depending how the number is
presented to you
it will produce a completely different
emotional response from you
and i’ll have an example here
let’s say an increase from 300 to 450
parts per million and this is not
supposed to be a climate change debate
it’s just like this number goes up
from 300 to 450. the problem is
if i don’t want to express it in parts
per million about 0.03 to 0.045
no matter what you know or what you
believe or what you feel about this
your brain will automatically have a
different response to the above and the
below numbers
because our brains don’t really work
that well when
dealing with numbers that are bigger
than let’s say how many fingers we have
so keep that in mind when a number is
presented to you
either the unit you don’t know or maybe
in a context you don’t know
maybe somebody comes up to you and says
hey i can deadlift 100 kilos
and you think okay i don’t know what the
deadlift is but 100 kilos i know that’s
kind of heavy that sounds pretty good
and then you have the people actually
know what the deadlift is and know that
100 kilo deadlift is
not very impressive at all so when
you’re given
an information about something where you
don’t know much about it you probably
need to look it up
even for me if i hear something that a
power generator produces a certain
amount of
energy or power i don’t know
exactly without looking up how to put
that into context with other sources of
energy
now other problems are again as i said
if you’re not given any context
so for example if i just put this number
on the board four million infants died
in 2018 according to unicef
obviously everybody knows that’s bad and
that number is really big so you think
well that’s horrible
we should really really do something
about that the problem is
do you have any other numbers to compare
this to
because one year previously the number
was slightly higher
when you previously it was still higher
in 1990 it was even more than twice as
high
and the most important thing about this
is these are absolute numbers so despite
population growth between 1990
to 2020 the number of infants so below
one year
dying has more than half worldwide
the problem is you don’t know this
unless you look at the numbers in
context so if i just show you 4 million
your brain says 4 million babies that’s
obviously bad so we should do something
about it and it’s horrible
but the matter as a matter of fact is
it’s getting
much better and it’s the best it’s ever
been
now when preparing this talk i asked my
brother for advice what i should include
his response was everything you’re going
to tell them is absolutely
obvious and it’s completely irrelevant
that you have this talk because
everybody knows this already
he has a phd in mathematics so he has a
very particular point
of view for this so i asked my sister
and she was a little bit more helpful
saying that i should at the end of my
time give you concrete advice what to do
in the future otherwise this was a
pointless exercise
so here are three pieces of advice
first when reading or being told about
an average the responses you should have
are what average are you talking about
and
keeping in mind that our brain really
likes to think the average
should happen and anything else there’s
something wrong
but i hope i showed you that it’s
actually very unlikely
that the average is going to happen in
most cases
and so you should expect something else
to happen
secondly but where percentages as i said
a percentage change which one did it go
down by 10
or 10 percent of the percentage i
already have it’s most of the time very
helpful if you’re given a potential
something to also ask for the absolute
values
to make a better informed decision
and finally you need context for numbers
if you’re just told a single number
this is the gdp of a country nothing
about the previous years
what am i supposed to do with that so
ask for numbers in comparison and
although i said three pieces of advice
the most important piece of advice is
a single number never almost never tells
the whole story
unless that number is 42. thank you