Sunday, March 7, 2010
Tuesday, February 16, 2010
Friday, February 12, 2010
Bayesian Network Repository
--------------------------------------------------------------------------------
Contents
About This Page
The datasets
Network formats and Utilities
Related Sites
--------------------------------------------------------------------------------
Mission
Our in intention is to construct a repository that will allow us empirical research within our community by facilitating (1)better reproducibility of results, and (2) better comparisons among competing approach. Both of these are required to measure progress on problems that are commonly agreed upon, such as inference and learning.
A motivation for this repository is outlined in "Challenge: Where is the impact of Bayesian networks in learning?" by N. Friedman, M. Goldszmidt, D. Heckerman, and S. Russell (IJCAI-97).
This will be achieved by several progressive steps:
Sharing domains. This would allow for reproduction of results, and also allow researchers in the community to run large scale empirical tests.
Sharing task specification. Sharing domains is not enough to compare algorithms. Thus, even if two papers examine inference in particular network, they might be answering different queries or assuming different evidence sets. The intent here is to store specific tasks. For example, in inference this might be a specific series of observations/queries. In learning, this might be a particular collection of training sets that have a particular pattern of missing data.
Sharing task evaluation. Even if two researchers examine the same task, they might use different measures to evaluate their algorithms. By sharing evaluation methods, we hope to allow for an objective comparison. In some cases such evaluation methods can be shared programs, such as a program the evaluates the quality of learned model by computing KL divergence to the "real" distribution. In other cases, such an evaluation method might be an agreed upon evaluation of performance, such as space requirements, number of floating point operations, etc.
Organized competitions. One of the dangers of empirical research is that the methods examined become overly tuned to specific evaluation domains. To avoid that danger, it is necessary to use "fresh" problems. The intention is to organize competitions that would address a specific problems, such as causal discovery, on unseen domains.
Plans for the future
Currently, this site contains several domains. The plan is to gradually add other components discussed above.
Please send suggestions and contributions to galel@cs.huji.ac.il.
Acknowledgements
Thanks to Fabio Cozman, Bruce D'Ambrosio, Moises Goldszmidt, David Heckerman, Othar Hansson, Daphne Koller, and Stuart Russell for discussions about the organization of this site. Thanks to John Binder, Jack Breese, David Heckerman, Uffe Kjaeruff, and Mark Peot, for contributing networks.
--------------------------------------------------------------------------------
galel@cs.huji.ac.il
Contents
About This Page
The datasets
Network formats and Utilities
Related Sites
--------------------------------------------------------------------------------
Mission
Our in intention is to construct a repository that will allow us empirical research within our community by facilitating (1)better reproducibility of results, and (2) better comparisons among competing approach. Both of these are required to measure progress on problems that are commonly agreed upon, such as inference and learning.
A motivation for this repository is outlined in "Challenge: Where is the impact of Bayesian networks in learning?" by N. Friedman, M. Goldszmidt, D. Heckerman, and S. Russell (IJCAI-97).
This will be achieved by several progressive steps:
Sharing domains. This would allow for reproduction of results, and also allow researchers in the community to run large scale empirical tests.
Sharing task specification. Sharing domains is not enough to compare algorithms. Thus, even if two papers examine inference in particular network, they might be answering different queries or assuming different evidence sets. The intent here is to store specific tasks. For example, in inference this might be a specific series of observations/queries. In learning, this might be a particular collection of training sets that have a particular pattern of missing data.
Sharing task evaluation. Even if two researchers examine the same task, they might use different measures to evaluate their algorithms. By sharing evaluation methods, we hope to allow for an objective comparison. In some cases such evaluation methods can be shared programs, such as a program the evaluates the quality of learned model by computing KL divergence to the "real" distribution. In other cases, such an evaluation method might be an agreed upon evaluation of performance, such as space requirements, number of floating point operations, etc.
Organized competitions. One of the dangers of empirical research is that the methods examined become overly tuned to specific evaluation domains. To avoid that danger, it is necessary to use "fresh" problems. The intention is to organize competitions that would address a specific problems, such as causal discovery, on unseen domains.
Plans for the future
Currently, this site contains several domains. The plan is to gradually add other components discussed above.
Please send suggestions and contributions to galel@cs.huji.ac.il.
Acknowledgements
Thanks to Fabio Cozman, Bruce D'Ambrosio, Moises Goldszmidt, David Heckerman, Othar Hansson, Daphne Koller, and Stuart Russell for discussions about the organization of this site. Thanks to John Binder, Jack Breese, David Heckerman, Uffe Kjaeruff, and Mark Peot, for contributing networks.
