Editing Misuse of statistics (section)

===Other fallacies===
[[Pseudoreplication]] is a technical error associated with [[analysis of variance]].  Complexity hides the fact that statistical analysis is being attempted on a single sample (N=1).  For this degenerate case the variance cannot be calculated (division by zero). An (N=1) will always give the researcher the highest statistical correlation between intent bias and actual findings.

The [[gambler's fallacy]] assumes that an event for which a future likelihood can be measured had the same likelihood of happening once it has already occurred. Thus, if someone had already tossed 9 coins and each has come up heads, people tend to assume that the likelihood of a tenth toss also being heads is 1023 to 1 against (which it was before the first coin was tossed) when in fact the chance of the tenth head is 50% (assuming the coin is unbiased).

The [[prosecutor's fallacy]]<ref>{{cite book | last = Seife | first = Charles | title = Proofiness: how you're being fooled by the numbers | publisher = Penguin | location = New York | year = 2011 | isbn = 9780143120070|pages=203–205 and Appendix C}}  Discusses the notorious British case.</ref> assumes that the probability of an apparently criminal event being random chance is equal to the chance that the suspect is innocent. A prominent example in the UK is the wrongful conviction of [[Sally Clark]] for killing her two sons who appeared to have died of [[Sudden Infant Death Syndrome]] (SIDS). In his expert testimony, now discredited Professor Sir [[Roy Meadow]] claimed that due to the rarity of SIDS, the probability of Clark being innocent was 1 in 73 million. This was later questioned by the [[Royal Statistical Society]];<ref name=rss2>Royal Statistical Society (23 October 2001).  "{{cite web |url= http://www.rss.org.uk/uploadedfiles/documentlibrary/744.pdf |archive-url= https://web.archive.org/web/20110824151124/http://www.rss.org.uk/uploadedfiles/documentlibrary/744.pdf |url-status= dead |archive-date= 2011-08-24 |title= Royal Statistical Society concerned by issues raised in Sally Clark case }}&nbsp;{{small|(28.0&nbsp;KB)}}"</ref> assuming Meadows figure was accurate, one has to weigh up all the possible explanations against each other to make a conclusion on which most likely caused the unexplained death of the two children. Available data suggest that the odds would be in favour of double SIDS compared to double homicide by a factor of nine.<ref>{{cite journal|title=Multiple sudden infant deaths – coincidence or beyond coincidence?|journal = Paediatric and Perinatal Epidemiology|volume = 18|issue = 5|pages = 320–6|pmid = 15367318|year = 2004|last1 = Hill|first1 = R.|doi = 10.1111/j.1365-3016.2004.00560.x}}</ref> The 1 in 73 million figure was also misleading as it was reached by finding the probability of a baby from an affluent, non-smoking family dying from SIDS and [[Square (algebra)|squaring]] it: this erroneously treats each death as [[statistically independent]], assuming that there is no factor, such as genetics, that would make it more likely for two siblings to die from SIDS.<ref>{{Cite web |title=Beyond reasonable doubt |url=https://plus.maths.org/content/beyond-reasonable-doubt |access-date=2022-04-01 |website=Plus Maths |language=en}}</ref><ref name=":0">{{Cite journal |last=Watkins |first=Stephen J. |date=2000-01-01 |title=Conviction by mathematical error?: Doctors and lawyers should get probability theory right |url=https://www.bmj.com/content/320/7226/2 |journal=BMJ |language=en |volume=320 |issue=7226 |pages=2–3 |doi=10.1136/bmj.320.7226.2 |issn=0959-8138 |pmc=1117305 |pmid=10617504}}</ref> This is also an example of the [[ecological fallacy]] as it assumes the probability of SIDS in Clark's family was the same as the average of all affluent, non-smoking families; social class is a highly complex and multifaceted concept, with numerous other variables such as education, line of work, and many more. Assuming that an individual will have the same attributes as the rest of a given group fails to account for the effects of other variables which in turn can be misleading.<ref name=":0" /> The conviction of [[Sally Clark]] was eventually overturned and Meadow was struck from the  medical register.<ref>{{Cite journal |last=Dyer |first=Clare |date=2005-07-21 |title=Professor Roy Meadow struck off |url=https://www.bmj.com/content/331/7510/177.1 |journal=BMJ |language=en |volume=331 |issue=7510 |pages=177 |doi=10.1136/bmj.331.7510.177 |issn=0959-8138 |pmc=1179752 |pmid=16037430}}</ref>

The [[ludic fallacy]].  Probabilities are based on simple models that ignore real (if remote) possibilities.  Poker players do not consider that an opponent may draw a gun rather than a card.  The insured (and governments) assume that insurers will remain solvent, but see [[American International Group#Financial crisis|AIG]] and [[Systemic risk#Systemic risk and insurance|systemic risk]].