Editing Statistical theory (section)

=== Data collection ===
Statistical theory provides a guide to comparing methods of [[data collection]], where the problem is to generate informative data using [[Optimization (mathematics)|optimization]] and [[randomization]] while measuring and controlling for [[observational error]].<ref>{{cite journal| author=[[Charles Sanders Peirce]] and [[Joseph Jastrow]]|year=1885|title=On Small Differences in Sensation| journal=Memoirs of the National Academy of Sciences|volume=3|pages=73–83|url=http://psychclassics.yorku.ca/Peirce/small-diffs.htm}} http://psychclassics.yorku.ca/Peirce/small-diffs.htm</ref><ref>{{cite journal|doi=10.1086/354775|first=Ian |last=Hacking|  author-link=Ian Hacking | title=Telepathy: Origins of Randomization in Experimental Design|journal=[[Isis (journal)|Isis]]|issue=3|volume=79|date=September 1988 |pages=427–451|jstor=234674 |mr=1013489|s2cid=52201011 }}</ref><ref>{{cite journal|doi=10.1086/444032|author=[[Stephen M. Stigler]]|title=A Historical View of Statistical Concepts in Psychology and Educational Research| journal=[[American Journal of Education]]| volume=101|issue=1|date=November 1992|pages=60–70|s2cid=143685203 }}</ref> Optimization of data collection reduces the cost of data while satisfying statistical goals,<ref name=OptDoE>Atkinson et al. (2007)</ref><ref>{{cite book |author-link=Jack Kiefer (mathematician)|last=Kiefer|first=Jack&nbsp;Carl|title=Jack&nbsp;Carl Kiefer: Collected papers&nbsp;III—Design of experiments| editor1-link=Lawrence D. Brown|editor1-last=Brown|editor2-first=Ingram|editor2-link=Ingram Olkin|editor2-last=Olkin|editor3-first=Jerome|editor3-last=Sacks|editor4-first=Henry P.|display-editors = 3 |editor4-last=Wynn|editor4-link=Henry P. Wynn|publisher=Springer-Verlag and the Institute of Mathematical Statistics |year=1985|pages=718+xxv|isbn=0-387-96004-X|editor1-first=Lawrence D.}}</ref> while [[randomization]] allows reliable inferences.  Statistical theory provides a basis for good data collection and the structuring of investigations in the topics of:
*[[Design of experiments]] to estimate treatment effects, to test hypotheses, and to optimize responses.<ref name="OptDoE"/><ref>Hinkelmann & Kempthorne (2008)</ref><ref>Bailey (2008).</ref>
*[[Survey sampling]] to describe [[statistical population|populations]]<ref>Kish (1965)</ref><ref>Cochran (1977)</ref><ref>Särndal et al. (1992)</ref>