--------------------------------------------------------------------------------
galel@cs.huji.ac.il
Graphical Models -software tools
Working Group Neural Networks and Fuzzy Systems
Graphical Models
Software Tools back to the main page
Contents
Overview
BayesBuilder
Bayesian Knowledge Discoverer / Bayesware Discoverer
Bayes Net Toolbox
Belief Network Power Constructor
GeNIe / SMILE
Hugin
Netica
Pulcinella
Tetrad
WinMine / MSBN
Overview
On this page we briefly describe some software tools that support reasoning with graphical models and/or inducing them from a database of sample cases. Of course, we do not claim this list to be complete (definitely it is not). Nor does it represent a ranking of the tools, since they are ordered alphabetically. More extensive lists of probabilistic network tools have been compiled by
Russel Almond (an old list, which is not maintained anymore):
http://www.stat.washington.edu/almond/belief.html
Kevin Patrick Murphy:
http://www.cs.berkeley.edu/~murphyk/Bayes/bnsoft.html
and Google:
http://directory.google.com/Top/Computers/Artificial_Intelligence/Belief_Networks/Software/
The Bayesian Network Repository is also a valuable resource. It lists examples of Bayesian networks and datasets, from which they can be learned:
http://www.cs.huji.ac.il/labs/compbio/Repository/
The software we developed in connection with our book is available at:
http://fuzzy.cs.uni-magdeburg.de/books/gm/software.html
Tools for troubleshooting Microsoft products, which are based on Bayesian networks (but do not allow you to access them directly), can be found at
http://support.microsoft.com/support/tshoot/default.asp
back to the top
BayesBuilder
SNN, University of Nijmegen
PO Box 9101, 6500 HB Nijmegen, The Netherlands
http://www.mbfys.kun.nl/snn/Research/bayesbuilder/
BayesBuilder is a tool for (manually) constructing Bayesian networks and drawing inferences with them. It supports neither parameter nor structure learning of Bayesian networks. The graphical user interface of this program is written in Java and is easy to use. However, the program is available only for Windows, because the underlying inference engine is written in C++ and has only been compiled for Windows yet. BayesBuilder is free software.
back to the top
Bayesian Knowledge Discoverer / Bayesware Discoverer
Knowledge Media Institute / Department of Statistics
The Open University
Walton Hall, Milton Keynes MK7 6AA, United Kingdom
http://kmi.open.ac.uk/projects/bkd/
Bayesware Ltd.
http://bayesware.com/
The Bayesian Knowledge Discoverer is a software tool that can learn Bayesian networks from data (structure as well as parameters). The dataset to learn from may contain missing values, which are handled by an approach called "bound and collapse" that is based on probability intervals. The Bayesian Knowledge Discoverer is free software, but it has been succeeded by a commercial version, the Bayesware Discoverer. This program has a nice graphical user interface with some powerful visualization options. A 30 days trial version may be retrieved free of charge. Bayesware Discoverer is available for Windows, Unix and Macintosh.
back to the top
Bayes Net Toolbox
Kevin Patrick Murphy
Department of Computer Science, UC Berkeley
387 Soda Hall, Berkeley, CA 94720-1776, USA
http://www.cs.berkeley.edu/~murphyk/Bayes/bnt.html
The Bayes Net Toolbox is an extension for Matlab, a well-known and widely used mathematical software package. It supports several different algorithms for drawing inferences in Bayesian networks as well as several algorithms for learning the parameters and the structure of Bayesian networks from a dataset of sample cases. It does not have a graphical user interface of its own, but profits from the visualization capabilities of Matlab. The Bayes Net Toolbox is distributed under the Gnu Library General Public License and is available for all systems that can run Matlab, an installation of which is required.
back to the top
Belief Network Power Constructor
Jie Cheng
Dept. of Computing Science, University of Alberta
155 Athabasca Hall, Edmonton, Alberta, Canada T6G 2E1
http://www.cs.ualberta.ca/~jcheng/bnpc.htm
The Bayesian Network Power Constructor uses a three phase algorithm that is based on conditional independence tests to learn the structure of a Bayesian network from data. The conditional independence tests rely on mutual information, which is used to determine whether a (set of) node(s) can reduce or even block the information flow from one node to another. The program comes with a graphical user interface, though a much less advanced one than those of, for instance, HUGIN and Netica (see below). It does not support drawing inferences, but has the advantage that it is free software. It is available only for Windows.
back to the top
GeNIe / SMILE
Decision Systems Laboratory, University of Pittsburgh
B212 SLIS Building, 135 North Bellefield Avenue, Pittsburgh, PA 15260, USA
http://www2.sis.pitt.edu/~genie/
SMILE (Structural Modeling, Inference and Learning Engine) is a library of functions for building Bayesian networks and drawing inferences with them. It does support neither parameter nor structural learning of Bayesian networks. GeNIe (Graphical Network Interface) is a graphical user interface for SMILE, that makes the functions of SMILE easily accessible. While SMILE is platform independent, GeNIe is available only for Windows, since it relies heavily on the Microsoft Foundation classes. Both packages are distributed free of charge.
