Type II Error: Definition, Examples, and How to Reduce Risk
Definition
A type II error (false negative) occurs when a researcher fails to reject a null hypothesis that is actually false. In other words, the test concludes there is no effect or difference when one truly exists.
- Symbolically: type II error = β = 1 − power of the test.
- Type I error (false positive) = α (the chosen significance level).
How it works
Statistical hypothesis testing involves:
– Null hypothesis (H0): no effect or no difference.
– Alternative hypothesis (Ha): an effect or difference exists.
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A type II error happens when data do not provide sufficient evidence to reject H0, despite H0 being false. The probability of this error depends on:
– Effect size (larger true effects are easier to detect)
– Sample size (larger samples increase power)
– Variability in the data (less variance increases power)
– Significance level α (lower α tends to increase β)
– Test design (one- vs. two-tailed tests, measurement precision)
Type II vs Type I
- Type I error (α): rejecting a true null hypothesis — false positive.
- Type II error (β): failing to reject a false null hypothesis — false negative.
There is a trade-off: reducing α (being more stringent) typically increases β, and vice versa. Researchers choose α and target power based on the consequences of each error.
Causes and risk factors
Common contributors to high type II error risk:
– Small sample size
– Small true effect size
– High variability or measurement error
– Overly strict significance level (very low α)
– Poor experimental design or insufficient control of confounders
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How to reduce type II errors
Practical steps to lower β (increase power):
– Increase sample size.
– Improve measurement precision to reduce variability.
– Use a more powerful test or a one-tailed test when justified.
– Increase α (accept a higher type I risk) when the cost of missing a true effect is greater than a false alarm.
– Pre-specify and maximize expected effect size through study design or pilot data.
A common guideline is to design studies with at least 80% power (β ≤ 0.20), though higher power may be appropriate when false negatives carry high cost.
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Example
A biotech company tests two diabetes drugs.
– H0: the two drugs are equally effective.
– Ha: the drugs differ in effectiveness.
If the trial fails to reject H0 even though one drug is actually better, the company commits a type II error. Risk of this error depends on sample size, true difference between drugs, variability, and the chosen α.
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Explain Like I’m 5
If you test whether age affects night vision:
– H0: age does not affect night vision.
– If you conclude age does not affect night vision when it actually does, that’s a type II error — you missed a real effect.
Quick memory tip
- Type I = “I” for Incorrectly rejecting a true null (false positive).
- Type II = “II” (two) for Failing to reject a false null (false negative).
FAQs
- How do you find type II errors?
You estimate β during power analysis before the study or calculate post hoc power given observed effect size and sample size. - How do you control type II errors?
Conduct a power analysis, increase sample size, reduce variability, or adjust α and test design. - What is a common target power?
80% is a common minimum; use higher power when missing true effects has serious consequences.
Bottom line
A type II error is failing to detect a real effect. Its probability (β) depends on effect size, sample size, variability, significance level, and study design. Proper planning—especially power analysis and appropriate sample size—helps minimize the risk of false negatives while balancing the trade-off with type I errors.