Type I and Type II errors: what they mean and how to remember which is which
Statistics questions on this are nearly free marks once the two are separated, and nearly impossible to guess if they are not. Here is the distinction, plus what actually changes each error rate.
6 min read · Updated
Both errors are wrong conclusions about the null hypothesis, which is why they blur together. Keeping them apart takes one sentence each, and every other question on the topic follows from those two sentences.
| The null is actually true | The null is actually false | |
|---|---|---|
| You reject the null | Type I error (false positive) | Correct decision (power) |
| You do not reject the null | Correct decision | Type II error (false negative) |
Type I: seeing something that is not there
A Type I error means the null hypothesis was true, there was no real effect, and your test told you otherwise. A drug that does nothing looks effective. A therapy that does not help appears to.
Its probability is alpha, which you set before running the test. An alpha of .05 means you accept a one in twenty chance of this error whenever the null is true. That figure is a choice, not a law, and questions sometimes test whether you know it can be moved.
Type II: missing something that is there
A Type II error means a genuine effect existed and your study failed to detect it. The usual cause is a sample too small to reveal it, though a weak effect or noisy measurement will do it too.
Its probability is beta, and power is 1 minus beta. If a study has power of .80, it has an 80% chance of catching an effect that is really present, and a 20% chance of committing a Type II error.
The trade-off examiners test
Lowering alpha from .05 to .01 makes a Type I error less likely, because you now demand stronger evidence before rejecting the null. The cost is that genuine effects are harder to detect, so Type II errors become more likely. Raising alpha does the reverse.
This is the trap in most exam items on the subject. A question asks how to reduce Type I errors, and the tempting option is to lower alpha, which is technically correct and comes with a consequence the question expects you to know.
Increasing the sample size is the one move that reduces both. A larger sample gives a more precise estimate, which narrows the range of results consistent with chance and makes real effects easier to see.
Which error matters more?
It depends entirely on the cost of being wrong, and scenario questions are built on this. In screening for a serious illness, a Type II error means telling a sick person they are healthy, so studies are designed to avoid it even at the price of more false alarms. In a criminal trial, the convention runs the other way: convicting an innocent person is treated as the worse mistake.
Test yourself
A researcher tests a new therapy and finds no significant improvement, p = .21. In reality the therapy does help. What has happened, and what would have helped most?
- Type I error; lower alpha to .01
- Type II error; recruit a larger sampleCorrect
- Type I error; recruit a larger sample
- Type II error; raise alpha to .10
A real effect was missed, which is a Type II error by definition. Raising alpha would technically make detection easier, but at the cost of more false positives, and it does nothing about the underlying problem. A larger sample reduces both error types, which is why it is the answer to nearly every question phrased this way.
Statistics items reward recognition rather than derivation: there is rarely time to reason from first principles. Answering enough of them is what turns the table above from something you reconstruct into something you simply know.
Reading it is not the same as recognising it
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Common questions
- What is a Type I error in simple terms?
- Rejecting a null hypothesis that was actually true. You conclude there is an effect when there is not one. It is the false positive, and its probability is alpha, usually set at .05.
- What is a Type II error?
- Failing to reject a null hypothesis that was actually false. A real effect existed and your study missed it. It is the false negative, and its probability is called beta.
- How do you reduce both types of error at once?
- Increase the sample size. Changing alpha trades one error for the other, but a larger sample reduces both, which is why questions about improving a study almost always have sample size as the answer.
- What is statistical power?
- The probability of detecting an effect that genuinely exists, calculated as 1 minus beta. Power rises with a larger sample, a bigger true effect, and less measurement noise.
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