Type 1 vs Type 2 Error Practice
Practice distinguishing Type 1 errors (false positive) from Type 2 errors (false negative) in hypothesis testing contexts, with instant feedback and explanations.
What is the difference?
A Type 1 error (false positive) is rejecting the null hypothesis when it is actually true — concluding there is an effect when there isn't one. Its probability is set by your significance level, α (usually 0.05).
A Type 2 error (false negative) is failing to reject the null hypothesis when it is actually false — missing a real effect. Its probability is β, and power = 1 − β.
A classic analogy: Type 1 error is a false alarm (convicting an innocent person), Type 2 error is a miss (letting a guilty person go free). Reducing one usually increases the other, so researchers balance them.
How to practice
Follow these steps:
- Ask: what is the null hypothesis (no effect) in this situation?
- Was the conclusion 'we found an effect' when the truth is no effect → Type 1. Was it 'no effect found' when the truth is a real effect → Type 2.
- Choose your answer, read the explanation, and continue.
Worked example
A drug trial concludes the drug works, but in reality it does nothing.
Frequently Asked Questions
Have another question? Let us know.
Which error is worse, Type 1 or Type 2?
It depends on the context. In medicine, a Type 2 error (missing a disease) can be fatal; in justice, a Type 1 error (convicting the innocent) is considered more severe. Researchers usually control Type 1 error tightly with α and also design studies with adequate power to limit Type 2 error.
How are Type 1 and Type 2 errors related?
They trade off against each other: making the significance level stricter (smaller α) reduces Type 1 errors but increases Type 2 errors. The only way to reduce both is to increase sample size, which increases power (1 − β).
What is statistical power?
Power is the probability of correctly rejecting a false null hypothesis — in other words, 1 − β, the chance of detecting a real effect when it exists. Higher power means fewer Type 2 errors, typically achieved with larger samples.
Does p < 0.05 guarantee no Type 1 error?
No. The p-value is the probability of the observed data under the null hypothesis; the 0.05 threshold means that, on average, about 5% of true null hypotheses will be wrongly rejected. This is why replication matters — single significant results can be Type 1 errors.
