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# Type 1 errors

Sal gives the definition of type 1 error and builds some intuition behind it. Created by Sal Khan.

Video transcript

I want to do a quick video on
something that you're likely to see in a statistics class,
and that's the notion of a Type 1 Error. And all this error means is that
you've rejected-- this is the error of rejecting-- let
me do this in a different color-- rejecting the
null hypothesis even though it is true. So for example, in actually all
of the hypothesis testing examples we've seen, we start
assuming that the null hypothesis is true. We always assume that the
null hypothesis is true. And given that the null
hypothesis is true, we say OK, if the null hypothesis is true
then the mean is usually going to be equal to some value. So we create some
distribution. Assuming that the null
hypothesis is true, it normally has some mean value
right over there. Then we have some statistic and
we're seeing if the null hypothesis is true, what is
the probability of getting that statistic, or getting a
result that extreme or more extreme then that statistic. So let's say that the statistic
gives us some value over here, and we say gee, you
know what, there's only, I don't know, there might be a 1%
chance, there's only a 1% probability of getting a result that extreme or greater. And then if that's low enough of
a threshold for us, we will reject the null hypothesis. So in this case we will--
so actually let's think of it this way. Let's say that 1% is
our threshold. We say look, we're going
to assume that the null hypothesis is true. There's some threshold that
if we get a value any more extreme than that value, there's
less than a 1% chance of that happening. So let's say we're looking
at sample means. We get a sample mean that
is way out here. We say, well, there's less
than a 1% chance of that happening given that the null
hypothesis is true. So we are going to reject
the null hypothesis. So we will reject the
null hypothesis. Now what does that
mean though? Let's say that this area, the
probability of getting a result like that or that much
more extreme is just this area right here. So let's say that's 0.5%, or
maybe I can write it this way. Let's say it's 0.5%. And because it's so unlikely to
get a statistic like that assuming that the null
hypothesis is true, we decide to reject the null hypothesis. Or another way to view it is
there's a 0.5% chance that we have made a Type 1 Error in
rejecting the null hypothesis. Because if the null hypothesis
is true there's a 0.5% chance that this could still happen. So in rejecting it we would
make a mistake. There's a 0.5% chance we've
made a Type 1 Error. I just want to clear that up. Hopefully that clarified
it for you. It's sometimes a little
bit confusing. But we're going to use what we
learned in this video and the previous video to now tackle
an actual example.