Type II Error

"False negative" error

What is a Type II Error?

In statistical hypothesis testing, a type II error is a situation wherein a hypothesis test fails to reject the null hypothesis that is false. In other words, it causes the user to erroneously not reject the false null hypothesis because the test lacks the statistical power to detect sufficient evidence for the alternative hypothesis. The type II error is also known as a false negative.

 

Type II Error

 

The type II error has an inverse relationship with the power of a statistical test. This means that the higher power of a statistical test, the lower the probability of committing a type II error. The rate of a type II error (i.e., the probability of a type II error) is measured by beta (β) while the statistical power is measured by 1- β.

 

How to Avoid the Type II Error?

Similar to the type I error, it is not possible to completely eliminate the type II error from a hypothesis test. The only available option is to minimize the probability of committing this type of statistical error. Since a type II error is closely related to the power of a statistical test, the probability of the occurrence of the error can be minimized by increasing the power of the test.

1. Increase the sample size

One of the simplest methods to increase the power of the test is to increase the sample size used in a test. The sample size primarily determines the amount of sampling error, which translates into the ability to detect the differences in a hypothesis test. A larger sample size increases the chances to capture the differences in the statistical tests, as well as increasing the power of a test.

2. Increase the significance level

Another method is to choose a higher level of significance. For instance, a researcher may choose a significance level of 0.10 instead of the commonly acceptable 0.05 level. The higher significance level implies a higher probability of rejecting the null hypothesis when it is true.

The larger probability of rejecting the null hypothesis decreases the probability of committing a type II error while the probability of committing a type I error increases. Thus, the user should always assess the impact of type I and type II errors on their decision and determine the appropriate level of statistical significance.

 

Example

Sam is a financial analyst. He runs a hypothesis test to discover whether there is a difference in the average price changes for large-cap and small-cap stocks.

In the test, Sam assumes as the null hypothesis that there is no difference in the average price changes between large-cap and small-cap stocks. Thus, his alternative hypothesis states that a difference between the average price changes does exist.

For the significance level, Sam chooses 5%. This means that there is a 5% probability that his test will reject the null hypothesis when it is actually true.

If Sam’s test incurs a type II error, then the results of the test will indicate that there is no difference in the average price changes between large-cap and small-cap stocks. However, in reality, a difference in the average price changes does exist.

 

More Resources

CFI is the official provider of the global Financial Modeling & Valuation Analyst (FMVA)™ certification program, designed to help anyone become a world-class financial analyst. To keep learning and advancing your career, the additional CFI resources below will be useful:

  • Type I Error
  • Conditional Probability
  • Framing Bias
  • Mutually Exclusive Events

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