Type I Error

Definition

A Type I error, or false positive, occurs when a hypothesis test incorrectly rejects a true null hypothesis. Its probability is equal to the significance level α, commonly set at 0.05. This means that even when there is no real effect, there is a 5% chance of obtaining a statistically significant result purely by chance.

Why It Matters

Type I errors lead to false claims, wasted resources on ineffective interventions, and erosion of public trust in science. When many tests are conducted simultaneously — for example, in genomics studies that test thousands of genes — the probability of at least one Type I error becomes very high. Corrective procedures such as the Bonferroni correction or false discovery rate control are essential safeguards.

Example

A researcher tests 20 different vitamins for their effect on memory. By chance alone, she expects one vitamin to show p < 0.05 even if none actually works. Vitamin Q7 yields p = 0.04. Without correction for multiple comparisons, she might conclude Vitamin Q7 improves memory. However, after applying the Bonferroni correction (α / 20 = 0.0025), the result is no longer significant. The initial finding was likely a Type I error.

Related Terms

• Type II Error
• Statistical Power
• P-Value
• Null Hypothesis
• Statistical Significance

Software Notes

• SPSS: SPSS reports p-values for each test, allowing manual comparison against α. For multiple comparisons in ANOVA, use post-hoc tests (Tukey, Bonferroni, Scheffé) under Analyze > Compare Means > One-Way ANOVA > Post Hoc.
• R: p.adjust(p_values, method = "bonferroni") applies Bonferroni correction. p.adjust(p_values, method = "fdr") controls the false discovery rate. multcomp::glht() offers advanced multiple-comparison procedures.
• Stata: ttest y, by(group) reports uncorrected p-values. For multiple comparisons after ANOVA: pwmean y, over(group) mcompare(bonferroni) or mcompare(tukey).