hello i'm jeffrey rosenthal i'm a
professor of statistics at the
university of toronto and this is stat
support
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question from king d weeb why do
statisticians get so worked up over
probability every event is just 50 50.
it either happens or it doesn't this is
something i've heard before this idea
that well if it can either happen or not
it must be 50 50. sometimes that's
referred to by philosophers as the
principle of indifference meaning that
anything that could happen they must all
have the same probability the thing is
it's just not true when i go home today
from the studio i might get killed by a
bolt of lightning or i might not get
pill killed by a bolt of lightning i'm
pretty sure there's not a 50 chance i'm
gonna get killed by a bolt of lightning
okay next we have a question from what
the fuss who says why is statistics
important in life really we're awash in
all kinds of different data so anything
from you know the spread of disease or
crime statistics or
studies of a medical treatment or
financial data or public opinion polls
there's so many facts and figures and
statistics out there the science of
statistics is a way to try to sort
through it so if you don't have any
statistical knowledge or understanding
or perspective then you're likely to say
well this must be true because my friend
said it or this must be true because i
heard it on the news or i just kind of
think it must be true but if you have
statistics you can try to analyze all
the facts and figures that are out there
and try to see what are the real trends
what's really happening versus what
things really aren't the way people
think they are next we have a question
from lawrenceitv
says question for statisticians why did
the polls get it so wrong explanations
please yeah so public opinion polling
especially when it's predicting
elections is a very high profile thing
but also a hard thing to do and usually
people notice the mistakes more than the
corrections so a lot of public opponent
for elections has actually been quite
accurate and it's predicted things quite
well but there have been some high
profile misses for example the us
presidential elections of 2016 and 2020.
now even in those cases typically the
polls prediction compared to the actual
results was usually only off by about
four or five percent which isn't such a
huge amount considering how hard it is
to figure out what's going to happen but
it's still a big enough error that if
the election's close it can make a big
difference so why is that well
election polls of course they don't ask
everybody how they're going to vote they
just ask a sample usually a few thousand
people and then try to figure out what
maybe a hundred million people are going
to do so that is a challenge the good
news is if the polling is done randomly
that is we're equally likely to pick
every person with the same probability
then we have good statistics to allow us
to figure out how accurate we're going
to be what will be the so-called margin
of error you know how close we'll
usually be to the true answer and
actually that works pretty well but what
makes it especially hard for the
pollsters is that it's hard to get a
random sample and the main reason is
because most people don't want to talk
to pollsters polling companies don't
necessarily like to talk about it but
their response rates are usually less
than 10
and that can lead to a lot of biases
because maybe people who support a
certain candidate are a little bit more
likely to agree to talk to the pollsters
than people who support another
candidate and any little response bias
like that can have a huge impact on the
results question from come on matt think
what are some common statistical errors
and how can we learn to spot them and if
possible correct them in others and our
own work one of the biggest things is
people don't think about what i like to
call the out of how many principle and
that's this idea that when something
happens at striking people will compute
the probability of it happening in that
exact way to that exact person but not
look at the chance that it will happen
in some way to somebody there was a a
woman in england who had two sons who
each died in infancy there is something
as you probably know called sids or a
sudden infant death syndrome so maybe
just two times she got really really
unlucky and her babies stopped breathing
or maybe she was a murderer and she'd
actually uh she actually suffocated them
and she was actually arrested and
charged and at her trial they said oh
it's so unlikely that there'd be two
sids cases in the same family that we
can rule that out she must have actually
tried to kill them and that's an
interesting example where if you just
look at the probability given two kids
in one family what's the chance they're
both gonna die of sids of course it is
very unlikely but then if you say out of
all the millions of families in the
united kingdom or in the whole world
what's the chance that somewhere there's
a family where two kids both died of
sids extremely likely and it seems like
that was the case with her there was
actually no other evidence that she had
actually tried to kill these kids she
was just extremely unlucky and yet she
was convicted she was jailed she spent
several years in jail before there was
enough of an outcry and eventually on
the second appeal the case was
overturned question from josh lev says
what's more likely than winning the
lottery the short answer is everything
that is to say if you're talking about
winning a lottery jackpot for one of the
big lotteries like mega millions or
powerball then the chance of winning
that jackpot with a single ticket is one
chance in a couple of hundred million
depending on which lottery so just
incredibly unlikely so compared to that
almost anything you can think of being
killed by a bolt of lightning or the
next person you meet will one day be the
president of the united states or any
crazy thing you can come up with we can
estimate the odds for all of them and
they're all more likely than the chance
you're going to win the powerball
lottery and in fact one that i like to
use as an example is if you drive to the
store to buy your lottery ticket you're
way more likely to be killed in a car
crash on your way to the store than you
are to win the jackpot next we have a
question from
s molly mall i'm just patiently waiting
for people to realize that all
statistics are skewed because the data
is skewed in so many ways that i can't
even list them all
so not a big fan of statistics maybe but
that's true there is that's a good point
that all data is going to have some
