In this video we'll take a look at Type
1 and Type 2 Errors in hypothesis
testing. In hypothesis testing, based on
the outcome of our statistical test, we
either reject the null or we fail to
reject the null, which is also referred
to sometimes as accepting the null.
So there's two possible outcomes, where
only one can occur in a given test:
either reject the null, or fail to reject the
null (or accept the null). If we reject the null
we are siding against it, while if we
accept the null, we are siding with it.
However when we conduct a hypothesis
test we cannot know for certain if the
null is true or false;
that's why we're conducting the test in
the first place. Because hypothesis tests
are based on probability, while we hope
to make correct decisions,
it is possible to get results that are
contrary to reality, such as the null
being true in reality but we reject it
based on our statistical test results.
When we get a result that is contrary to
the truth,
this is known as making an error in
hypothesis testing.
There are two different kinds of errors,
we have the error where the null is true
but we reject it based on our test,
and then we have the other kind of error
where the null is false but we accept it, or
using the other language, fail to reject,
based on the results of our test. Now you
should take a moment to look at this and
make sure that you can see the
inconsistency in these two statements. If
the null is true we reject it that's an
error or mistake and if the null is
false and we accept it that's also an error
or mistake. And these terms do not agree
as I just said so that's why we have
errors here. So whenever this happens we
have made an error if we do either 1
or 2. There are also two types of
correct decisions in hypothesis testing.
The first one is the null is true and we
accept it.
So if you think about that, if the null
is true and, from our test, we accept it,
then we've made a correct decision there,
so that's good. And the other scenario is
where the null is false and we reject it,
based on our data, so that's also a correct
decision.
While these are the two types of possible
correct outcomes in hypothesis testing,
let's take a closer look at the two
different types of errors that can be
made, those two we looked at previously,
we'll examine those more closely next.
So let's consider a
situation where the null is true, where
there's really no difference between the
groups. And to make this a little more
concrete assume that we're looking at
the first year collegiate experience in
males' and females' perception towards
college, how much they feel like they're
part of the experience at the University.
And let's say for the purpose of this
example that it's known that males and
females really there's no difference
between them, how cohesive or how much
they feel like they're part of the
University, on average. Just assume that
for this example.
But let's say that we conduct a
hypothesis test and our numbers indicate
that we should reject the null. So with
our example, let's suppose that females
in our study that we did indicated that
they felt more connected or engaged in
the university than did males for
whatever reason. Let's say that we
sampled, we did a random sample, but we
happened to get more females who were
involved in sports and more females who
were involved in activities or groups at
the university than males just by chance
alone. And that those factors had them
more engaged in the University and as a
result our hypothesis test indicated
that females were more engaged than males.
So if we got that result here but, as I
said earlier, if the null is really true
but we reject it because our data
suggest that females were more engaged
in the University than males then we've
made a mistake - an error has been made
here. And when we reject the null, when
the null is true, that's known as a Type
I Error. So our formal definition - Type
I Error - is reject the null hypothesis
when it is true. And our example again
there was really no difference in truth
between males and females and how
engaged they are on campus after their
first year at the university, but our
study led us to conclude that females
are more engaged, and that led us to
reject the null. So we rejected the null
when it was true,
that's a Type I Error.