So let's look at some data.
we're gonna try to figure out what the effect of having property
rights is on things like child health, okay using this as if natural
experiment from Argentina.
Now just like in regular randomized experiments there are many problems
that are arise in as if natural experiments, one of them being non
compliance, okay.
So in this case some people lived on land that the government took,
the owners said fine, have the land, okay, but the squatters didn't
actually get property rights to the land they didn't actually get
a title in their name and that could be for many reasons but maybe
they just didn't fill up the paper work for example, you've to actually
fill up the paper work and apply to get a title.
So they had the option of getting property rights but they didn't
actually receive it, so they did not comply with the treatment, they
were assigned to get property rights but they didn't. So what we're
going to start out with is an intention to treat
analysis where we just completely sort of ignore this
problem and we forget about the fact that we wanna learn about the
actual causal effect of having property rights on your child's health
and instead we're just going to look at the effect of having an option
of getting property rights on child health, so we're gonna have
in this column effects for people who had the option of getting property
rights, and this column effects for people who did not have the
option, and our outcome variable here is called wait for high Z score
now this is a short time measure of children's health status and
larger numbers are better, and that's all I'm gonna do to explain
exactly what this number is, and if you really wanna know more this
is a really important part of research, trying to define where your
outcome variable are etc and it will talk about a lot more in the paper
in this literature on how to measure health, but for now larger
is better
and it's a measure of child health. So we've kids from
age 0 to 11 and this first row they are looking at all kids, in
the second row they are looking at just kids 0 to 4, at the third
row they are looking at kids 5 to 11. So let's just look at the
all kids effect, so over here the people who had the option of getting
property rights had an average weight for high Z score of 0.279,
the people who didn't have the option of getting property rights
it was 0.065, the difference, the average treatment effect is 0.214,
this is the average treatment effect of having an option to get
property rights. Now, is this a true difference or not?
In order to know that we have to unfortunately do some statistical
inference, some confidence intervals, hypothesis tests, and stuff
like that.
The reason is, our sample sizes are not enormous.
In brackets here they've got the sample sizes
So the treatment group, there are 239 kids, in the control group,
people don't get property rights, they were 132 kids, so it's not
a huge number of kids.
So what are we gonna do?
Well, what we're gonna do is take this difference, which is our
estimated effects size and then this number parenthesis here, 0.109.
That's called the standard error, and it tells us something about
the variance, the variation and effect sizes so we're gonna take
these two numbers and construct a confidence interval.
So I've got that over here to just remind you from our earlier modules
what's going on, the confidence interval is gonna be the effect size 0.214
minus 1.96 times the standard error 0.109, that's gonna be the lower
bound, and here's it's minus 0.004 and then the upper bound in our interval
is gonna be effects size 0.214
plus 1.96 times the standard error which was 0.109.
And I've done math for you, 0.432.
So how I've constructed this isn't super important, what matters
is you get to this interval here, and now we got to interpret it
so remember, the first thing we do is Interval or not yes zero is
in the interval minus 0.0004 to 0.432.
Now what we do is we claim zero is an the interval this is not a
true effect we're not sure whether there's actually causal effect
or whether this big difference we found and it was quite big.
It was five times larger outcome variable in the treatment group
than it was in the control group.
But just because it wasn't a big enough sample size we can't tell.
But you may look at this and say well is minus 0.004 that's almost zero
is almost on that interval.
So what you ca do in this case is say maybe the criteria for deciding
whether we have big enough sample or not is a little too stringent.
Maybe we're being a little harsh so what you can do is you can use
something and I'll call it less stringent Confidence interval okay,the
way you do that is replace this two numbers here with 1.64 and then
you do the same thing and if you do that you're gonna get this interval
I've drawn here.
Okay goes from 0.0 35 up to 0.397 , zero is no longer in this interval
and so we say here zero is not an interval.
Looks like this actually is a true effect we actually have found
that having the option of getting property rights has a positive
causal effect on
the child's health okay so this first thing I drew is something
called a 95% confidence interval.
The second thing I drew is called 90% confident interval.
Okay,so 95% 90% here is telling us a measure of how stringent we
want to be okay.
So going from 95 down to 90 we say we don't want to be as stringent
really as this first one.
We wanna allow for a little bit more Statistical noise basically.
What that did is shrunk the interval, we went from a bigger interval
that contains a down to smaller one,okay? So sometimes that's what
done in practice as you look at few different confidence intervals
in order to see maybe the effect doesn't look that but if you
If you relax your criteria a little bit, you get an effect.
Okay, ideally every researcher out there would want to have their
interval not contain zero for like 99% you get even stronger, no
matter how stringent you are, you still find effects, that's ideal.
I know research is hard to do And sometimes you don't always get
clear cut answers like that, so in cases like this there's some
subjective judgement about is there an effect here or not .There
is if you are not too stringent but there isn't if you're not very
stringent,okay and whether you believe this one or this one that's
really just up to your own judgement [MUSIC].