What is a Type 1 Error?
A type 1 error (AKA Type I error) occurs when you reject a true null hypothesis in a hypothesis test. In other words, a statistically significant test result indicates that a population effect exists when it does not. A type 1 error is a false positive because the test detects an effect in the sample that doesn’t exist in the population.
In hypothesis testing, the null hypothesis typically states that an effect does not exist in the population. Consequently, when you reject the null, you conclude that the effect exists.
By rejecting a true null hypothesis, you incorrectly conclude that the effect exists when it doesn’t. Of course, you don’t know that you’re committing an error at the time. You’re just following the results of your hypothesis test.
Type 1 errors can have serious consequences. When testing a new medication, a false positive could mean putting a useless drug on the market. Understanding and managing these errors is essential for reliable statistical conclusions.
Related post: Hypothesis Testing Overview
Type 1 Error Example
Let’s take that technical information and bring it to life with an example of a type 1 error in action. For the study in this example, we’ll assume we know that the effect doesn’t exist. You wouldn’t know that in the real world, which is why you conduct the study!
Suppose we’re testing a new medicine that is completely ineffective. We perform a study, collect the data, and perform the hypothesis test.
The hypotheses for this test are the following:
- Null: The medicine has no effect in the population
- Alternative: The medicine is effective in the population.
Unfortunately, these results are incorrect because the medicine is ineffective. The statistically significant results make us think the medicine is effective when it isn’t. It’s a false positive. A type 1 error has occurred and we don’t even know it!
Learn more about the Null Hypothesis.
Why Do They Occur?
Hypothesis tests use sample data to infer the properties of populations. You gain incredible benefits by using random samples because it is usually impossible to evaluate an entire population.
Unfortunately, using samples introduces potential problems, including Type 1 errors. Random samples tend to reflect the population from which they’re drawn. However, they can occasionally misrepresent the population enough to cause false positives.
Type 1 errors sneak into our analysis due to chance during random sampling. Even when we do everything right – following assumptions and using correct procedures – randomness in data collection can lead to misleading results.
Imagine rolling a die. Sometimes, purely by chance, you get more sixes than expected. Similarly, randomness can produce unusual samples that misrepresent the population.
In short, the luck of the draw can cause Type 1 errors (false positives) to occur.
Probability of a Type 1 Error
While we don’t know when studies produce false positive results, we do know their rate of occurrence. The probability of making a Type 1 error is denoted by the Greek letter alpha (α), which is the significance level of the test. By choosing your significance level, you’re setting the false positive rate.
A standard value for α is 0.05. This significance level produces a 5% chance of rejecting a true null hypothesis.
A critical benefit for hypothesis testing is that when the null hypothesis is true, the probability of a Type 1 error (false positive) is low. This fact helps you trust statistically significant results.
Minimizing False Positives
There’s no way to eliminate Type 1 errors entirely, but you can reduce them by lowering your significance level (e.g., from 0.05 to 0.01). However, lower alphas also lessen the probability of detecting an effect if one exists.
It’s a balancing act. Set α too high, and you risk more false positives. Set it too low, and you might miss real effects (Type 2 errors or false negatives). Choosing the right α depends on the context and consequences of your test.
In hypothesis testing, understanding Type 1 errors is vital. They represent a false positive, where we think we’ve found something significant when we haven’t. By carefully choosing our significance level, we can reduce the risk of these errors and make more accurate statistical decisions.
Compare and contrast Type I vs. Type II Errors.
Acosta, Griselda; Smith, Eric; and Kreinovich, Vladik, “Why Area Under the Curve in Hypothesis Testing?”
(2019). Departmental Technical Reports (CS). 1360.