Type I error, type II error

I then gave examples to examples to explain the difference between the two types of error one can make when doing a signifcance test.

I gave the toaster-fire alarm example about what the two errors would be in that situation.

The following table gives a summary of possible results of any hypothesis test:

			Decision
			Reject H0	Don't reject H0
	Truth	H0	Type I Error	Right Decision
		HA	Right Decision	Type II Error

Type I error is the error made when the null hypothesis is rejected when in fact the null hypothesis is true. Alpha ($\alpha$) is the probability of rejecting a true null hypothesis.

Type II error is the error made when the null hypothesis is not rejected when in fact the alternative hypothesis is true.

$$\mbox{Beta }(\beta)\mbox{ is the probability of not rejecting a false null hypothesis}\qquad \mbox{Power}=1-\beta$$

The probability of rejecting false null hypothesis. The power of a test tells us how likely we are to find a significant difference given that the alternative hypothesis is true (the true mean is different from the mean under the null hypothesis).

Power

More about Power

Even more about Power

Hypothesis Testing Glossary