back to the top
Hugin
Hugin Expert A/S
Niels Jernes Vej 10, 9220 Aalborg, Denmark
http://www.hugin.com
Hugin is one of the oldest and best-known tools for Bayesian network construction and inference. It comes with an easy to use graphical user interface, but also has an API (application programmers interface) for several programming languages, so that the inference engine can be used in other programs. It supports estimating the parameters of a Bayesian network from a dataset of sample cases. In a recent version it has also been extended by a learning algorithm for the structure of a Bayesian network, which is based on conditional independence tests. Hugin is a commercial tool, but a demo version with restricted capabilities may be retrieved free of charge. Hugin is available for Windows and Solaris (Sun Unix).
back to the top
Netica
Norsys Software Corp.
2315 Dunbar Street, Vancouver, BC, Canada V6R 3N1
http://www.norsys.com
Like Hugin, Netica is a commercial tool with an advanced graphical user interface. It supports Bayesian network construction and inference and also comprises an API (application programmers interface) for C++, so that the inference engine may be used in other programs. Netica offers quantitative network learning (known structure, parameter estimation) from a dataset of sample cases, which may contain missing values. It does not support structural learning. A version of Netica with restricted capabilities may be retrieved free of charge, but the price of a full version is also moderate. Netica is available for Windows and Macintosh.
back to the top
Pulcinella
IRIDA, Université Libre de Bruxelles
50, Av. F. Roosevelt, CP 194/6, B-1050 Brussels, Belgium
http://iridia.ulb.ac.be/pulcinella/Welcome.html
Pulcinella is more general than the other programs listed on this page, as it is based on the framework of valuation systems [Shenoy 1992a]. Pulcinella supports reasoning by propagating uncertainty with local computations w.r.t. different uncertainty calculi, but does not support learning graphical models from a dataset of sample cases in any way. The current version of Pulcinella does not have a graphical user interface, but an outdated version of such an interface may be retrieved for Solaris (Sun Unix). Pulcinella is available for Solaris (Sun Unix) and Macintosh, but requires a Common Lisp system.
back to the top
Tetrad
Tetrad Project, Department of Philosophy
Carnegie Mellon University, Pittsburgh, PA, USA
http://hss.cmu.edu/html/departments/philosophy/TETRAD/tetrad.htm
Tetrad is based on the algorithms developed in [Spirtes et al 1993], i.e. on conditional independence test approaches to learn Bayesian networks from data, and, of course, subsequent research in this direction. It can learn the structure as well as the parameters of a Bayesian network from a dataset of sample cases, but does not support drawing inferences. Currently the program is being ported to Java (Tetrad IV). Older versions are available for MSDOS (Tetrad II) and Windows (Tetrad III). Tetrad II is commercial, but available at a moderate fee. Free beta versions are available of Tetrad III and Tetrad IV.
back to the top
WinMine / MSBN
Machine Learning and Statistics Group
Microsoft Research, One Microsoft Way, Redmond, WA 98052-6399, USA
http://research.microsoft.com/~dmax/WinMine/tooldoc.htm
WinMine is a toolkit, i.e. a set of programs for different tasks, rather than an integrated program. Most programs in this toolkit are command line driven, but there is a graphical user interface for the data converter and a network visualization program. WinMine learns the structure and the parameters of Bayesian networks from data and uses decision trees to represent the conditional distributions. It does not support drawing inferences. However, Microsoft Research also offers MSBN (Microsoft Bayesian Networks), a tool for (manually) building Bayesian networks and drawing inferences with them, MSBN comes with a graphical user interface. Both programs, WinMine as well as MSBN, are available for Windows only.
back to the top
© 2002 Christian Borgelt
Last modified: Fri Oct 25 11:05:52 MEST 2002
Graphical Models
Software Tools back to the main page
Contents
Overview
BayesBuilder
Bayesian Knowledge Discoverer / Bayesware Discoverer
Bayes Net Toolbox
Belief Network Power Constructor
GeNIe / SMILE
Hugin
Netica
Pulcinella
Tetrad
WinMine / MSBN
Overview
On this page we briefly describe some software tools that support reasoning with graphical models and/or inducing them from a database of sample cases. Of course, we do not claim this list to be complete (definitely it is not). Nor does it represent a ranking of the tools, since they are ordered alphabetically. More extensive lists of probabilistic network tools have been compiled by
Russel Almond (an old list, which is not maintained anymore):
http://www.stat.washington.edu/almond/belief.html
Kevin Patrick Murphy:
http://www.cs.berkeley.edu/~murphyk/Bayes/bnsoft.html
and Google:
http://directory.google.com/Top/Computers/Artificial_Intelligence/Belief_Networks/Software/
The Bayesian Network Repository is also a valuable resource. It lists examples of Bayesian networks and datasets, from which they can be learned:
http://www.cs.huji.ac.il/labs/compbio/Repository/
The software we developed in connection with our book is available at:
http://fuzzy.cs.uni-magdeburg.de/books/gm/software.html
Tools for troubleshooting Microsoft products, which are based on Bayesian networks (but do not allow you to access them directly), can be found at
http://support.microsoft.com/support/tshoot/default.asp
back to the top
BayesBuilder
SNN, University of Nijmegen
PO Box 9101, 6500 HB Nijmegen, The Netherlands
http://www.mbfys.kun.nl/snn/Research/bayesbuilder/
BayesBuilder is a tool for (manually) constructing Bayesian networks and drawing inferences with them. It supports neither parameter nor structure learning of Bayesian networks. The graphical user interface of this program is written in Java and is easy to use. However, the program is available only for Windows, because the underlying inference engine is written in C++ and has only been compiled for Windows yet. BayesBuilder is free software.
