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Back around 2002 target came to a statistician with a question, in which is the answer
could potentially make the company millions of dollars. They asked, "using only computers
can you determine which customers are pregnant even if they don't want us to know?" and
From then on statistician Andrew Pole was in search of an algorithm to do just that
What he did was analyzed the shopping patterns of expectant mothers and noticed some common behaviors like an increase in lotion purchases
Loading up on vitamins and more stuff that I know nothing about and he used this information
To not only determine which customers were likely pregnant
But what their expected due date was and after developing his mathematical model the statistician had a list of hundreds of thousands of women
who were likely pregnant along with their expected due date and what trimester they were in and
From then on target could send coupons at just the right time over the next several months and even after the baby was born
Now, although target was cautious about following secrecy laws. It still might turn women away
if all of a sudden they started getting coupons like cribs and diapers and other related items when they didn't in fact
Tell the company that they were pregnant
So what target did was just sprinkle these items in along with some other unrelated products when coupons arrived so it would seem more natural
But about a year after creating this algorithm something happened though, and this is where it gets interesting
One day a man walked into a Minnesota Target demanding to see a manager
He was very angry
and apparently what had been going on was target was sending coupons for things like diapers and
Cribs and other related items to this guy's high school daughter and he was very upset about this
He was saying things like are you guys trying to encourage her to get pregnant?
And the manager didn't really know what was going on
He of course apologized and a few days later the manager called the dad back to apologize again
But this time the dad wasn't so much angry but a little more embarrassed
I think you guys know where this is going. on the phone The dad said I in fact owe you an apology
There's been some things going on around here that haven't been fully aware of and in fact
My daughter is pregnant and she's due in August
So yes this statistical algorithm figured out that this girl was pregnant before her dad even knew about
That right there is the power of statistics and we're just getting started. In
1964 an elderly woman was walking home from grocery shopping when she was all of a sudden pushed to the ground and had her purse stolen
Now she was able to get a glimpse of the thief and saw a blonde woman in a ponytail who then fled the scene
Then there was also a man nearby who heard the screaming
And saw the woman run into a yellow car that was driven by a black man who had a beard and a mustache
And yes
This is all needed for the story by the way. a few days after the incident police ended up catching
Janet Collins and her husband Malcolm who matched all the descriptions given by the witnesses
They were then charged with the crime and put in front of a jury
now since most of the evidence that could be provided for this was just from the victim and the man who saw the event and
what they both witnessed they brought in a mathematician as well to help prove the guilt of this couple. This mathematician calculated the
Probability of just randomly selecting a couple that was innocent
But also happened to share all these characteristics that were observed by the witnesses. Based on data
The mathematician came up with these numbers and assuming independent events
We can multiply them all together to find the joint probability that they all happened to apply to an innocent couple
Turns out there was less than a 1 in 12 million chance that this random couple who just happen to fit all those descriptions
Was innocent, so the jury returned a guilty verdict
This is actually a very famous case in terms of using statistics in the courtroom. Another quick example
is that of Sally Clark who was found guilty of murdering her two infant son's back in the 90s. Her first son died suddenly in
1996 due to unknown causes so it was assumed it was a case of SIDS, or sudden infant death syndrome
But about a year later she gave birth to her second son
Who was then found dead 8 weeks after his birth again of unknown causes
So after this happened and it was reported, the police ended up arresting her and her husband on suspicion of murder
During the trial a pediatrician professor
Testified that the chance of two infants dying due to SIDS at around the same time relative to their birth
Was about 1 in 73 million and again one in 73 million is way beyond a reasonable doubt
so it was more likely this was an event of shaking or smothering or whatever and
Sally Clark was found guilty and sentenced to life in prison
So you can see statistics has a lot of power in our world whether it be advertising
Criminal cases and so on but what's also really powerful and way easier to do is lie
mislead and misinform
Using statistics and you don't even have to use wrong data to do this
I mean, I've already done that multiple times in this video. I'm going to talk about that soon
so yes this next part for all you people who comment on videos before watching the entire thing because there is more I'm going to
Say but let's start off light though. In
2007 in the UK an ad was released for Colgate that claimed the classic "80% of dentists recommend Colgate"
It wasn't long before the advertising standard authority of the UK ordered they abandon this claim because although it was true
They knew people would not really understand what it meant
The study that was done allowed dentists to answer with more than one toothpaste
So like dentist one might say I recommend Colgate, crest, oral-b
Dentist two might say Colgate, crest, or Sensodyne and similar for dentists three, four, and five
In this scenario 80% of dentists do recommend Colgate. That is true.
But 100% of dentists recommend crest in this hypothetical and 80% recommend oral B as well
All of these numbers are factual and you can make an advertisement with any of these claims
But again, we know people would not understand what they really meant
now for this next part I'm going to ask you guys a question. If
Let's say hypothetically the high school dropout rates of a certain country go from 5% one year to 10%,
Is that a 5% increase or 100% increase?
