Type II Error

A type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one fails to reject a null hypothesis that is actually false. In other words, it produces a false positive. The error rejects the alternative hypothesis, even though it does not occur due to chance.

[Important: taking steps that reduce the chances of encountering a type II error tends to increase the chances of a type I error.]

A 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 risks of making a type I error or type II error should be considered.

• A type II error is defined as the probability of incorrectly retaining the null hypothesis, when in fact it is not applicable to the entire population.
• A type II error is essentially a false positive.
• A type II error can be reduced by making more stringent criteria for rejecting a null hypothesis.
• Analysts need to weigh the likelihood and impact of type II errors with type I errors.

The difference between a type II error and a type I error is that a type I error rejects the null hypothesis when it is true (a false negative). The probability of committing a type I error is equal to the level of significance that was set for the hypothesis test. Therefore, if the level of significance is 0.05, there is a 5% chance a type I error may occur.

The probability of committing a type II error is equal to 1 minus the power of the test, also known as beta. The power of the test could be increased by increasing the sample size, which decreases the risk of committing a type II 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.