back to the top
Bayesian Knowledge Discoverer / Bayesware Discoverer
Knowledge Media Institute / Department of Statistics
The Open University
Walton Hall, Milton Keynes MK7 6AA, United Kingdom
http://kmi.open.ac.uk/projects/bkd/
Bayesware Ltd.
http://bayesware.com/
The Bayesian Knowledge Discoverer is a software tool that can learn Bayesian networks from data (structure as well as parameters). The dataset to learn from may contain missing values, which are handled by an approach called "bound and collapse" that is based on probability intervals. The Bayesian Knowledge Discoverer is free software, but it has been succeeded by a commercial version, the Bayesware Discoverer. This program has a nice graphical user interface with some powerful visualization options. A 30 days trial version may be retrieved free of charge. Bayesware Discoverer is available for Windows, Unix and Macintosh.
back to the top
Bayes Net Toolbox
Kevin Patrick Murphy
Department of Computer Science, UC Berkeley
387 Soda Hall, Berkeley, CA 94720-1776, USA
http://www.cs.berkeley.edu/~murphyk/Bayes/bnt.html
The Bayes Net Toolbox is an extension for Matlab, a well-known and widely used mathematical software package. It supports several different algorithms for drawing inferences in Bayesian networks as well as several algorithms for learning the parameters and the structure of Bayesian networks from a dataset of sample cases. It does not have a graphical user interface of its own, but profits from the visualization capabilities of Matlab. The Bayes Net Toolbox is distributed under the Gnu Library General Public License and is available for all systems that can run Matlab, an installation of which is required.
back to the top
Belief Network Power Constructor
Jie Cheng
Dept. of Computing Science, University of Alberta
155 Athabasca Hall, Edmonton, Alberta, Canada T6G 2E1
http://www.cs.ualberta.ca/~jcheng/bnpc.htm
The Bayesian Network Power Constructor uses a three phase algorithm that is based on conditional independence tests to learn the structure of a Bayesian network from data. The conditional independence tests rely on mutual information, which is used to determine whether a (set of) node(s) can reduce or even block the information flow from one node to another. The program comes with a graphical user interface, though a much less advanced one than those of, for instance, HUGIN and Netica (see below). It does not support drawing inferences, but has the advantage that it is free software. It is available only for Windows.
back to the top
GeNIe / SMILE
Decision Systems Laboratory, University of Pittsburgh
B212 SLIS Building, 135 North Bellefield Avenue, Pittsburgh, PA 15260, USA
http://www2.sis.pitt.edu/~genie/
SMILE (Structural Modeling, Inference and Learning Engine) is a library of functions for building Bayesian networks and drawing inferences with them. It does support neither parameter nor structural learning of Bayesian networks. GeNIe (Graphical Network Interface) is a graphical user interface for SMILE, that makes the functions of SMILE easily accessible. While SMILE is platform independent, GeNIe is available only for Windows, since it relies heavily on the Microsoft Foundation classes. Both packages are distributed free of charge.
back to the top
Hugin
Hugin Expert A/S
Niels Jernes Vej 10, 9220 Aalborg, Denmark
http://www.hugin.com
Hugin is one of the oldest and best-known tools for Bayesian network construction and inference. It comes with an easy to use graphical user interface, but also has an API (application programmers interface) for several programming languages, so that the inference engine can be used in other programs. It supports estimating the parameters of a Bayesian network from a dataset of sample cases. In a recent version it has also been extended by a learning algorithm for the structure of a Bayesian network, which is based on conditional independence tests. Hugin is a commercial tool, but a demo version with restricted capabilities may be retrieved free of charge. Hugin is available for Windows and Solaris (Sun Unix).
back to the top
Netica
Norsys Software Corp.
