Machine Learning - Hypothesis Testing - Possible Outcomes of a Hypothesis Test

Here we are going to discuss possible outcomes of hypothesis tests

So here we are having the respective diagram for the better ysis

So we are having two types of errors, one is a type 1 error and another one is a type 2

error and there are two cases where the decision is correct, so this case and this case

So rejects when H0 is false. So obviously here we are having this correct decision

And do not reject H0 when H0 is true and that is a correct decision

So, that means when H0 is true and we are not rejecting H0, that is a null hypothesis

that is a correct decision. And here when the H0 is false and we are rejecting H0 and that is our correct decisions

Now what about the other erroneous conditions? So in H0, H0 is true but you are rejecting H0, that is what about the other erroneous conditions

known as type 1 error. And the other one is that when the 8-0 is false

but you are not rejecting 8-0, and then the type 2 error will be found

So a type 1 error occurs if you reject the null hypothesis when it is true

and type 2 error occurs if you do not reject the null hypothesis when it is false

So the hypothesis testing situation can be likened to a jury- trial. In a jury trial, there are four possible outcomes that defendant is either guilty

or innocent and he or she will be convicted or acquitted So now the hypotheses are H0 that is a null hypothesis is that is this the defendant is innocent and the h1 is the defendant is not innocent that means he or she is guilty so for that very

particular case study we have drawn the same diagram once again so h0 is the defendant

is innocent and h1 means the defendant is not innocent the results

of a trial can be shown as follows. So, at first, we are going for the correct decisions

So, H0 is false. That means the defendant is not innocent. In that case, what will happen

And reject H0, that is convict. So obviously, that is a correct decision

And then we are having this one, because here you see, the H0 is false, that means the defendant

is innocent is false, that means not innocent, and then rejects H0 that is convict so that is a true case here next one for this one so

h0 is true that means the defendant is innocent and do not reject H0 that is acute

so that is the correct decision next one this is our type 1 error so that means

h0 is true that is innocent but he or she is getting convicted and this is our

type 2 error when H0 is false that is not innocent but he or

she is getting acquitted. So, that is, do not reject H0, that is acquit. So, in this way

the previous case study has been mapped on this respective table and here you are finding

that there are two situations where the decisions are correct and there are two situations where

errors will occur in the form of type 1 and type 2. Thanks for watching this video