Concept Architecture
Concept
Theoretically, Type I Error is a statistical decision error that occurs when a true null hypothesis is incorrectly rejected. It represents a false-positive conclusion, whereby evidence is judged sufficient to declare an effect or association when none exists. The concept is fundamental to classical hypothesis testing and statistical decision theory, providing the basis for controlling the probability of incorrect inferences through the significance level.
Mathematically, the probability of committing a Type I error is denoted by �, known as the significance level. This probability is specified before analysis and defines the maximum acceptable risk of falsely rejecting the null hypothesis. The significance level determines the critical region of the sampling distribution, and if the observed test statistic falls within this region, the null hypothesis is rejected despite the possibility that it is true.
In practice, Type I error is controlled by selecting an appropriate significance level, commonly � = 0.05 or � = 0.01, before conducting statistical analyses. Additional methods such as multiplicity adjustments, gatekeeping procedures and sequential testing are used to maintain the overall Type I error rate when multiple hypotheses are evaluated. In health economics, controlling Type I error is essential when comparing costs, health outcomes, treatment effects and economic endpoints to minimise the risk of adopting ineffective or inefficient healthcare interventions.
Purpose
Used to quantify and control the probability of falsely concluding that a treatment effect, association or difference exists when the null hypothesis is in fact true, thereby supporting valid statistical inference and evidence-based decision making.
Mathematical Formulae
Primary Formula
� = P(Reject H? | H? is true)
Supporting Formulae
Reject H? if p < �
Family-wise error rate:
FWER = P(at least one Type I error)
Bonferroni-adjusted significance level:
�? = � / m
where:
- � = significance level
- �? = adjusted significance level
- m = number of statistical tests
Related Mathematical Methods
- Hypothesis Testing
- Significance Level
- p-Value
- Family-Wise Error Rate
- Bonferroni Correction
- Holm Procedure
- Gatekeeping Procedures
- Multiple Comparisons
Example
A health economist compares the mean annual healthcare costs of two treatments using a significance level of � = 0.05. The statistical test produces a p-value of 0.03, leading to rejection of the null hypothesis. If, in reality, the treatments have identical mean costs, this decision represents a Type I error. The probability of making this incorrect decision was controlled at 5% before the analysis.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =IF(P2<0.05,"Reject H?","Do not reject H?") | Apply the predefined significance level when interpreting statistical tests. |
| COUNTIF | =COUNTIF(P2:P101,"<0.05") | Count statistically significant results across multiple analyses. |
| MIN | =MIN(0.05/10,0.05) | Apply a Bonferroni-adjusted significance threshold for multiple comparisons. |
| T.TEST | =T.TEST(B2:B101,C2:C101,2,2) | Perform a hypothesis test while controlling the Type I error rate through the chosen significance level. |
VBA (Optional)
Automate hypothesis testing across multiple health economic outcomes while applying user-selected procedures to control the overall Type I error rate.
Sources
- Casella G, Berger RL. Statistical Inference.
- Lehmann EL, Romano JP. Testing Statistical Hypotheses.
- Agresti A. Foundations of Linear and Generalized Linear Models.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
Bayesian Methods in Health Economics — Gianluca Baio, 1st Edition ed., 2012 (Chapman & Hall / CRC Press)
An overview of Bayesian statistical methods for the analysis of health economic data, covering economic evaluation concepts, statistical cost-effectiveness analysis, Bayesian computation and MCMC, and applied health economic evaluation.
BookView source →
Frequently Asked Questions (6)
What is a type I error?
In hypothesis testing, the error of incorrectly rejecting a true null hypothesis, concluding a genuine effect exists when it does not.
Source: Neyman & Pearson 1933
What mistake is a type I error in hypothesis testing?
A type I error is the mistake of rejecting a null hypothesis that is actually true, concluding that a real effect exists when in fact there is none, a false positive. Its probability is set by the significance level, so testing at five per cent accepts a one-in-twenty chance of such an error on a true null. It matters because false positives can lead to adopting treatments that do not work, and running many tests multiplies the risk. Wrongly declaring an effect that is not there is its nature. Kirkwood and Sterne (2003) describe this.
Source: Kirkwood & Sterne 2003
What causes a type I error?
A type I error occurs by chance when the data happen to be extreme enough to reject a true null hypothesis, even though there is no real effect; the probability of this is set by the significance level. So a type I error is caused by random variation producing an apparently significant result when the null is actually true, and its likelihood is controlled by the chosen significance level, which is why a five per cent level means accepting a five per cent chance of a type I error, and why conducting many tests increases the overall chance of at least one false positive, the problem of multiplicity.
Source: Neyman & Pearson 1933
How is the type I error rate controlled?
The type I error rate is controlled by setting the significance level, alpha, which is the accepted probability of a type I error for a single test, and, when multiple tests are conducted, by using methods such as the Bonferroni correction or other multiplicity adjustments to limit the overall rate. So the type I error rate is controlled through the significance level and, for multiple tests, through multiplicity control, which keeps the chance of false positives at the intended level, since without such control, testing many hypotheses would inflate the overall type I error, which is why prespecification and adjustment are used to maintain reliable conclusions.
Source: Neyman & Pearson 1933
How does a type I error differ from a type II error?
A type I error is rejecting a true null hypothesis, a false positive, while a type II error is failing to reject a false null hypothesis, a false negative. The probability of a type I error is the significance level, alpha, and that of a type II error is beta, with power being one minus beta. So the two errors are opposite kinds of mistake, with the type I error wrongly finding an effect and the type II error missing a real one, and there is a trade-off between them for a fixed sample size, which is why both are considered in designing a study, balancing the risks of false positive and false negative conclusions.
Source: Neyman & Pearson 1933
Why does the type I error matter?
The type I error matters because a false positive conclusion, finding an effect that does not exist, can lead to wrong decisions, such as adopting an ineffective treatment, and wastes resources; controlling its probability keeps conclusions reliable. So the type I error matters for the credibility of findings, since an inflated false positive rate undermines trust in results, which is why the significance level is set to limit it and why multiplicity is controlled when many tests are conducted, ensuring that a declared effect is unlikely to be a chance finding and that confirmatory conclusions can be relied upon.
Source: Neyman & Pearson 1933
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 26 Dec 2025
Content version: 1.0.0
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- Term code
- HE-ES-SA-224
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