I’m kinda struggling with the differences of Type I and Type II errors. Every time I think I get it, I look at it again and I’m confused. I think what is most confusing for me is the double/triple negatives that I’m trying to get my head around (i..e. FAILING to REJECT the NULL hypothesis).
Has someone got a good way of explaining the difference in these errors.
Type I error: the rejection of the null hypothesis when it is actually true.
Type II error: the failure to reject the null hypothesis when it is actually true.
If I say took the example of taking a sample from CFA exam results. Let’s just say that we know the std. dev is 10, What we want to disprove is that the mean of the population is 70. We take a sample of 100 scores. So our std. error is 10 / sqrt(100) = 1. We want to prove this to 5% significance (i.e. 2 tailed test, 1.96 std dev on each side, let’s just round to 2 std. dev for simplicity)
So the null hypothesis is u = 70
Type I error as I understand it:
Our sample returns a result of 65, so the mean should lie between 63 and 67, we reject the null hypothesis. The Type I error in this case would be if it turned out that real population mean was actually 69. We rejected the null hypothesis when it was actually true. The chance of this happening is the 5% (i.e. the chance that for a normally distributed population with mean of 69, that we should have been unlucky enough to pick that sample of 65).
Is the above correct before we move on to Type II error?
Type II error as I understand it:
Our sample returns a result of 70, so the mean should lie between 68 and 72. We fail to reject the null hypothesis. The Type II error in this case would be that the real population mean turned out to be 65. We just failed to reject the null hypothesis because of our dodgy sample.
Is the above correct?
I seem to be able to explain the differences, but there is just something that isn’t clicking for me with these explanations. It’s as if type I and type II errors are simply inverses of each other which I know they are not (i.e. P(Type I) is not equal to P(1 - Type II).
Does someone have a good analogy for explaining this that will make this stick. It’s really hurting my brain each time working this out again.
Has someone got a good way of explaining the difference in these errors.
Type I error: the rejection of the null hypothesis when it is actually true.
Type II error: the failure to reject the null hypothesis when it is actually true.
If I say took the example of taking a sample from CFA exam results. Let’s just say that we know the std. dev is 10, What we want to disprove is that the mean of the population is 70. We take a sample of 100 scores. So our std. error is 10 / sqrt(100) = 1. We want to prove this to 5% significance (i.e. 2 tailed test, 1.96 std dev on each side, let’s just round to 2 std. dev for simplicity)
So the null hypothesis is u = 70
Type I error as I understand it:
Our sample returns a result of 65, so the mean should lie between 63 and 67, we reject the null hypothesis. The Type I error in this case would be if it turned out that real population mean was actually 69. We rejected the null hypothesis when it was actually true. The chance of this happening is the 5% (i.e. the chance that for a normally distributed population with mean of 69, that we should have been unlucky enough to pick that sample of 65).
Is the above correct before we move on to Type II error?
Type II error as I understand it:
Our sample returns a result of 70, so the mean should lie between 68 and 72. We fail to reject the null hypothesis. The Type II error in this case would be that the real population mean turned out to be 65. We just failed to reject the null hypothesis because of our dodgy sample.
Is the above correct?
I seem to be able to explain the differences, but there is just something that isn’t clicking for me with these explanations. It’s as if type I and type II errors are simply inverses of each other which I know they are not (i.e. P(Type I) is not equal to P(1 - Type II).
Does someone have a good analogy for explaining this that will make this stick. It’s really hurting my brain each time working this out again.