Type 1 Error: Definition, False Positives, and Examples

What Is a Type I Error?

In statistical research, a type 1 error is when the null hypothesis is rejected, which incorrectly leads to the study stating that notable differences were found in the variables when actually there were no differences. Put simply, a type I error is a false positive result.

Making a type I error often can't be avoided because of the degree of uncertainty involved. A null hypothesis is established during hypothesis testing before a test begins. In some cases, a type I error assumes there's no cause-and-effect relationship between the tested item and the stimuli to trigger an outcome to the test.

How a Type I Error Works

Hypothesis testing is a testing process that uses sample data. The test is designed to provide evidence that the hypothesis or conjecture is supported by the data being tested. A null hypothesis is a belief that there is no statistical significance or effect between the two data sets, variables, or populations being considered in the hypothesis. A researcher would generally try to disprove the null hypothesis.

For example, let's say the null hypothesis states that an investment strategy doesn't perform any better than a market index like the S&P 500. The researcher would take samples of data and test the historical performance of the investment strategy to determine if the strategy performed at a higher level than the S&P. If the test results show that the strategy performed at a higher rate than the index, the null hypothesis is rejected.

This condition is denoted as n=0. If the result seems to indicate that the stimuli applied to the test subject caused a reaction when the test is conducted, the null hypothesis stating that the stimuli do not affect the test subject then needs to be rejected.

False Positive Type I Error

A type I error is also called a false positive result. This result leads to an incorrect rejection of the null hypothesis. It rejects an idea that shouldn't have been rejected in the first place.

Rejecting the null hypothesis under the assumption that there is no relationship between the test subject, the stimuli, and the outcome may sometimes be incorrect. If something other than the stimuli causes the outcome of the test, it can cause a false positive result.

Examples of Type I Errors

Let's look at a couple of hypothetical examples to show how type I errors occur.

Criminal Trials

Type I errors commonly occur in criminal trials, where juries are required to come up with a verdict of either innocent or guilty. In this case, the null hypothesis is that the person is innocent, while the alternative is guilty. A jury may come up with a type I error if the members find that the person is found guilty and is sent to jail, despite actually being innocent.

Medical Testing

In medical testing, a type I error would cause the appearance that a treatment for a disease has the effect of reducing the severity of the disease when, in fact, it does not. When a new medicine is being tested, the null hypothesis will be that the medicine does not affect the progression of the disease.

Let's say a lab is researching a new cancer drug. Their null hypothesis might be that the drug does not affect the growth rate of cancer cells.

After applying the drug to the cancer cells, the cancer cells stop growing. This would cause the researchers to reject their null hypothesis that the drug would have no effect. If the drug caused the growth stoppage, the conclusion to reject the null, in this case, would be correct.

However, if something else during the test caused the growth stoppage instead of the administered drug, this would be an example of an incorrect rejection of the null hypothesis (i.e., a type I error).

The Bottom Line

Hypothesis testing is a form of testing that uses data sets to either accept or determine a specific outcome using a null hypothesis. Although we often don't realize it, we use hypothesis testing in our everyday lives.

This comes in many areas, such as making investment decisions or deciding the fate of a person in a criminal trial. Sometimes, the result may be a type I error. This false positive is the incorrect rejection of the null hypothesis even when it is true.