# Type II Error: Definition, Example, vs. Type I Error

![Type II Error](https://www.investopedia.com/thmb/m-jefhqd7o-FUtlimTmCT3YhT-E=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Type-ii-error-9cc11d433d314976bf9b7466dc88a0ff.jpg)

*Reducing the risk of type II error can increase the risk of type I error, and vice versa. — Michela Buttignol / Investopedia*

> **Definition**
>
> A type II error, also known as a false negative, is the miscalculation that occurs when a researcher accepts a false null hypothesis.

## What Is a Type II Error?

A type II error is a statistical term used to describe the error that results when a null hypothesis that is actually false is not rejected by an investigator or researcher. A type II error produces a false negative, also known as an error of omission.

A type II error can be contrasted with a type I error, where researchers incorrectly reject a true null hypothesis.

### Key Takeaways

*   A type II error is defined as the probability of incorrectly failing to reject the null hypothesis, when in fact it is not applicable to the entire population.
*   A type II error is essentially a false negative.
*   A type II error can be made less likely by creating more stringent criteria for rejecting a null hypothesis, although this increases the chances of a false positive.
*   The sample size, the true population size, and the preset alpha level influence the magnitude of risk of an error.
*   Analysts need to weigh the likelihood and impact of type II errors with type I errors.

## Understanding a Type II Error

When testing a statistical hypothesis, there are two primary types: the null hypothesis and the alternative hypothesis.

### Null and Alternative Hypotheses

The null hypothesis generally suggests that for the data being evaluated, there is no difference between groups or no relationships between variables.

The alternative hypothesis would state the researcher's expectations (their claims), such as what they expect to find between variables. Like everyone else, researchers can make errors in their assumptions.

### Type II Error

A type II error, also known as an error of the second kind or a beta error, confirms that a null hypothesis should have been rejected (because two variables that were claimed to be unrelated actually were related).

A researcher makes a type II error in this instance by not rejecting the null hypothesis—that is, by not rejecting the idea that two variables are unrelated after the research is completed and it's proven false.

### Reducing Type II Errors

The likelihood of making a type II error can be reduced by creating more stringent criteria for rejecting a null hypothesis (H0).

For example, if an analyst is considering anything that falls within the +/- bounds of a 95% [confidence interval](https://www.investopedia.com/terms/c/confidenceinterval.asp) as statistically insignificant (a negative result), then by decreasing that tolerance to +/- 90%, and subsequently narrowing the bounds, you will get fewer negative results, and thus reduce the chances of a false negative.

Taking these steps, however, tends to increase the chances of encountering a type I error—a false-positive result.

When conducting a hypothesis test, the probability or risk of making a type I error or type II error should be considered.

> **Important**
>
> The steps taken to reduce the probability of a type II error tend to increase the probability of a type I error.

## Type II Errors vs. 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 (i.e., a false positive).

The probability of committing a type I error is equal to the [level of significance](https://www.investopedia.com/terms/s/statistical-significance.asp) that was set for the hypothesis test. Therefore, if the level of significance is 0.05, there is a 5% chance that a type I error may occur.

The probability of committing a type II error is equal to one minus the power of the test, also known as beta. The power of the test could be raised by increasing the [sample](https://www.investopedia.com/terms/s/sample.asp) size, which decreases the risk of committing a type II error.

> **Fast Fact**
>
> Some statistical literature will include overall significance level and type II error risk as part of the report’s analysis. For example, a 2021 meta-analysis of exosomes in the treatment of spinal cord injury recorded an overall significance level of 0.05 and a type II error risk of 0.1.

## Example of a Type II Error

Assume a biotechnology company wants to compare how effective two of its drugs are for treating diabetes.

The null hypothesis (H0) states that the two medications are equally effective, and is the hypothesis that the company hopes to reject using the [one-tailed test](https://www.investopedia.com/terms/o/one-tailed-test.asp).

The alternative hypothesis (Ha) states that the two drugs are not equally effective. This hypothesis is the state of nature that is supported by rejecting the null hypothesis.

The biotech company implements a large [clinical trial](https://www.investopedia.com/terms/c/clinical-trials.asp) of 3,000 patients with diabetes to compare the treatments. The company randomly divides the 3,000 patients into two equally sized groups, giving one group one of the treatments and the other group the other treatment.

It selects a significance level of 0.05, which indicates it is willing to accept a 5% chance it may reject the null hypothesis (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 97.5%.

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, then a type II error occurs.

## Explain Like I'm 5

Consider the following question:

> Does eye color determine how well humans see in the dark?

You would form two hypotheses from this question:

*   H0 (null): Age does not affect how well humans see in the dark
*   Ha (alternative): Age does affect how well humans see in the dark

You would then set out to answer this question by conducting an experiment using a statistically significant number of humans. Once you'd recorded data on the population, you'd sort and analyze it, and draw conclusions about it.

It's pretty common knowledge that the older you get, the harder it is to see in the dark due to many factors, one of which is that the eye's rod cells become weaker with age.

If you conclude from your data that age doesn't affect how well humans see in the dark, you have failed to reject a false null hypothesis—a type II error.

If, for some reason, age actually did not affect how well humans see in the dark, but your data showed it did, you would probably reject a true null hypothesis—a type I error.

## How Do I Remember the Difference Between Type I and Type II Errors?

A type I error occurs if a null hypothesis that is actually true in the population is rejected. Think of this type of error as a false positive. The type II error, which involves not rejecting a false null hypothesis, can be considered a false negative.

## How Do You Find Type II Errors?

A type II error is commonly caused if the statistical power of a test is too low. The higher the statistical power, the greater the chance of avoiding an error. It’s often recommended that the statistical power should be set to at least 80% prior to conducting any testing.

## How Do You Control Type II Errors?

You can lower the chances of a type II error by increasing the sample size of a study. As the true population effect size increases, the probability of a type II error should decrease. Additionally, the preset alpha level set by the research influences the magnitude of risk. As the alpha level set decreases, the risk of a type II error increases.

## The Bottom Line

In statistics, a type II error is accepting a null hypothesis that should be rejected. A type II error can occur if there is not enough power in statistical tests, often resulting from sample sizes that are too small. Increasing the sample size can help reduce the chances of committing a type II error.

> **Article Sources**
>
> 1.  Yi, Hanxiao, et al. "[A Meta-Analysis of Exosome in the Treatment of Spinal Cord Injury](https://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC8284334&blobtype=pdf)." _Open Medicine_, July 12, 2021. vol 16, pp. 1043-1049.
>     
> 2.  American Academy of Ophthamology. "[21 Ways Aging Changes Your Eyes](https://www.aao.org/eye-health/tips-prevention/20-ways-aging-changes-your-eyes)."