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# Hypothesis testing

- Concept

Start by assuming there is no difference, then check whether the data would be rare enough under that assumption to reject it.

Updated Nov 5, 2026

## Key points

- H0 (null hypothesis): no difference or association. H1 (alternative): there is one.
- Decision rule: if p

## What it is

A hypothesis test is a procedure for deciding whether the data give enough evidence against a null hypothesis (H0), which almost always states that there is no difference or association. A significance level α is set in advance, a test statistic is calculated and compared with a critical value, or its p value is obtained. It underlies nearly every result of clinical trials, and grasping its logic prevents misreading a ‘non-significant’ result.

## Function

- 1. State H0 and H1 before seeing the data.
- 2. Choose α and whether the test is one- or two-sided.
- 3. Calculate the test statistic from the data.
- 4. Compare it with the critical value, or obtain the p value.
- 5. Decide, and report the result with its confidence interval.

## Worked example

- Data: a service historically cured 70% with one protocol; with a new one, 80 of 100 patients are cured.
- H0: the cure proportion is 0.70. H1 (two-sided): it differs from 0.70. α = 0.05.
- SE under H0 = √(0.70 × 0.30 / 100) = √0.0021 = 0.0458.
- z = (0.80 − 0.70) / 0.0458 = 2.18 (rounded).
- Two-sided critical value = ±1.96. Since 2.18 > 1.96, H0 is rejected; the two-sided p value is about 0.029.
- A one-sided test would use 1.645, but it is justified only if chosen before seeing the data.
- Reading: an 80% cure rate is hard to reconcile with the historical 70%, although the study had no concurrent control group.

## Markers

- H0
- H1
- α
- z

## Common pitfalls

- Saying ‘H0 is accepted’: the correct wording is ‘H0 is not rejected’; absence of evidence is not evidence of absence.
- Switching to a one-sided test after seeing the data to reach p

## Memory aid

‘Innocent until proven guilty’: H0 is the innocent defendant; only strong evidence can reject it.

## Test yourself

Think of the answer, then tap the question to see it.

## What does the null hypothesis usually state?

That there is no difference between groups and no association between variables.

## If p = 0.20, what is concluded at α = 0.05?

H0 is not rejected: the data do not give enough evidence of a difference, which does not show there is none.

## What is the critical z value for a two-sided test at α = 0.05?

±1.96.

## When is a one-sided test justified?

Only when, before seeing the data, it was decided that a difference in the other direction is impossible or would not matter.

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## Connections

## Related 5

- [P value](https://durgical.com/en/epidemiology/p-value/)
- [Type I and type II errors](https://durgical.com/en/epidemiology/type-i-and-type-ii-errors/)
- [Statistical power](https://durgical.com/en/epidemiology/statistical-power/)
- [Confidence interval](https://durgical.com/en/epidemiology/confidence-interval/)
- [Choosing a statistical test](https://durgical.com/en/epidemiology/choosing-a-statistical-test/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.

Sources: [What are statistical tests?](https://www.itl.nist.gov/div898/handbook/prc/section1/prc13.htm) (NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology, 2012); [Critical values and p values](https://www.itl.nist.gov/div898/handbook/prc/section1/prc131.htm) (NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology, 2012); [What is the relationship between a test and a confidence interval?](https://www.itl.nist.gov/div898/handbook/prc/section1/prc15.htm) (NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology, 2012).

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Representative model, for educational purposes only.

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