How to Calculate the Probability of a Type 2 Error

Type I and II errors can debunk an entire research study if not properly calculated and accounted for.

Statistics is a vast field in mathematics with many practical uses. For academic purposes, many topics can be explored by conducting a statistical research study. A research study involves a researcher selecting a hypothesis and then conducting research that will either prove or disprove the hypothesis. Because studies are conducted by humans, errors can occur. In research studies, errors are classified as Type I and Type II errors. A Type I error occurs when a researcher incorrectly rejects a hypothesis that is actually true. A Type II error is the opposite of a Type I, where a researcher fails to reject the hypothesis.

Instructions

1. Calculate your standard deviation and population for your data set.

2. Find Z by subtracting your sample population from your total population and dividing the result by your standard deviation.

3. Find the rejection region in terms of x-bar by referencing the number you just calculated to your Z table, which will give you the probability that a Type II error has occurred.

Tips & Warnings

• Beyond mathematical calculations, consider outside influences that could cause a hypothesis to appear to be correct when it is not.

References

• Duquesne University: Calculating the Probability of a Type II Error

Resources

• University of Northern Iowa: Type I and II Error