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| {{Expert-subject|statistics|date=November 2008}}
| | == 間違った == |
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| In the [[statistical]] theory of the [[design of experiments]], '''blocking''' is the arranging of [[experimental unit]]s in groups (blocks) that are similar to one another. For example, an experiment is designed to test a new drug on patients. There are two levels of the treatment, ''[[drug]]'', and ''[[placebo]]'', administered to ''male'' and ''female'' patients in a [[double blind]] trial. The sex of the patient is a ''blocking'' factor accounting for treatment variability between ''males'' and ''females''. This reduces sources of variability and thus leads to greater precision.
| | 奇妙な [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_7.php クリスチャンルブタン 激安]。<br>才能のある人を<br>、なぜこれほど長い間8セントティモールで停止？でも皇帝西安修飾一般的で、それは9セントの皇帝に到達するために長い年月を突破することが可能である [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_8.php クリスチャンルブタン スニーカー]。<br><br>「エネルギーを吸収しない意図的に清朝皇帝ですか？間違った。 [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_8.php クリスチャンルブタン 直営店] '秦ゆうが意図的に練習していない場合には、「実務家は、、体が自動的に、自動的に体内に吸収してもエネルギーをエネルギーを吸収するまで顔をしかめ、速度が非常に遅いが、そのように長いです年。エネルギー9セント十分な吸収は、天皇の領域に到達できるようにする。 '<br>マスターの練習はおろか<br> [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_11.php クリスチャンルブタン 取扱店]。<br><br>は、体が自動的にエネルギーを吸収し、理解のスクリーンセーバーを達成することである [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_11.php クリスチャンルブタン 取扱店]。<br><br>エネルギー自給吸収し、よりゆっくりだけの体は、吸収率を投げたコントロール感についていくことはできません。<br><br>「若い皇帝の9セント天皇に到達するためにしたくないですか？それは体が生体内で消費されるエネルギーの一部にでも時間をかけて、エネルギーを吸収しない制御されている？ '秦Yuはそれを信じていない。<br><br>常に8セント天皇何が良い？ただのための |
| | | 相关的主题文章： |
| Reducing known variability is exactly what blocking does. Its principle lies in the fact that a variability that cannot be overcome (e.g. needing two batches of raw material to produce 1 container of a chemical) is [[Confounding|confound]] or aliased with a(n) (higher/highest order) interaction to eliminate its influence on the end product. High order [[Interaction (statistics)|interactions]] are usually of the least importance (think of the fact that temperature of a reactor or the batch of raw materials is more important than the combination of the two - this is especially true when more (3, 4, ...) factors are present) thus it is preferable to confound this variability with the higher interaction.
| | <ul> |
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| Suppose a process is invented that intends to make the soles of shoes last longer, and a plan is formed to conduct a field trial. Given a group of ''n'' volunteers, one possible design would be to give ''n/2'' of them shoes with the new soles and ''n/2'' of them shoes with the ordinary soles, [[randomization|randomizing]] the assignment of the two kinds of soles. This type of experiment is a [[completely randomized design]]. Both groups are then asked to use their shoes for a period of time, and then measure the degree of wear of the soles. This is a workable experimental design, but purely from the point of view of statistical accuracy (ignoring any other factors), a better design would be to give each person one regular sole and one new sole, randomly assigning the two types to the left and right shoe of each volunteer. Such a design is called a [[randomized complete block design]]. This design will be more sensitive than the first, because each person is acting as their own control and thus the [[control group]] is more closely matched to the [[treatment group]].
| | <li>[http://www.dushizixun.com/forum.php?mod=viewthread&tid=6590 http://www.dushizixun.com/forum.php?mod=viewthread&tid=6590]</li> |
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| The theoretical basis of blocking is the following mathematical result. Given random variables, ''X'' and ''Y''
| | <li>[http://www.penshurst-online.co.uk/cgi-bin/spamwxyz/guestbook.cgi http://www.penshurst-online.co.uk/cgi-bin/spamwxyz/guestbook.cgi]</li> |
| | | |
| :<math>
| | <li>[http://54.178.28.151/forum.php?mod=viewthread&tid=145835 http://54.178.28.151/forum.php?mod=viewthread&tid=145835]</li> |
| \operatorname{Var}(X-Y)= \operatorname{Var}(X) + \operatorname{Var}(Y) - 2\operatorname{Cov}(X,Y).
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| </math> | | </ul> |
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| The difference between the treatment and the control can thus be given minimum variance (i.e. maximum precision) by maximising the covariance (or the correlation) between ''X'' and ''Y''.