Because if you're at 5% and you add five you get to 10% obviously
But if you're making let's say $5 an hour and you get a 100% raise you'll be at $10 an hour
So which one of these is it and I'm sure many of you are saying that seems like a pointless question
Yes
You do add five to get to 10, but the physical amount of people who are dropping out would be increasing by 100%
Well in the spirit of this video
Let's ask something else. Which one of these paints a more accurate picture
Like if one of these was posted in the New York Times or on Forbes or whatever
Which one tells the people more about what's going on?
And I'm actually curious what you guys have to say about that because I think we're gonna hear different answers from different people
But for this next part, I think we're all going to agree
What if hypothetically the dropout rates are one in a million people and then the next year they go to two in a million people
So that's .0001% to .0002%, a difference of again .0001
But that's also a 100% increase in the physical amount of people dropping out
So which one of these two headlines do think paints a better picture?
Well again, we might hear different answers
But I think we can agree the 100% makes it seem like a worse problem than it is
Like if five people in the whole nation are dropping out and the next year ten people do I
Wouldn't necessarily call that an epidemic just yet
Now using numbers like this in the misleading way is actually not hypothetical because it happened a few decades ago in the UK
But not with college dropout rates, but rather a birth control pill. In
1995 the UK Committee on safety of medicines issued a warning that a certain type of birth control pill
Increased the risk of life-threatening blood clots by 100%
What that actually meant was that with the older second-generation pill about 1 in 7,000 women developed a blood clot
Whereas with the new pill about 2 in 7,000 women developed a blood clot
So yes, the physical amount of women receiving a blood clot did go up by a hundred percent. That is true
But if we dig just a little deeper we see with the older pill is about .014%
Whereas with the new pill it was about .028%, which hardly seems worthy of a breaking news alert
But articles were posted about this misleading statistic and as a result naturally tens to hundreds of thousands of women stopped taking this birth control
pill
fast forward one year and that scare was blamed for
13,000 unwanted pregnancies many of which were teenage pregnancies... a lot of teenage pregnancy stories in this video... moving on
Do you guys actually know head lice is good for your health?
Seems pretty stupid
Right, but people actually thought this at one point and that brings us to the part of this video titled correlation or causation
or both
Remember, it's usually very easy to determine that two things are correlated from a statistical test but causation is a completely different thing
That isn't so easy to spot. yet
People are very quick to assume that A causes B just because A is correlated to B
Sometimes the logic can be stupidly obvious like fast-moving wind turbines are positively correlated to fast wind. As one goes up
The other goes up, but does that mean that fast-moving wind turbines cause fast wind?
Well, obviously not it's the other way around
But in many cases it isn't this obvious like what if I said that kids who watch more violent TV shows are more violent themselves
Does this mean that those shows cause kids to be more violent?
I mean that could be possible and definitely would be an immediate thought for many people
But what if kids who are more violent just happen to watch more violent TV shows that also seems perfectly reasonable
So we can't just jump to conclusions too early
Even though that's what many people would probably do. Or in the Middle Ages European
Saw that people who had head lice were normally healthy. Whereas people who were sick rarely ever had head lice. as a result
They assumed that lice would cause people to be more healthy when in reality head lice is very sensitive the body temperature
So people had a fever or anything like that the head lice would find another host
Then on the subject we have the third cause fallacy where two correlated events
Actually, don't cause each other at all, but it's rather a third thing causing both. For example ice cream sales
Do not cause an increase in heat strokes nor the other way around
Even though they are correlated. Hot weather is instead the cause of both of them. Or for the past several decades
Atmospheric co2 has increased along with obesity levels. So does one cause the other
Well, no richer populations tend to eat more and also produce more co2
And sometimes it can just be really unclear what's causing what.
Like a while back they found that students who smoke cigarettes get lower grades and that could mean smoking causes lower grades
Or maybe it means that getting bad grades causes smoking... Maybe the added stress that comes along with lower grades
Increases the chance that a student will pick up that first cigarette. That also seems like a reasonable explanation
Or it could be a variety of third factors is actually responsible for both
So even when looking at a statistical test with accurate numbers, it's pretty crazy how far you can still be from the truth?
Next we have a story that will probably have people making assumptions really early in the 1970s
Someone noticed that Berkeley was accepting 44% of male applicants to their graduate school
But only 35% of female applicants. Now right there half the Internet's like well say no more...
