Editing Chi-squared test (section)

==Applications==

In [[cryptanalysis]], the chi-squared test is used to compare the distribution of [[plaintext]] and (possibly) decrypted [[ciphertext]]. The lowest value of the test means that the decryption was successful with high probability.<ref name=practicalcrypto>{{cite web|title=Chi-squared Statistic|url=http://practicalcryptography.com/cryptanalysis/text-characterisation/chi-squared-statistic/|website=Practical Cryptography|access-date=18 February 2015|archive-url=https://web.archive.org/web/20150218203349/http://practicalcryptography.com/cryptanalysis/text-characterisation/chi-squared-statistic/|archive-date=18 February 2015|url-status=dead}}</ref><ref name=ibmath>{{cite web|title=Using Chi Squared to Crack Codes|url=http://ibmathsresources.com/2014/06/15/using-chi-squared-to-crack-codes/|website=IB Maths Resources|date=15 June 2014 |publisher=British International School Phuket}}</ref> This method can be generalized for solving modern cryptographic problems.<ref name=elsevier>{{cite journal|last1=Ryabko|first1=B. Ya.|last2=Stognienko|first2=V. S.|last3=Shokin|first3=Yu. I.|title=A new test for randomness and its application to some cryptographic problems|journal=Journal of Statistical Planning and Inference|date=2004|volume=123|issue=2|pages=365–376|url=http://boris.ryabko.net/jspi.pdf|access-date=18 February 2015|doi=10.1016/s0378-3758(03)00149-6}}</ref>

In [[bioinformatics]], the chi-squared test is used to compare the distribution of certain properties of genes (e.g., genomic content, mutation rate, interaction network clustering, etc.) belonging to different categories (e.g., disease genes, essential genes, genes on a certain chromosome etc.).<ref name=pnas-bics>{{cite journal|last1=Feldman|first1=I.|last2=Rzhetsky|first2=A.|last3=Vitkup|first3=D.|title=Network properties of genes harboring inherited disease mutations|journal=PNAS|date=2008|volume=105|issue=11|pages=4323–432|doi=10.1073/pnas.0701722105|bibcode=2008PNAS..105.4323F|pmc=2393821|pmid=18326631|doi-access=free}}</ref><ref name=chi-bics>{{cite web|title=chi-square-tests|url=https://visa.pharmacy.wsu.edu/bioinformatics/documents/chi-square-tests.pdf|access-date=29 June 2018|archive-url=https://web.archive.org/web/20180629131548/https://visa.pharmacy.wsu.edu/bioinformatics/documents/chi-square-tests.pdf|archive-date=29 June 2018|url-status=dead}}</ref>