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