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| ==References== | |
| | |
| * {{cite journal
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| |doi=10.2307/2681737
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| |title=The Generalized Randomized Block Design <!-- |authorlink=Sidney Addelman -->
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| |first=Sidney
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| |last=Addelman
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| |journal=The American Statistician
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| |volume=23
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| |issue=4
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| |date=Oct 1969
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| |pages=35–36
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| |jstor=2681737
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| }}
| |
| | |
| * {{cite journal
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| |doi=10.2307/2284277
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| |title=Variability of Treatments and Experimental Units in the Design and Analysis of Experiments
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| |first=Sidney
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| |last=Addelman
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| |journal=Journal of the American Statistical Association
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| |volume=65
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| |issue=331
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| |date=Sep 1970
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| |pages=1095–1108
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| |jstor = 2284277
| |
| }}
| |
| | |
| * {{cite book |author=[http://www.maths.qmw.ac.uk/~rab/ Bailey, R. A]|title=Design of Comparative Experiments|url=http://www.maths.qmul.ac.uk/~rab/DOEbook/|publisher=[http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521683579 Cambridge University Press]|year=2008 |isbn=978-0-521-68357-9}} Pre-publication chapters are available on-line.
| |
| | |
| * {{cite book
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| |author=Caliński, Tadeusz and Kageyama, Sanpei
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| |title=Block designs: A Randomization approach, Volume '''I''': Analysis
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| |series=Lecture Notes in Statistics
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| |volume=150
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| |publisher=Springer-Verlag
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| |location=New York
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| |year=2000
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| |isbn=0-387-98578-6
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| }}
| |
| | |
| * {{ cite journal
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| |doi=10.2307/2684574
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| |title=What Really Is Experimental Error in Block Designs?
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| |first=Charles E.
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| |last=Gates
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| |journal=The American Statistician
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| |volume=49
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| |issue=4
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| |date=Nov 1995
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| |pages = 362–363
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| |jstor = 2684574
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| }}
| |
| | |
| *{{cite book
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| |author=[[Oscar Kempthorne|Kempthorne, Oscar]]
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| |year=1979
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| |title=The Design and Analysis of Experiments
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| |edition=Corrected reprint of (1952) Wiley
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| |publisher=Robert E. Krieger
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| |isbn=0-88275-105-0
| |
| }}
| |
| *{{cite book
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| |author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]
| |
| |year=2008
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| |title=Design and Analysis of Experiments
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| |volume=I and II
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| |edition=Second
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| |publisher=Wiley
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| |isbn=978-0-470-38551-7}}
| |
| **{{cite book
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| |author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]
| |
| |year=2008
| |
| |title=Design and Analysis of Experiments, Volume I: Introduction to Experimental Design
| |
| |edition=Second
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| |publisher=Wiley
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| |isbn=978-0-471-72756-9
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| }}
| |
| **{{cite book
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| |author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]
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| |year=2005
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| |title=Design and Analysis of Experiments, Volume 2: Advanced Experimental Design
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| |edition=First
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| |publisher=Wiley
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| |isbn=978-0-471-55177-5
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| }}
| |
| | |
| * {{cite book
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| |first=Marvin
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| |last=Lentner
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| |coauthor=Thomas Bishop <!-- |chapter=The Generalized RCB Design (Chapter 6.13) -->
| |
| |pages=225–226
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| |title=Experimental design and analysis
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| |edition=Second
| |
| |publisher=Valley Book Company
| |
| |location=P.O. Box 884, Blacksburg, VA 24063
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| |year=1993
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| |isbn=0-9616255-2-X
| |
| }}
| |
| | |
| * {{cite journal
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| |title=The Randomization Analysis of a Generalized Randomized Block Design
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| |first=M. B.
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| |last=Wilk
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| |journal=Biometrika
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| |volume=42
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| |issue=1–2
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| |date=June 1955
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| |pages=70–79
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| | jstor = 2333423
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| }}
| |
| | |
| * {{ cite journal
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| |title=Some Consequences of randomization in a Generalization of the Balanced Incomplete Block Design
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| |first=George
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| |last=Zyskind
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| |journal=The Annals of Mathematical Statistics
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| |volume=34
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| |issue=4
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| |date=Dec 1963
| |
| |pages=1569–1581
| |
| |jstor = 2238364
| |
| |doi = 10.1214/aoms/1177703889
| |
| }}
| |
| | |
| ==See also==
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| {{Portal|Statistics}}
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| * [[Block design]]
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| * [[Paired difference test]]
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| * [[Randomized block design]]
| |
| | |
| {{Statistics|collection|state=collapsed}}
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| {{Experimental design}}
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| | |
| {{DEFAULTSORT:Blocking (Statistics)}}
| |
| [[Category:Design of experiments]]
| |
間違った
奇妙な クリスチャンルブタン 激安。
才能のある人を
、なぜこれほど長い間8セントティモールで停止？でも皇帝西安修飾一般的で、それは9セントの皇帝に到達するために長い年月を突破することが可能である クリスチャンルブタン スニーカー。
「エネルギーを吸収しない意図的に清朝皇帝ですか？間違った。 クリスチャンルブタン 直営店 '秦ゆうが意図的に練習していない場合には、「実務家は、、体が自動的に、自動的に体内に吸収してもエネルギーをエネルギーを吸収するまで顔をしかめ、速度が非常に遅いが、そのように長いです年。エネルギー9セント十分な吸収は、天皇の領域に到達できるようにする。 '
マスターの練習はおろか
クリスチャンルブタン 取扱店。
は、体が自動的にエネルギーを吸収し、理解のスクリーンセーバーを達成することである クリスチャンルブタン 取扱店。
エネルギー自給吸収し、よりゆっくりだけの体は、吸収率を投げたコントロール感についていくことはできません。
「若い皇帝の9セント天皇に到達するためにしたくないですか？それは体が生体内で消費されるエネルギーの一部にでも時間をかけて、エネルギーを吸収しない制御されている？ '秦Yuはそれを信じていない。
常に8セント天皇何が良い？ただのための
相关的主题文章：