Type I Error
A Type I Error occurs when you reject the null hypothesis even though it is actually true. In other words, you conclude there is an effect or difference when there really isn't one — a false positive.
In hypothesis testing, a Type I Error is the incorrect rejection of a true null hypothesis. The probability of committing a Type I Error is denoted by , which is the significance level chosen before conducting the test. For example, setting means you accept a 5% chance of rejecting the null hypothesis when it is in fact true.
Key Formula
Where:
- = the null hypothesis
- = the significance level (probability of a Type I Error)
Example
Problem: A pharmaceutical company tests whether a new drug lowers blood pressure more than a placebo. They set a significance level of α = 0.05 and obtain a p-value of 0.03. In reality, the drug has no effect. Identify what kind of error occurs and explain why.
Step 1: State the null hypothesis.
Step 2: Compare the p-value to the significance level.
Step 3: Based on the decision rule, since the p-value is less than α, you reject the null hypothesis. You conclude the drug does lower blood pressure.
Step 4: However, we are told the drug actually has no effect — meaning the null hypothesis is true. Rejecting a true null hypothesis is a Type I Error.
Answer: This is a Type I Error (false positive). The researchers incorrectly concluded the drug works when it does not. The probability of this happening was at most 5%, as set by α = 0.05.
Why It Matters
Type I Errors have real consequences. In medicine, a false positive might lead to approving a drug that doesn't actually work, exposing patients to side effects for no benefit. In criminal justice, a Type I Error is analogous to convicting an innocent person. Understanding this error helps you choose an appropriate significance level — balancing the risk of a false alarm against the ability to detect real effects.
Common Mistakes
Mistake: Confusing Type I and Type II Errors
Correction: Type I is rejecting a true null hypothesis (false positive). Type II is failing to reject a false null hypothesis (false negative). A helpful mnemonic: Type I = false alarm, Type II = missed detection.
Mistake: Thinking a small p-value means no Type I Error occurred
Correction: A small p-value makes rejection seem justified, but if the null hypothesis happens to be true, you have still committed a Type I Error. The p-value does not tell you whether the null hypothesis is true — it only measures how surprising the data would be if it were.