in this video we're going to talk about the type 1 and type 2 error that you need to understand in a typical statistics course the type 1 error occurs when you reject a null hypothesis when the null hypothesis is true the type 2 error occurs when you fail to reject the null hypothesis when it's false the probability of making a type 1 error given that the null hypothesis is true this is alpha the probability of making a type ii error when h0 is false is beta and the probability of rejecting a false null hypothesis is one minus beta that's also referred to as the power of the test now what we're going to do is we're going to make a table that's going to summarize all of this bear with me uh one moment so here we have a atro the null hypothesis and there's two possibilities either h o is true or it's false we can't control that what we can control is our decisions we can choose to reject the null hypothesis or we can fail to reject the null hypothesis which means that we accept it so those are our our two options so let's say if the null hypothesis is true and we reject it when it's true that's an error specifically that is a type 1 error now if the null hypothesis is false and we've ejected then we've made a good decision that is not an error now if the null hypothesis is true and we fail to reject it or we accept it that is also a good decision but if the null hypothesis is false and we don't reject it that's bad we don't want to accept a false null hypothesis so that's another error that is the type 2 error so hopefully this table helps you to see the difference between a type 1 error and the type 2 error the type 1 error occurs when the null hypothesis is true and we make a bad decision we've ejected the type 2 error occurs when the null hypothesis is false and we make a bad decision we don't reject it now let's work on some example problems number one let's say that the null hypothesis atro is this statement john's used car is safe to drive so that's the null hypothesis part a which statement represents a type 1 error and we could also do part b simultaneously which statement represents a type 2 error so what i like to do is distinguish the good decisions from the bad ones let's look at answer choice a first john thinks that his car may be safe when in fact it is not safe is that a good decision or a bad decision let's say if he drives his car believing that it's safe when it's really not safe that's a bad decision that would be an error b john thinks that his car may be safe when in when in fact it is safe if it's if the car is safe and he decides to drive it that is not a bad decision that's a good one see john thinks that his car may not be safe when in fact it is not safe so if the car is not safe and he doesn't drive it that's a good decision d john thinks that his car may not be safe when in fact it is safe that's a bad decision if the car is good to drive and he doesn't drive it that's not really helpful so that's an error right there now we want to identify the type 1 error so we can eliminate answer choice b and c now looking at answer choice a would you say it's a type 1 error or a type 2 error feel free to pause the video and think about it for a moment now remember the type 1 error occurs when we reject the null hypothesis when h0 is true it never occurs when h0 is false the type 2 error this one occurs when we don't reject the null hypothesis when h0 is false so at this point we need to determine when h0 is true and when h0 is false so we know h0 is john's used car is safe to drive as choice a is saying that it's not safe to drive so it's saying that the null hypothesis is false because it doesn't agree with it so since we have a false ho and he fails to reject the false atro this is a type ii error now looking at the other option we could see that it agrees with the null hypothesis the car is safe to drive however he doesn't accept it he rejects the card he doesn't feel that it's safe so this is a type one error he rejects the null hypothesis when it is true so that's a simple way to distinguish a type 1 error from a type 2 error now let's move on to part c which type of error has greater consequence would you say it's the type 2 error or the type 1 error well let's look at answer choice d first d says the car is safe but john doesn't believe that it's safe to drive so if he feels that way he's probably not going to drive the car he's probably going to stay at home eat some pizza watch tv and that decision really doesn't have a significant consequence he's going to continue to be alive so he's not going to get into a car accident now looking at the type 2 error in answer choice a if the car is not safe to drive but he believes that it's safe and he goes and drives the vehicle gets into a car accident ends up in the hospital that's pretty bad i mean he could lose his life so answer choice a the type 2 error has greater consequence because if he makes that error it can cost him big time it can cost him his life now for the sake of practice let's work on another example number two in a criminal court case the null hypothesis ho is that the defendant is presumed innocent part a which statement represents a type 1 error and b which statement represents a type 2 error well let's distinguish the good decisions from the bad ones looking at answer choice a the jury believes that the defendant is guilty when in fact he is innocent that's not good so if they pronounce him guilty when he is innocent that is a bad decision that is an error part b the jury believes that the defendant is guilty when in fact he is not innocent okay that's a good decision if he's not innocent he's guilty so let's put a check for that one see the jury believes that the defendant is not guilty when in fact he is not innocent if he's not innocent he's guilty and if they believe he's not guilty that is an error d the jury believes that the defendant is not guilty when in fact he's innocent if he's innocent he's not guilty so that is a good decision so now let's analyze the two errors that we have b and d have been eliminated because those are not errors so let's focus on answer choice a the jury believes that the defendant is guilty when in fact he is innocent so h.o says that he is innocent so ant's choice a is saying that h o the null hypothesis is true however the jury rejects h or when it is true they believe he is guilty when he is innocent so therefore this is going to be a type 1 error now what about c c disagrees with h o so basically answer choice c is saying that the null hypothesis is false he is not innocent but the jury believes that the defendant is not guilty they believe that he is innocent so they fail to reject the false null hypothesis and this is a type two error they're accepting a false null hypothesis now let's move on to part c which type of error has greater consequence would you say it's the type 1 error or the type 2 error looking at the type 1 error here we have a man who is innocent but the jury believes that he is guilty and as a result if he does prison time when he is innocent that is a very very bad thing that should happen now looking at answer choice c here we have a man that's not innocent but the jury believes that he's not guilty they believe that he's innocent that's also a bad decision but who knows next time he does something bad he may get caught however having an innocent man be in punch for something that he hasn't done that is very very bad so i believe that is that type of error has the greater consequence you might feel differently but that's just my opinion on it so that's it for this video if you like it don't forget to subscribe and thanks again for watching