Glossary
Type II Error
A Type II error, or false negative, occurs when a hypothesis test fails to reject a false null hypothesis. Its probability is denoted β. The complement of β is statistical power (1 − β), which represents the probability of correctly detecting a true effect. Reducing one type o...
Definition
A Type II error, or false negative, occurs when a hypothesis test fails to reject a false null hypothesis. Its probability is denoted β. The complement of β is statistical power (1 − β), which represents the probability of correctly detecting a true effect. Reducing one type of error typically increases the other, so researchers must balance the two based on the relative costs of each mistake.
Why It Matters
Type II errors are particularly costly in medical research, where an effective treatment might be abandoned because a trial was too small to detect its benefit. They also contribute to the replication crisis: under-powered studies that miss true effects are rarely published, while the few that do find effects by chance may be overestimated. Ensuring adequate statistical power before data collection is the primary defence against Type II errors.
Example
A pharmaceutical company tests a new antidepressant in a trial with only 30 participants per group. The true effect is a clinically meaningful reduction of 5 points on a depression scale, but because the sample is small, the study has only 40% power. The observed p-value is 0.12, and the company abandons the drug. A later meta-analysis with larger trials confirms the drug is effective, but the opportunity has been lost. The initial trial committed a Type II error.
Related Terms
Software Notes
- SPSS: SPSS does not directly report Type II error rates. Power analysis tools (Analyze > Power Analysis) or G*Power are used prospectively to estimate β and ensure adequate power.
- R:
pwr::pwr.t.test(d = 0.5, n = 30, sig.level = 0.05)returns power = 0.48, implying β = 0.52.pwr::pwr.t.test(d = 0.5, power = 0.80, sig.level = 0.05)solves for the required sample size. - Stata:
power twomeans 0 0.5, sd(1) n1(30) n2(30)computes power (and thus β = 1 − power) for a given sample size.power twomeans 0 0.5, sd(1) power(0.8)solves for the required sample size.