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 errꦉor of omission.

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

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 nul🐬l 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 hyp🥃othesis should have been rejected (because two va🅺riables 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 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 chan𝔍ces of a false negative.

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

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

Type II Errors vs. Type I Errors

The dif🍎ference 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 that was set for the hypothesis test. Therefore, if the level of significance is 0.05, there is a 5% c🃏hance 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 size, which decreases the ri𒀰sk of committing a type II error.

Example of a Type II Error

As🍃sume a biotechnology company wants to compare how effective two of its drugs are for treati𓆉ng 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.

The alternative hypothesis (H_a) states that the two drug𝄹s 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 澳洲幸运5官方开奖结果体彩网:clinical trial of 3,000 patients with di𓄧abetes 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 0𒁃.05, which indicates it is willing toꦡ 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 prꦇobability of committing a type II er🍌ror is 97.5%.

If the two m🔥edications 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 hy💙potheses from this question:

• H₀ (null): Age does not affect how well humans see in the dark
• H_a (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 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 af🌊fect 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.

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 resultin🍌g from sample sizes that are too small. Increasing the sample size can help reduce the chances of committing a type II error.