Question

Describe and tell me the difference between a Type 1 and Type 2 error. Which error is directly related to your alpha? Which error is also called your beta? When your answer is more conservative, does your error rate go up or down? Give an example of two alphas and tell me which one is the more conservative choice.

Answer 1

Type I error, also known as a “false positive”: the error of rejecting a null hypothesis when it is actually true. In other words, this is the error of accepting an alternative hypothesis (the real hypothesis of interest) when the results can be attributed to chance.

Type II error, also known as a "false negative": the error of not rejecting a null
hypothesis when the alternative hypothesis is the true state of nature. In other words, this is the error of failing to accept an alternative hypothesis when you don't have adequate power.

The error of rejecting null hypothesis (H0) (accepting H1) when H0 is true is called type 1 error and the error of accepting H0 when it is false(H1 is true) is called type 2 error

The probabilities of type 1 error and type 2 error are denoted by alpha and beta respectively.

Alpha= probability of type 1 error

probability of rejecting H0 when Ho is true

Beta= probability of type 2 error

probability of accepting H0 when it is false

A conservative test always keep the probability of rejecting the null hypothesis well below the significance level. Suppose you’re running a hypothesis test where you set the alpha level at 5%. That means that the test will (falsely) give you a significant result 1 out of 20 times. This is called the Type I error rate. A conservative test would always control the Type I error rate at a level much smaller than 5%, which means your chance of getting it wrong will be well below 5% (perhaps 2%).i.e.error rate will go down.