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id:
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  - authorship/other-for-now
  - destiny/permanent
  - status/incomplete
  - topic/math/statistics
  - type/encyclopedia
title: Statistical Significance
---
# Statistical Significance

[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.
