---
tags:
  - authorship/other-for-now
  - topic/math/statistics
  - type/encyclopedia
title: Statistical Significance
---
# Statistical Significance

> [!quote] [Statistical significance - Wikipedia](https://en.wikipedia.org/wiki/Statistical_significance)
> In statistical hypothesis testing,
> a result has statistical significance
> when a result at least as "extreme"
> would be very infrequent if the null hypothesis were true.
>
> More precisely,
> a study's defined **significance level**, denoted by $\alpha$,
> is the probability of the study rejecting the null hypothesis,
> given that the null hypothesis is true;
> and the p-value of a result, $p$,
> is the probability of obtaining a result at least as extreme,
> given that the null hypothesis is true.
> The result is said to be statistically significant,
> by the standards of the study, when $p \leq \alpha$
>
> The significance level for a study
> is chosen before data collection,
> and is typically set to 5% or much lower---
> depending on the field of study.
>
> The [**null hypothesis**](https://en.wikipedia.org/wiki/Null_hypothesis)
> (often denoted $H_{0}$)
> is the claim that the effect being studied does not exist,
> or that no relationship exists
> between two sets of data or variables being analyzed.
>
> If the null hypothesis is true,
> any experimentally observed effect is due to chance alone.
>
> In research,
> the researcher develops an [**alternative hypothesis**](https://en.wikipedia.org/wiki/Alternative_hypothesis)
> (often denoted $H_{A}$ or $H_{1}$)
> which claims that an effect or relationship _does_ exist.