2315 Dunbar Street, Vancouver, BC, Canada V6R 3N1
http://www.norsys.com
Like Hugin, Netica is a commercial tool with an advanced graphical user interface. It supports Bayesian network construction and inference and also comprises an API (application programmers interface) for C++, so that the inference engine may be used in other programs. Netica offers quantitative network learning (known structure, parameter estimation) from a dataset of sample cases, which may contain missing values. It does not support structural learning. A version of Netica with restricted capabilities may be retrieved free of charge, but the price of a full version is also moderate. Netica is available for Windows and Macintosh.
back to the top
Pulcinella
IRIDA, Université Libre de Bruxelles
50, Av. F. Roosevelt, CP 194/6, B-1050 Brussels, Belgium
http://iridia.ulb.ac.be/pulcinella/Welcome.html
Pulcinella is more general than the other programs listed on this page, as it is based on the framework of valuation systems [Shenoy 1992a]. Pulcinella supports reasoning by propagating uncertainty with local computations w.r.t. different uncertainty calculi, but does not support learning graphical models from a dataset of sample cases in any way. The current version of Pulcinella does not have a graphical user interface, but an outdated version of such an interface may be retrieved for Solaris (Sun Unix). Pulcinella is available for Solaris (Sun Unix) and Macintosh, but requires a Common Lisp system.
back to the top
Tetrad
Tetrad Project, Department of Philosophy
Carnegie Mellon University, Pittsburgh, PA, USA
http://hss.cmu.edu/html/departments/philosophy/TETRAD/tetrad.htm
Tetrad is based on the algorithms developed in [Spirtes et al 1993], i.e. on conditional independence test approaches to learn Bayesian networks from data, and, of course, subsequent research in this direction. It can learn the structure as well as the parameters of a Bayesian network from a dataset of sample cases, but does not support drawing inferences. Currently the program is being ported to Java (Tetrad IV). Older versions are available for MSDOS (Tetrad II) and Windows (Tetrad III). Tetrad II is commercial, but available at a moderate fee. Free beta versions are available of Tetrad III and Tetrad IV.
back to the top
WinMine / MSBN
Machine Learning and Statistics Group
Microsoft Research, One Microsoft Way, Redmond, WA 98052-6399, USA
http://research.microsoft.com/~dmax/WinMine/tooldoc.htm
WinMine is a toolkit, i.e. a set of programs for different tasks, rather than an integrated program. Most programs in this toolkit are command line driven, but there is a graphical user interface for the data converter and a network visualization program. WinMine learns the structure and the parameters of Bayesian networks from data and uses decision trees to represent the conditional distributions. It does not support drawing inferences. However, Microsoft Research also offers MSBN (Microsoft Bayesian Networks), a tool for (manually) building Bayesian networks and drawing inferences with them, MSBN comes with a graphical user interface. Both programs, WinMine as well as MSBN, are available for Windows only.
back to the top
© 2002 Christian Borgelt
Last modified: Fri Oct 25 11:05:52 MEST 2002
Wednesday, January 27, 2010
Robert Burns 罗伯特·彭斯
Robert Burns 罗伯特·彭斯
Robert Burns
Born in Alloway, Scotland, on January 25, 1759, Robert Burns was the first of William and Agnes Burnes' seven children. His father, a tenant farmer, educated his children at home. Burns also attended one year of mathematics schooling and, between 1765 and 1768, he attended an "adventure" school established by his father and John Murdock. His father died in bankruptcy in 1784, and Burns and his brother Gilbert took over farm. This hard labor later contributed to the heart trouble that Burns' suffered as an adult.
At the age of fifteen, he fell in love and shortly thereafter he wrote his first poem. As a young man, Burns pursued both love and poetry with uncommon zeal. In 1785, he fathered the first of his fourteen children. His biographer, DeLancey Ferguson, had said, "it was not so much that he was conspicuously sinful as that he sinned conspicuously." Between 1784 and 1785, Burns also wrote many of the poems collected in his first book, Poems, Chiefly in the Scottish Dialect, which was printed in 1786 and paid for by subscriptions. This collection was an immediate success and Burns was celebrated throughout England and Scotland as a great "peasant-poet."
In 1788, he and his wife, Jean Armour, settled in Ellisland, where Burns was given a commission as an excise officer. He also began to assist James Johnson in collecting folk songs for an anthology entitled The Scots Musical Museum. Burns' spent the final twelve years of his life editing and imitating traditional folk songs for this volume and for Select Collection of Original Scottish Airs. These volumes were essential in preserving parts of Scotland's cultural heritage and include such well-known songs as "My Luve is Like a Red Red Rose" and "Auld Land Syne." Robert Burns died from heart disease at the age of thirty-seven. On the day of his death, Jean Armour gave birth to his last son, Maxwell.
Most of Burns' poems were written in Scots. They document and celebrate traditional Scottish culture, expressions of farm life, and class and religious distinctions. Burns wrote in a variety of forms: epistles to friends, ballads, and songs. His best-known poem is the mock-heroic Tam o' Shanter. He is also well known for the over three hundred songs he wrote which celebrate love, friendship, work, and drink with often hilarious and tender sympathy. Even today, he is often referred to as the National Bard of Scotland.
