Mathematics Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! === Statistics and other decision sciences === {{Main|Statistics|Probability theory}} [[File:IllustrationCentralTheorem.png|upright=1.5|thumb|right|Whatever the form of a random population [[Probability distribution|distribution]] (μ), the sampling [[mean]] (x̄) tends to a [[Gaussian]] distribution and its [[variance]] (σ) is given by the [[central limit theorem]] of probability theory.<ref>{{cite book |last=Rouaud |first=Mathieu |date=April 2017 |orig-date=First published July 2013 |title=Probability, Statistics and Estimation |page=10 |url=http://www.incertitudes.fr/book.pdf |url-status=live |archive-url=https://ghostarchive.org/archive/20221009/http://www.incertitudes.fr/book.pdf |archive-date=October 9, 2022 |access-date=February 13, 2024}}</ref>]] The field of statistics is a mathematical application that is employed for the collection and processing of data samples, using procedures based on mathematical methods especially [[probability theory]]. Statisticians generate data with [[random sampling]] or randomized [[design of experiments|experiments]].<ref>{{cite book |last=Rao |first=C. Radhakrishna |author-link=C. R. Rao |year=1997 |orig-date=1989 |title=Statistics and Truth: Putting Chance to Work |edition=2nd |pages=3–17, 63–70 |publisher=World Scientific |isbn=981-02-3111-3 |lccn=97010349 |mr=1474730 |oclc=36597731}}</ref> The design of a statistical sample or experiment determines the analytical methods that will be used. Analysis of data from [[observational study|observational studies]] is done using [[statistical model]]s and the theory of [[statistical inference|inference]], using [[model selection]] and [[estimation theory|estimation]]. The models and consequential [[Scientific method#Predictions from the hypothesis|predictions]] should then be [[statistical hypothesis testing|tested]] against [[Scientific method#Evaluation and improvement|new data]].{{efn|Like other mathematical sciences such as [[physics]] and [[computer science]], statistics is an autonomous discipline rather than a branch of applied mathematics. Like research physicists and computer scientists, research statisticians are mathematical scientists. Many statisticians have a degree in mathematics, and some statisticians are also mathematicians.}} [[Statistical theory]] studies [[statistical decision theory|decision problems]] such as minimizing the [[risk]] ([[expected loss]]) of a statistical action, such as using a [[statistical method|procedure]] in, for example, [[parameter estimation]], [[hypothesis testing]], and [[selection algorithm|selecting the best]]. In these traditional areas of [[mathematical statistics]], a statistical-decision problem is formulated by minimizing an [[objective function]], like expected loss or [[cost]], under specific constraints. For example, designing a survey often involves minimizing the cost of estimating a population mean with a given level of confidence.<ref name="RaoOpt">{{cite book |last=Rao |first=C. Radhakrishna |author-link=C.R. Rao |editor1-last=Arthanari |editor1-first=T.S. |editor2-last=Dodge |editor2-first=Yadolah |editor2-link=Yadolah Dodge |chapter=Foreword |title=Mathematical programming in statistics |series=Wiley Series in Probability and Mathematical Statistics |publisher=Wiley |location=New York |year=1981 |pages=vii–viii |isbn=978-0-471-08073-2 |lccn=80021637 |mr=607328 |oclc=6707805}}</ref> Because of its use of [[mathematical optimization|optimization]], the mathematical theory of statistics overlaps with other [[decision science]]s, such as [[operations research]], [[control theory]], and [[mathematical economics]].{{sfn|Whittle|1994|pp=10–11, 14–18}} Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Christianpedia:Copyrights for details). Do not submit copyrighted work without permission! Cancel Editing help (opens in new window) Discuss this page