But just looking at these sample statistics, it's not possible to determine

if the differences we're observing are statistically significant.

So in this unit, we're going to discuss methods for comparing means to each other.

In this case, we're comparing many means to each other.

But we're also going to learn what methods we use when we have only

two groups to compare, as well as more than two groups to compare.

Now, let's shift our focus to another data set.

And let's look at the distribution of inflation adjusted total family income in

the US.

These data come from a random sample of Americans.

They were collected as part of the general social survey in 2012.

We can see that the distribution, as expected, is pretty right-skewed.

Suppose we would like to estimate the typical total family income in the US.

In the previous unit, we were introduced to the central limit theorem

which provided the basis for constructing a confidence interval for the mean.

But what if we're not interested in the mean, but the median?

There's actually no central limit theorem for the median.

So in this unit, we're going to introduce a new technique for

creating confidence intervals.

Namely boots strapping which takes it's name from

pulling one self up by one boots straps.

Which basically means accomplishing an impossible task, this is simulation base

method that doesn't have adds rigid conditions as the central limit theorem,

and, therefore, also works for many estimates beyond the mean, as well.

So in this unit, we're going to start by extending the methods we learned in

the previous unit to comparing two means.

So no longer will the focus just be on one single population mean,

but how do we compare means from two populations?

And we're actually going to specifically discuss what do we do if these populations

are dependent, so our means are dependent, versus if they're independent.

We're also, as we mentioned earlier, going to discuss bootstrapping.

We're going to define what it means.

How to bootstrap?

As well as when to bootstrap and when not to bootstrap.

We're going to also learn to work with small samples.

What if we don't have a sample size greater than 30?

What do we do then?

Namely, the T distribution is going to come into play.

And finally, we're going to wrap up our discussion by methods for

comparing many means to each other.

So extending what we've learned from comparing two means

to comparing many means to each other, namely.