外部链接：彭斯官方网：http://www.robertburns.org/
英国诗人 。1759年1月25日生于苏格兰艾尔郡阿洛韦镇的一个佃农家庭，1796年7月21日卒于邓弗里斯。自幼家境贫寒，未受过正规教育，靠自学获得多方面的知识。最优秀的诗歌作品产生于1785～1790年 ，收集在诗集《主要以苏格兰方言而写的诗》中。诗集体现了诗人一反当时英国诗坛的新古典主义诗风，从地方生活和民间文学中汲取营养，为诗歌创作带来了新鲜的活力，形成了他诗歌创作的基本特色。以虔诚的感情歌颂大自然及乡村生活；以入木三分的犀利言辞讽刺教会及日常生活中人们的虚伪。诗集使彭斯一举成名，被称为天才的农夫。后应邀到爱丁堡，出入于上流社会的显贵中间。但发现自己高傲的天性和激进思想与上流社会格格不入，乃返回故乡务农。一度到苏格兰北部高原地区游历，后来当了税务官，一边任职一边创作。
彭斯的诗歌作品多使用苏格兰方言，并多为抒情短诗，如歌颂爱情的名篇《我的爱人像朵红红的玫瑰》和抒发爱国热情的《苏格兰人》等。他还创作了不少讽刺诗（如《威利长老的祈祷》），诗札（如《致拉布雷克书》）和叙事诗（如《两只狗》和《快活的乞丐》）。作品表达了平民阶级的思想感情，同情下层人民疾苦，同时以健康、自然的方式体现了追求“美酒、女人和歌”的快乐主义人生哲学。彭斯富有敏锐的幽默感。对苏格兰乡村生活的生动描写使他的诗歌作品具有民族特色和艺术魅力。
除诗歌创作外，彭斯还收集整理大量的苏格兰民间歌谣，编辑出版了6卷本的《苏格兰音乐总汇》和8卷本的《原始的苏格兰歌曲选集》。其中《友谊地久天长》不仅享誉苏格兰，而且闻名世界。
在地球的各个角落，在亲朋的离别或是会议的告别仪式，人们以各种不同语言齐唱《友谊地久天长》(Auld Lang Syne，又名《骊歌》)，朋友们紧紧挽着手，歌唱永不相忘的友谊。它驱走了人们离别的哀愁，使人们满怀激情各奔前程。这首家喻户晓的苏格兰民歌的词作者，即是著名的民族诗人罗伯特·彭斯(Robert Burns，1759－1796)。
彭斯出生在一个贫苦农民家庭，以租地耕种为生。幼时在苏格兰家乡附近上小学。不久校长离去，父亲请老师来家教学。老师认为彭斯兄弟不比年长的同学差。父亲晚上教他们文法及神学。12岁时彭斯二兄弟又轮流去离家四英里的村落上学，14岁在学习英语之余，开始学习法文。
彭斯15岁时成为父亲身边主要的劳动力，驾驭马匹在土墩及洼地上耕作。劳动极为艰辛。虽数次更换土地租耕，因土地贫瘠，收获仍然不佳。劳动之余，彭斯爱读苏格兰诗人申斯通(Shenstone，1714-1793)、蒲柏（Pope，1688-1744）及弗格森（Fergusson 1750-1774）的作品，也浏览苏格兰小说家麦肯齐(MacKenzie，1745-1831)的书。他希望能成为苏格兰艾尔郡(Ayrshire)的诗人，歌唱故乡的山河。
1784年他的父亲去世，全家迁去莫斯吉尔（Mossgiel)，耕作收获并无好转。幸而他的主要用苏格兰方言写的诗集得以出版并迅即获得成功，爱丁堡的出版商又很快为之再版。编辑文学杂志的麦肯齐在评论中称赞这位庄稼汉是位诗歌天才。
于是在爱丁堡，彭斯穿起深色大衣、浅背心、皱边的衬衫，足登鹿皮鞋或长靴，过起出入文学集会及酒馆的双重生活。
彭斯在爱丁堡生活及游历苏格兰一段时期后，仍回乡务农。1788年他考取税务局职员，除了在农田干活外，还要每周在马背上驰骋200英里去上班。执法时，他不放过大鱼，但对贫穷者则手下留情。他为了全力做好税务局的工作，1791年放弃农活迁往邓弗里斯（Dumfries），在那儿度过了他的最后的岁月。
彭斯写了大量的抒情诗，还写讽刺诗及叙事诗。他也喜爱歌曲，有敏锐的音乐耳朵，对节奏有良好的反应。他把最后十年的精力，主要放在为二个丛刊的整理及收集民歌上，使濒临失传的三百多首民歌得以保存下来。