things that are wrong with it maybe it
was biased maybe it wasn't measured
correctly maybe it only shows part of
the story but i don't think that means
we should just forget about it and just
forget about statistics and data i think
what it means is we have to think
carefully when we get data we have to
say how is this data collected is it an
accurate reflection of the truth in what
ways is it going to be biased or
misleading and then we can still draw
inferences from it but it's true that we
have to be careful we have a question
from john friedberg says about to play
what must be the absolute worst casino
game in terms of play rods any guesses
well it's an interesting question
there's different casinos with different
games but one of the games which to my
surprise is one of the most popular and
also has one of the worst odds against
you is the video lottery terminals so
people love them but they usually have
at least a five percent and maybe 10 or
even 15 house edge so they're really not
the best game now there are some casino
games which have odds which are much
better for the player so for example of
the pure chance games the game craps
where you repeatedly roll a pair of dice
kind of like these you have a
49.2929 percent chance of winning uh
next question from shava khadzi are
murder rates skyrocketing or the media
doesn't have much to report so they are
focusing more on that yeah it's a good
question so murder rates have generally
been coming down a little bit in the
last couple of decades but in the last
few years there's been a little bit of
an uptick so they're now a little bit
higher than they were a few years ago
but they're still quite a bit lower than
they were
a decade or two ago also i've noticed
for example politicians and police
spokespeople and so on they all will at
times say oh crime rates are way up for
their own reasons they have reasons for
wanting that to be said even though you
know maybe it's not actually true so
it's just one more reason that if you
want to know what's happening with
something like you know rates of crime
well don't listen to what a few people
are saying look at the actual statistics
and then you can see the truth
next we have a question from brentaclan
says how does probability work in the
roulettes so it's a good question
roulettes are fairly simple so the
standard american roulette wheel has uh
38 of those little wedge slots and two
of them are green there's the zero and
the double zero and then the others are
divided into 18 red and 18 black the
person at the casino spins the wheel and
presumably it's equally likely to come
up any of those 38 different wedges so
what it means is if you bet on for
example red well 18 out of the 38 wedges
are red so you have an 18 out of 38
chance of getting red which is a little
bit less than 50
and that's why if you bet on red there's
an even money payout but on average
you're going to lose a little bit more
money than you win you can also
sometimes bet on different things like
all the even numbers or something like
that but whichever bet you do it works
out to the same thing there's a slight
edge in favor of the casino and that's
why if you play roulette over a long
period of time it's going to be more and
more sure that you're going to lose more
money than you win a question from six
latin six lover six who makes betting
odds is it an algorithm so it's a really
interesting uh problem for the bookies
or the people who are making these um
odds now the goal is pretty easy to
understand because if you're a bookie
what you want is pretty much to have the
same amount of betting on both sides so
that in the end you don't really care if
the horse wins or not or you don't
really care if the team wins or not
because either way you're going to make
money because you're going to get your
cut whereas if everybody bet on one side
and then they all won then you could
lose a lot of money but on the other
hand how they do that is kind of a
challenge and usually they're updating
their odds as they go and if they see
everybody's betting on this one tmg we
better change the odds so that the next
bettors are more likely to bet on the
other side and i'm not a bookie but my
impression is that in the old days it
used to be on just kind of by their
judgment or you know experienced people
looking things over and tweaking things
whereas now there's so much online
gambling that a lot of it is automated
and they have algorithms which i think
are not simple based on how everybody's
betting and trying to adjust things but
the goal is pretty easy to understand
trying to balance out those bets
question from xenodotis what is a
stochastic process really well i'm glad
you asked so stochastic is just another
word for random so it means random
processes or things that proceed
randomly in time and the simplest
example is actually one i sometimes like
to illustrate with my students using a
stuffed frog so i'll do that here and we
imagine we have a frog which every
second randomly decides either to move
one step this way
or to move one step this way and once it
does then the next second it again
decides randomly to move one step this
way or one step this way and yet it's
actually
really interesting for mathematicians to
study this what's the chance that the
frog will eventually return to where it
started turns out it's 100 it's certain
it might take a really long time but
eventually it's going to return to where
it started and in fact eventually it's
going to be a million steps that way and
eventually it's going to be a billion
steps that way it's going to go to every
single place eventually if you wait long
enough with probability one we can prove
that next a question from anna cell x
says what does it mean to be
statistically significant so
statistically significant is saying
probably it wasn't just chance that this
is enough of an effect that we can
pretty much you can never do it for sure
but you can pretty much say it's
probably not due to chance alone
probably this actually shows something
real there was really a difference or
there was really an increase or
something really happened it wasn't just
the random luck so the basic idea is
pretty simple it sometimes gets lost in
the details but when you notice
something that happens you know maybe
this classroom did better on the test
than this other classroom then as
statisticians the fundamental question
you're always asking is does that mean
something real like oh maybe the
teaching was better in this class or
maybe people in that class are are you
smarter or was it just random luck so
you'd never expect any two results to be
exactly the same there's always going to
