Question

What is the true state of the population and what decision was made in a Type 2 error. Give a concrete example.

Answer 1

type II error confirms an idea that should have been rejected, claiming the two observances are the same, even though they are different. A type II error does not reject the null hypothesis, even though the alternative hypothesis is the true state of nature. In other words, a false finding is accepted as true. A type II error is sometimes called a beta error.

A type II error can be reduced by making more stringent criteria for rejecting a null hypothesis. For instance, if an analyst is considering anything that falls within a +/- 95% confidence interval as statistically significant, by increasing that tolerance to +/- 99% you reduce the chances of a false positive. However, doing so at the same time increases your chances of encountering a type I error. When conducting a hypothesis test, the probability or risk of making a type I error or type II error should be considered.

Example of a Type 2 Error

Assume a biotechnology company wants to compare how effective two of its drugs are for treating diabetes. The null hypothesis states the two medications are equally effective. A null hypothesis

, H_0, is the claim that the company hopes to reject using the one-tailed test.

The alternative hypothesis,

H_a, states the two drugs are not equally effective.

The alternative hypothesis, H_a, is the measurement that is supported by rejecting the null hypothesis.

The biotech company implements a large clinical trial of 3,000 patients with diabetes to compare the treatments. The company expects the two drugs to have an equal number of patients to indicate that both drugs are effective. It selects a significance level of 0.05, which indicates it is willing to accept a 5% chance it may reject the null hypothesis when it is true or a 5% chance of committing a type I error.

Assume the beta is calculated to be 0.025, or 2.5%. Therefore, the probability of committing a type II error is 2.5%. If the two medications are not equal, the null hypothesis should be rejected. However, if the biotech company does not reject the null hypothesis when the drugs are not equally effective, a type II error occurs.