Editing Statistical significance (section)

=== Significance thresholds in specific fields ===
{{Further|Standard deviation|Normal distribution}}
In specific fields such as [[particle physics]] and [[manufacturing]], statistical significance is often expressed in multiples of the [[standard deviation]] or sigma (''σ'') of a [[normal distribution]], with significance thresholds set at a much stricter level (for example 5''σ'').<ref name=Vaughan>{{cite book |last1 = Vaughan|first1 = Simon |title = Scientific Inference: Learning from Data | edition=1st |publisher = Cambridge University Press|location = Cambridge, UK | year = 2013 |isbn = 978-1-107-02482-3 |pages=146–152}}</ref><ref name=Bracken>{{cite book |last1 = Bracken|first1 = Michael B.|title = Risk, Chance, and Causation: Investigating the Origins and Treatment of Disease |url = https://archive.org/details/riskchancecausat0000brac|url-access = registration| edition=1st |publisher =Yale University Press|location = New Haven, CT | year = 2013 |isbn = 978-0-300-18884-4 |pages=[https://archive.org/details/riskchancecausat0000brac/page/260 260–276]}}</ref> For instance, the certainty of the [[Higgs boson]] particle's existence was based on the 5''σ'' criterion, which corresponds to a ''p''-value of about 1 in 3.5 million.<ref name="Bracken"/><ref name=franklin>{{cite book |last1 = Franklin|first1 = Allan|chapter= Prologue: The rise of the sigmas |title=Shifting Standards: Experiments in Particle Physics in the Twentieth Century|edition=1st |publisher = University of Pittsburgh Press|location = Pittsburgh, PA | year = 2013 |isbn = 978-0-8229-4430-0 |pages=Ii–Iii}}</ref>

In other fields of scientific research such as [[Genome-wide association study|genome-wide association studies]], significance levels as low as {{val|5|e=-8}} are not uncommon<ref name="Clarke et al">{{cite journal | last1 =  Clarke | first1 = GM | last2 = Anderson | first2 = CA | last3 = Pettersson | first3 = FH | last4 = Cardon | first4 = LR | last5 = Morris | first5 = AP | last6 = Zondervan | first6= KT | title = Basic statistical analysis in genetic case-control studies | journal = Nature Protocols | volume = 6 | issue = 2 | pages = 121–33 | date = February 6, 2011 | pmid = 21293453 | doi = 10.1038/nprot.2010.182 | pmc=3154648}}</ref><ref name="Barsh et al">{{cite journal | last1 = Barsh | first1 = GS | last2 = Copenhaver | first2 = GP | last3 = Gibson | first3 = G | last4 = Williams | first4 = SM | title = Guidelines for Genome-Wide Association Studies | journal = PLOS Genetics | volume = 8 | issue = 7 | pages = e1002812 | date = July 5, 2012 | pmid = 22792080 | doi = 10.1371/journal.pgen.1002812 | pmc=3390399 | doi-access = free }}</ref>—as the number of tests performed is extremely large.