So in addition to the map that John Snow drew, showing the
deaths of cholera around Broad Street, he had one other piece of
evidence to conclude that cholera's being spread through contaminated
water.
He had a really nice natural experiment.
So in London at the time, many at the time
many households were provided water by two companies, either the
Southwark and Vaxhaull Company or the Lambeth Company.
Now in 1852 one year before the epidemic started, the Lambeth Company
moved it's water intake pipe up-stream on the Thames River before
So at the time, people were just dumping sewage into the water,
because we didn't know any better, and that was the same place that
we're getting the water to drink from,so Southwark and Vauxhall,
their intake pipe was in the middle of the city.
So it was taking in sewage, nasty infested water
whereas the [UNKNOWN] because they moved their pipe.
They were getting clean water that wasn't filled with sewage.
So the households in the city were split into two groups.
Those who got clean water, because their water was provided by Lambeth
and those who got dirty water, because their water was provided
by Southwark and Vauxhall so there are about 40,000 houses in the
Southwark and Vauxhall group and about 26,000 in the London Clean
Water Group.
So if you believe that houses were basically randomly assigned to
which company they got water from, then this is an [UNKNOWN] natural
experience as if natural experiment.
All we have to do is compare average rates of deaths due to cholera
in these two groups, to learn about causal effect of consuming dirty
water and whether you'll die from cholera.
So I'll talk about how we justify the as if randomized assumption
in few minutes, but now let's just
now let's just look at the data and see what we get.
So here we've got the number of people who died from cholera in
each of the groups.
So in South Vauxhall this is the people who were drinking sewage
water, about 1,263 died. m
From Lamberth/g, these are the people who were drinking clean water.
98 people died so if we look at the rates, because we can't directly
compare these numbers, because there's different total umber of
people for these different companies, so if you compare to the rates
and Vauxhall there are 313 deaths per 10,000 people whereas Lamberth
It was 37 deaths per 10,000 people, so this is a huge increase 315
over 37 which you can could also see in this many, many, many ,
many more people died who were drinking the sewage water than the
ones who were drinking the clean water, and if you look at the
and if you're lookngi through the rest of London, which is provided
water from other companies, a lot of people died there but the rate
wasn't nearly as bad as the people who were getting water from [UNKNOWN]
Vauxhall and from Lamberth they were much better on average than the rest
of London.
So, that's just the raw data.
If you wanted to just know the average treatment effect, it's the
difference between these two things, huge, very huge.
And by the way, I pointed out that there are no standard errors,
no confidence intervals, no p values or anything in this table.
Well none of that stuff existed at that time.
This is from 1885, P values, confidence intervals, they hadn't been
invented invented for another, 50, 60, 70 years.
So the whole idea of doing statistical inference was completely
foreign to John Snow at the time.
They really didn't matter, the sample sizes are really big here,
40,000, 26,000, even if you did that, this effect would be statistically
insignificant so what we
So what we see it loos like if you just do this comparison drinking
dirty water is going to give you cholera during this epidemic.
Okay so all we have to do is figure out is the [INAUDIBLE] assumption
true do we really believe that?
If so this conclusion that it's the water that's spreading cholera
is valid, okay.
So how did John Snow justify this?
Well I'm gonna read you a quote because it's really amazing what
he said.
He said quote, the mixing of the water supply of the most intimate
kind, the pipes of each company go down all the streets and into
nearly all the courts and alleys A few houses are supplied by one
company and a few by the other according to the decision or owner
of occupier at the time when the water companies were in active
competition.
In many cases a single house has a supply different from that in
either side okay.
So houses on the other side of the street have different
On the other side of the streets are supplied by different companies
even though they are on the same street.
Quote each company supplies both rich and poor both larger houses
and small and there's no difference either in the condition or occupation
of the persons receiving the water of the different companies.
It is obvious that no experiment could have been devised which would
more thoroughly test the effect of water supply on the progress
of cholera than this.
That's John [UNKNOWN] speaking in 1855 after doing this analysis.
So, what did he do?
Well, he just did a balance check.
He said we observe some variales about people living in these hether
they're rich or poor, whether they're living in a big house or small
house, okay?
So are these variables the same across these two groups or not.
He says yes.
Basically the percentage of rich people and [UNKNOWN] The percentage
of the poor is the same age group.
The percentage of large
In each group and the size of the house, the condition of the house
there's no difference.
So he checked that we have balance on observable/g which is exactly
what you would see if you had [INAUDIBLE] randomization okay.
Now even though So we've done a balance check and it looks good
we still guaranteed that we have balance on observable okay.
For example suppose there are really healthy people only choose
the Lambert company, because they thought the Lambert company was
healthier for some reason.
So they choose the They chose the Lambert company.
Then when cholera hits, maybe if not the water that's causing it,
it's just the fact that healthier people are more robust and then
they're not gonna get wiped out by cholera.
That will be a confounder, that will be a problem here.
Well Snow also argues that this is not the case.
And the reason is he says one out of 300
300,000 of all people of social classes were not [UNKNOWN] to him.
Divided into two groups without their choice, and in most cases
without their knowledge, one group been supplied with water contaminated
containing the sewage of London and amongst it whatever might have
come from the cholera patients, the other group having water quite
free From such impurities.
So, he basically argues that people don't even know that Lambert
they wouldn't even make a decision because their landlords are doing
it.
So how could they possibly have selected into picking Lambert
because it was healthier.
It's just not possible.
Finally in parts most importantly The air conditions that people
live in these two things were the same.
Okay, so that's constant across the two groups.
The air conditions, cuz people all lived in the same area in London
so that's what held constant.
And that's important because that was the prevailing theory at the
time.
That people thought it was [UNKNOWN] in the air causing this
Causing this, so the only way that we could see difference like
this due to Measnas/g would be if the number of measnas/g were different,
were much higher in this people than in this.
But that's not true because they were living across the street from
each other.
So the air cannot explain this data It has to be something else,
and because we think that there's rich people living in Lamberth/g
and poor people living in South oak/g that's not the case.
The main difference is the quality of the water.
That these people are drinking sewage water adn this people weren't.
That's what John Snow concluded in 1855.
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