1796年他患了风湿性关节炎及心脏病，于同年7月21日英年早逝。前来送葬的多达二万人。
当年彭斯出生并度过了七年童年的茅屋，位于艾尔郡的阿洛韦镇(Alloway)，现由彭斯纪念碑信托基金机构管理。与茅屋相连接的红瓦顶、前面为长廊及花园的博物馆，为信托机构理事会于1920年所扩建。1994年该理事会重铺稻草屋顶，再建18世纪的菜园及石堤。这就是现在世界著名的彭斯茅舍。
彭斯雕像位于艾尔市中心。从市中心附近坐开往杜恩河老桥(Auld Brig O’Doon)的公共汽车，在终点老桥前一站下车，即见到茅草顶的白色平房，木制的门窗是深棕色的。门上方的黑色纪念板上写着“彭斯茅舍”，接着是“罗伯特·彭斯—艾尔郡诗人”及他的生卒年月。进门后先是谷仓，然后是牛棚及马厩。依稀传来牲畜的叫声，蜡制的耕牛旁还有几只母鸡在啄食谷粒。起居室中以蜡像布置一家人当时融洽的情景。父亲在烛光下读《圣经》，母亲抱着妹妹坐在对面，弟弟坐在一边，彭斯则光着脚站在一旁专心听讲。一个小妹妹躺在摇篮里。厨房里熏黑的炉灶还生着火，彭斯出生的床即在厨房内。布置一如当年。幼年时母亲在这里教孩子们唱苏格兰民歌，姨母则介绍给他们大量有关鬼怪神仙的故事和歌曲。“彭斯茅屋”对崇拜彭斯的人来说是圣地，但也是当年贫苦农家家居生活的写照。
彭斯长期生活在农村，从事繁重的农活。地主的剥削，加上土地的贫瘠，欠收、负债、迁居……使他常常过着没有温饱的生活。但他热爱生活，对劳动人民有深厚的感情。在《两只狗》这首诗里，通过两只分属贫富人家的狗之间的对话，描绘了地主家的骄奢淫逸。贫穷的佃户虽然耕作及劳动辛苦，但同欢共乐聚在一起。而这两家的狗能够融洽相处，成为人类不公平生活的鲜明对照。
诗人也理解农民对牲口的深厚感情。他在《新年早晨老农向老马麦琪致辞》一诗中，回顾了老马一生的辛劳后，写道：“我将在留下的麦地上面，把你的缰绳系好，不用费大力气，你就在那边舒舒畅畅吃个饱。”
与彭斯茅屋相通连的彭斯博物馆，收藏了彭斯珍贵的手稿、他的包括早期版本的作品、有关的画像等，有些收藏品来自美国、加拿大甚至南非。
大展览室介绍他一生的劳动、写作和生活。以图片的形式，配合他的诗句、信件或日记，生动地叙述了他当年的经历。这里还展出了他的怀表、记事本、墨水瓶、鼻烟壶，两把柄上刻有“R.B.”的手枪，以及当税务员测酒用的长棒，也展有1786年版的主要用苏格兰方言写的诗集。笔者自然记得寻找《友谊地久天长》的原稿，它原来出自彭斯于1788年写给友人的一封信中。
第二室展出数幅著名的油画。《羊杂宴》描绘彭斯夫妇款待客人的场景。彭斯喜欢这种热闹场面。另有一组四幅的版画，描绘他的作品《汤姆·奥桑特的故事》(Tam o’Shanter)，彭斯这部根据民间传说写的长诗，讲的是汤姆深夜回家途中遇鬼的故事。他去除了传说中迷信的成分，以喜剧形式讲魔法，寓有深意。同时，它也把儿时听到的传说，与故乡阿罗韦他幼时熟悉的界标、陈旧的教堂、古老的石桥和石冢等联系起来，具有沧桑感和神秘感。
离开这里步行一里，抵达老杜恩河桥，彭斯纪念碑即位于附近的山丘上。这座希腊式建筑由爱丁堡著名建筑师设计，1823年完成，耗资3247镑。登上这座台式纪念碑，可眺望杜恩河及卡里克山(Carrick Hill)的优美景色。纪念碑的基座建有展览室，展出15种外国文字的彭斯著作。在附近花园里，还建有一个雕像室，内有三座《汤姆·奥桑特的故事》中的人物雕像，真人大小，造型风趣。
归途中于老杜恩河老桥公共汽车站，见到一家大百货公司，里面的多种商品以彭斯命名。如果时间合适(回到艾尔的公共汽车每小时一班)，还可看一看介绍彭斯的记录影片。
在他住过的基尔马诺克（Kilmarnock）及邓弗里斯也建有彭斯博物馆、雕像或纪念碑，欧文（lrving）也有他的雕像。甚至远在加拿大和澳大利亚，也有他的纪念碑。位于苏格兰首府爱丁堡的“三作家博物馆”介绍了彭斯、司各特(Walter Scott，1771-1832)及斯蒂文森(Robert L.Stevenson， 1850-1894)的生平，也值得一去。
