The Null Hypothesis (H₀), Error Types, and Confidence Intervals
Why we fail to reject rather than 'accept' H₀, how Type I and Type II errors trade off, and how 95% confidence intervals compare against the MCID.
In this lesson you will learn
- 1Formulate Null (H₀) and Alternative (H₁) hypotheses and explain why failing to reject H₀ is not proof that H₀ is true.
- 2Distinguish Type I error (α, false positive), Type II error (β, false negative), and Statistical Power (1 − β).
- 3Evaluate 95% Confidence Intervals against both the null value (0) and the Minimum Clinically Important Difference (MCID).
On this page▼
Hypothesis Testing & The Courtroom Framework
This section maps the four possible outcomes of a hypothesis test—True Negative, Type I Error, Type II Error, and Statistical Power—to a courtroom decision matrix.
Understanding the trade-off between α (false alarm) and β (missed discovery) is essential for justifying your sample size calculation to ethics committees and reviewers.
Hypothesis testing operates like a criminal trial: the Null Hypothesis (H₀) is presumed innocent until sample evidence is strong enough to reject it beyond a pre-specified threshold (α = .05).
| Term | Clinical Meaning | Courtroom Counterpart |
|---|---|---|
| Null Hypothesis (H₀) | Baseline assumption that the intervention and control arms have identical population parameters. | Presumption of innocence. |
| Alternative (H₁) | The research claim that a genuine population difference or association exists. | Prosecution charge of guilt. |
| Type I Error (α) | False positive: rejecting H₀ when the intervention actually has no effect in the population (typically capped at 5%). | Convicting an innocent defendant. |
| Type II Error (β) | False negative: failing to reject H₀ when a real clinical effect exists, usually due to small sample size (typically capped at 20%). | Acquitting a guilty defendant for lack of evidence. |
| Power (1 − β) | Probability of detecting a true effect of a specified magnitude when it exists (standard target ≥ 80%). | Thoroughness of the investigation. |
Clinical Example
A pilot sepsis trial tests a novel adjunct therapy in 24 patients (12 per arm) and observes a 12% lower mortality rate, but p = .18.
Interpretation: Concluding that the therapy 'has no effect' is a classic Type II error trap. With only 12 patients per arm, the trial was severely underpowered; the non-significant p-value reflects sample imprecision rather than proof of non-efficacy.
Common Pitfall
Writing 'we accepted the null hypothesis and proved the two groups are identical' whenever p > .05.
Included with Any Analysez AI Study Package
This deep interactive chapter (The Null Hypothesis (H₀), Error Types, and Confidence Intervals) and its clinical simulation labs are unlocked for everyone who has bought any Analysez AI study package.