But only 35% of female applicants
That was an actual unedited clip of everyone on the Internet
Now these numbers that we saw are true
But very misleading when you look at how male and female applicants applied to each program within the Graduate School the assumed bias
Not only goes away but kind of flips. Look closely here in this row
You see there was a high acceptance rate for the program
In fact women had a much higher acceptance rate, but still overall it was high for everyone
however way more men applied to this one
Whereas more women applied to these programs down here with much lower acceptance rates
So since a higher percentage of women were applying to these programs with higher rejection rates
The overall acceptance of women would be lower guaranteed even though they are in fact slightly favored across a couple of departments
so either of these headlines could be published with the necessary stats to back them up and
All you gotta do is pick which one you want to use
toss
the other
Throw that into an article put it in bold right on the top, put the cleverly selected statistics down below it to back it up,
And you've got yourself a story
This here was an example of Simpsons paradox
Where looking at data as a whole tells a totally different story than grouping the data appropriately which I'm sure many of
You know, but I had to include it here
You guys remember the story of the blonde woman who robbed the elderly lady
Well, like I said, this is a famous case but not for the use of statistics
But rather the misuse of statistics in the courtroom, this was a classic example of the prosecutors fallacy
now this fallacy comes up when people assume that the probability of A given B is the same as the probability of B given A
Which I'm sure many of you know is not usually true from this equation.
Like if I said behind this curtain is an animal with four legs, that's the given. What is the chance that it's a dog?
Well, you probably do some thinking like well, it could be a dog, it could be a cat, it could be a cheetah
It could be a lot of other things and if you had to come up with a number you might say one in a hundred
One in a thousand or whatever, but if instead I said behind this curtain is a dog
That's the given, what's the chance that it has four legs?
Well, that's almost a guarantee because most dogs have four legs
So you see switch the given and the question at hand and the probability can change by a lot
So now let's look at what I said earlier
Turns out there was less than a 1 and 12 million chance that this random couple who just happened to fit all those descriptions
Was innocent, so the jury returned a guilty verdict.
This here was wrong
The stats actually showed us that given an innocent couple the odds that they fit the descriptions was one in 12 million
But then I said what the jury had also assumed that if you switch the given and the question at hand
The probability stays the same which we just saw can be very wrong
This left side should make sense like if I just grabbed a random couple out of a mall
That's the given there was a very small chance all of these would apply to them
But this is the false assumption that is the prosecutors fallacy
We're told or given
Hey
Here's a couple that fits all those descriptions. If maybe ten people in the entire city fit all of those given a random one
There's a 1 out of 10 chance that they're guilty or a 9 in 10 chance of being innocent. Not one in 12 million.
And remember Sally Clark who was found guilty of murdering her two children
This is also a famous case of the misuse of statistics
It turns out bacterial tests had actually been withheld that would reveal more specific information than a simple multiplication of two probabilities
Which didn't tell the full story at all.
Like it assumed that the two events were independent of each other when genetic or environmental factors could have definitely been at play
Like I said, sally was found guilty and sentenced to life in prison
But she only served three years when the convictions were finally overturned in early 2003. Up until then though
Sally Clark was widely criticized in the press as a child murderer
And she was never able to recover mentally from the false accusation. A few years after her release
She developed psychiatric problems and died in her home from alcohol poisoning in 2007
I'm gonna repeat that for everyone who didn't follow it. A woman lost two of her children due to natural causes
was accused of murdering them, was put on trial and found guilty due to a misuse of
Statistics, spent 3 years in prison, and even after her release was not able to recover mentally and died
Just about four years later
If you guys don't find that story
Insane then I don't know what to tell you
And actually the result of this case prompted the Attorney General to order a review of hundreds of other similar cases
Now because I don't want that to be where we end this video
Let's look at one more classic misuse of Statistics
This one has to do with how data is represented and it often involves bar graphs that don't have zero as their baseline
For example FoxNews one showed a chart detailing the numbers what would happen if the Bush tax cuts expired?
Do you guys see a problem?
Yeah
It starts at 34 percent at the bottom making a not even 15 percent increase look like a few hundred percent in
Reality the chart should look like this
Or take the Terri Schiavo case that occurred about two decades ago
Which involved a debate of whether a feeding tube should be removed from a woman in an irreversible vegetative state
During that time CNN posted this graph detailing which political parties agreed with the courts
It seems like Democrats supported the decision significantly more but because the baseline is not zero
It appears way different than it should, this is what the actual graph would look like
Or in 2015 the White House published a tweet about the increase in students receiving high school diplomas with an extremely misleading graphic
They made around a ten percent increase look like nearly 200%. Or in music
There was a chart released showing views between top artists that made drake look like he was ahead by a large margin
When in fact it was about a five percent lead
Now I'm guessing the comments on this video will be rather interesting
But remember these were cherry-picked events and it's not like everything. I said paints the full picture either
I just find it interesting that these numbers can change the way we think about a person
They can peek into some of the most intimate moments of our lives based on our grocery list
They can make very trivial events seem very serious and vice versa
You don't even need use wrong numbers for this
But hopefully this show just how not cut and dry math and statistics can be in the real world outside of a school setting
Especially and with that I'm gonna end that video there if you guys enjoyed be sure to LIKE and subscribe
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