be some differences okay next question
from john elworthy can someone please
help with this what are the odds of
having three generations of family
members being born on the same day
first was born on january 10 1943 the
second same day 1994 and the third same
day in in 2022. it's actually a good
example of the sort of question that
there's different ways of looking at the
probabilities so if you just say there's
three people one of the chants they'll
all have been born on the same day well
that's pretty straightforward so you can
think well the first one could be born
on any day it doesn't really matter then
the second one has roughly one chance in
365 of being born on that same day and
then the third one has roughly one
chance in 365 of being born again on
that same day so it's one chance in 365
times 365 which was a little less than
one chance in 100 000 i think so uh it's
quite unlikely one way i'd like to look
at these kind of questions is this is
sort of out of how many different ways
that this could have happened so even in
this one family probably there's a lot
of other people in each of those
generations and if any three of them had
matched up their birthdays then this
same tweet could have been written so
right away the chance is a lot bigger
because there's lots of different
combinations which all could have led to
the same conclusion it's not incredible
that it happens but it's still pretty
cool when it does happen to you from
adjayo cie
says how best can a statistician explain
p-value to a non-statistician yeah so
that's a good question the basic idea of
a p-value is the idea of
what is the probability that the thing
you just observed
would have happened just by pure chance
if there was no true effect if we look
at let's say you know we have some
people with a disease and we give them a
new treatment
and then a certain number of them get
better do you say oh well that means the
new treatment really helped well no
because some of them would have gotten
better even without this new treatment
maybe more of them got better than you'd
expect on average from the new treatment
yeah but how much more and the p-value
question would be what's the probability
if we hadn't given any treatment that
that same number or more of the people
would still have gotten better and if
that p-value is pretty high you know
maybe there was there was a 40 chance
that they would have gotten better even
without the treatment we haven't really
proven anything and the typical standard
is that if the p-value is less than five
percent or less than one chance in 20
then we say okay it's pretty unlikely
that they all would have gotten better
if it hadn't been for this new treatment
so this provides some evidence that the
new treatment is helping but if the
p-value is larger it doesn't okay so
next a question from king ambuso says
statistically what are the chances and
right and this is a display of a draw
results and i believe this was from the
south africa powerball lottery back in
december of 2020 and what happened was a
little surprising so of the main numbers
there were five numbers chosen in a row
five six seven eight nine and then the
bonus powerball number chosen was a 10.
so we had six numbers all in a row for
the draw seemed very surprising so you
could say what are the chances of that
happening well the rules of the south
africa powerball then where you choose
five numbers between 1 and 50 and then a
bonus number between 1 and 20. so you
can say how many different ways could
you get them all in a row like that well
the first five numbers would have to be
five numbers in a row starting with
something from 1 2 3 up to 15 really so
that's only 15 ways and then the
powerball number would have to be the
next one so there's a very small number
and then when you divide that by the
total number of different ways you could
have chosen those five balls plus the
one bonus thing there's many more of
those so when you divide it you get that
there's a little less than one chance in
two million that such a sequence like
that would have come up question from uh
chris masterson is it statistically less
likely to be in a plane crash if you've
already been in one well no and of
course the answer is no if you think
about it how could it be you know how
could this new plane
know wait a minute there's somebody on
here who was on another crash so i
better not crash this time that's just
not the way science works it's not the
way airplanes work it's not the way
pilots work but a lot of people will
think that and the reason people think
that is because it's very unlikely any
one person is going to be on two
different planes that crash right that's
really bad luck but once you've already
been on one
that was very unlucky but now it doesn't
have any effect on the probability of
the next plane they're what we call
statistically independent events so
neither one affects the probability of
the other so a question from a tetraform
says hey what is the most statistically
improbable thing to happen to you well
when i was in my early teens my family
went on a trip to disney world florida
and in the middle of it all we looked up
and we saw my father's cousin phil and
he lived in connecticut at the time and
we lived in toronto canada and we had no
idea he was going to be there he said
you know what are the odds that out of
all of the hundreds of millions of
people in the united states and all the
people that visit disney world that my
dad's cousin would be there it's a good
example that on the one hand if you just
say what's the chance that one guy would
be my dad's cousin phil it's incredibly
unlikely but as with a lot of things if
you take the bigger picture you can say
well my dad's cousin phil isn't the only
person we would have been so surprised
to see what about my dad's other cousins
or my mom's cousins or my cousins or my
piano teacher or my friend from school
or there's probably a few hundred people
that we would have been really surprised
to see and then you say well we were at
disneyland for a couple of days and we
went on lots of different rides and so
on and we probably saw thousands of
people and just one of them was my dad's
cousin phil the other ones were other
people so it's actually not so unlikely
and i end up computing there's about one
chance in 200 or so about half of one
percent that if you go on a trip to
disney world and spend a couple of days
there on all the rides that you run into
somebody that you know so it's not so
incredible even though it sure was a
surprise at the time okay so i think
that's all the questions for today i
hope you learned something and i hope
i'll see you again