When we first introduced hypothesis testing in unit

one, we likened it to a court case.

And just like court cases, hypothesis tests are not flawless.

In the court system, innocent people sometimes are

wrongly convicted and sometimes the guilty walk free.

Similarly, we can make wrong decision in statistical hypothesis tests as well.

The difference, though, is that we have the

tools necessary to quantify how often we make errors

in statistics.

So, in this video we're going to first introduce type one and type two errors

and we're also going to discuss a little bit how we can balance these error rates.

Just to give you a sneak peak, the likelihood of making a type

one error and likelihood of making a

type two error are actually inversely proportional.

So it's actually not that easy to keep both of those error rates down.

So sometimes we have to choose and we're going to talk

about how do we choose between which one we are okay with being

a little higher versus which one we really want to minimize as much as possible.

Here's a two by two table that basically tells us what the true

state of the hypotheses are, and remember we usually don't know whether the

null hypothesis or the alternative hypothesis is true, but we make a decision

regardless based on the evidence that we collect or on the statistical significance

of that evidence.

If the null hypothesis is indeed true and you

fail to reject it, you've done the right thing.

There's absolutely no reason to worry.

Similarly, if the alternative hypothesis is true and you reject the null

hypothesis in favor of the alternative, once again, you've done the right thing.

But how about the other two cells?

A type one error is rejecting the null hypothesis when the null hypothesis

is actually true.

So in other words, rejecting the null hypothesis when you should not have.

A type two error is failing to reject

the null hypothesis when the alternative is true.

In other words, it's failing to reject the null hypothesis when you shouldn't have.

We almost never know if the null or the alternative is true.

But we need to consider all possibilities.

So if we

again think of a hypothesis test as a criminal trial, then it makes

sense to frame the verdict in terms of the null and the alternative hypotheses.

The null hypothesis says that the defendant is innocent.

Remember usually it's innocent until proven guilty, at least in the US, so it

makes sense that the status quo the

null hypothesis says that the defendant is innocent.

The alternative says that the defendant is guilty.

So let's take a look at these two questions.

Which type of error is being committed in the following circumstances?

Declaring the defendant innocent when they are actually guilty.

So in this case, we are saying that

the defendant is innocent, however they are actually guilty.

This means that we are failing to reject

the null hypothesis when the alternative is actually true.