Null hypothesis

A null hypothesis specifies a reference condition about a population or process, often no effect or association, against which data are evaluated.

Alternative hypothesis: A statistical claim that differs from the null hypothesis and is considered when assessing data. It states the effect or pattern a test may detect instead of the null condition.
Statistical hypothesis: A claim about a probability distribution, population parameter, or data-generating process. A null hypothesis is one particular role a statistical hypothesis can take.
Fisher's significance testing: An approach that uses a p-value to measure how incompatible data are with a specified null hypothesis. It treats the null as a reference for evidence, without requiring a formal alternative hypothesis.
Randomized controlled trial: An experiment that randomly assigns participants to intervention and control groups to estimate causal effects. A common null states that assignment to the intervention does not change the outcome.
Null result: A study result that does not provide sufficient evidence to reject its specified null hypothesis. It is a decision about evidence under a test, not proof that the null condition is true.
Test statistic: A quantity computed from sample data to measure evidence relevant to a statistical hypothesis. Its observed value is compared with outcomes expected under the null hypothesis.
Point null hypothesis: A null hypothesis that assigns a parameter one exact value. Many standard tests use a precise reference value, such as a zero difference.
Neyman–Pearson lemma: A theorem identifying the most powerful tests for distinguishing two simple hypotheses at a fixed significance level. It frames null testing as a decision between specified hypotheses with controlled error rates.
Chi-squared test: A family of tests using chi-squared statistics to assess categorical data against specified expectations. Its null may assert independence between variables or agreement with a stated distribution.
Multiple comparisons problem: The increased risk of false-positive findings when many hypotheses or outcomes are tested. Testing many null hypotheses can make nominal significance thresholds misleading without adjustment.

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