在彭斯的故乡苏格兰，有数千个彭斯联谊会，苏格兰各地每年都庆祝他的生日。
如此广受故乡人民爱戴的诗人，在世界上也不多见。因为除了长期生活在农村并写出描绘故乡及朴直人民的诗歌外，身受民族压迫的他十分热爱苏格兰，并热情歌颂民主及自由。
在彭斯的青年时代，先后爆发了美国独立战争和法国大革命。他关心世界政治及苏格兰祖国的命运。他写的《华盛顿将军生辰颂》，赞扬美国人民的独立斗争。在法国大革命的影响下，他写了《自由树》和《苏格兰人》两首著名长诗。《自由树》声言有了法兰西这棵自由树，人类将变得平等，世界将获得和平。《苏格兰人》重温历史，以颂扬早年民族英雄华莱士等人的事迹来激励人民：
谁愿为苏格兰国君和法律，
奋力把自由之剑拔出？
生为自由人，死为自由魂，
让他跟我前进！
彭斯是人民的诗人，也是为自由而斗争的战士。这颗明亮的星，永远闪耀在苏格兰的上空，也永远闪耀在爱好和平与友谊的人们心中。
【作品选译】
一朵红红的玫瑰 【英文朗诵：下载地址】
啊，我的爱人象朵红红的玫瑰，
六月里迎风初开，
啊，我的爱人象支甜甜的曲子，
奏得合拍又和谐。
我的好姑娘，多么美丽的人儿！
请看我，多么深挚的爱情！
亲爱的，我永远爱你，
纵使大海干涸水流尽。
纵使大海千涸水流尽，
太阳将岩石烧作灰尘，
亲爱的，我永远爱你，
只要我一息犹存。
珍重吧，我唯一的爱人，
珍重吧，让我们暂时别离，
但我定要回来，
哪怕千里万里！
王佐良译
往昔的时光
老朋友哪能遗忘，
哪能不放在心上？
老朋友哪能遗忘，
还有往昔的时光？
为了往昔的时光，老朋友，
为了往昔的时光，
再干一杯友情的酒，
为了往昔的时光，
你来痛饮一大杯，
我也买酒来相陪。
干一杯友情的酒又何妨？
为了往昔的时光。
我们曾邀游山岗，
到处将野花拜访。
但以后走上疲惫的旅程，
逝去了往昔的时光！
我们曾赤脚瞠过河流，
水声笑语里将时间忘。
如今大海的怒涛把我们隔开，
逝去了往昔的时光！
忠实的老友，伸出你的手，
让我们握手聚一堂，
再来痛饮—杯欢乐酒，
为了往昔的时光！
王佐良译
给我开门，哦！
曲调：轻轻地开门
哦，开门，纵使你对戬无情，
也表一点怜悯，哦。
你虽变了心，我仍忠于糟．
哦，给我开门，哦。
风吹我苍白的双颊，好冷！
但冷不过你对我的心，哦．
冰霜使我心血凝冻，
也没你给我的痛深，哦。
残月沉落白水中，
时间也随我沉落，哦。
假朋友，变心人，永别不再逢！
我决不再采烦渎，哦。
她把门儿大敞开，
见了平地上苍白的尸体，哦，
只喊了一声“爱’就倒在尘埃，
从此再也不起，哦。
王佐良译
走过麦田来
（合唱）啊，珍尼是可怜的人儿，
珍尼哭得悲哀。
她拖着长裙，
走过麦田来。
可怜的人儿，走过麦田来，
走过麦田来，
她拖着长裙
走过麦田来。
如果一个他碰见一个她，
走过麦田来，
如果一个他吻了一个她，
她何必哭起来？
如果一个他碰见一个她
走过山间小道，
如果一个他吻了一个她，
别人哪用知道！
（合唱）啊，珍尼是可怜的人儿，
珍尼哭得悲哀。
她拖着长裙，
走过麦田来。
王佐良译
如果你站在冷风里
呵，如果你站在冷风里，
一人在草地，在草地，
我的小屋会挡住凶恶的风，
保护你，保护你。
如果灾难象风暴袭来，
落在你头上，你头上，
我将用胸脯温暖你，
一切同享，一切同当。
如果我站在可怕的荒野，
天黑又把路迷，把路迷，
就是沙漠也变成天堂，
只要有你，只要有你。
如果我是地球的君王，
宝座我们共有，我们共有，
我的王冠上有一粒最亮的珍珠——
它是我的王后，我的王后。
王佐良译
选自《彭斯诗选》，人民文学出版社(1959)
苏格兰人①
跟华莱士流过血的苏格兰人，
随布鲁斯作过战的苏格兰人，
起来！倒在血泊里也成——
要不就夺取胜利！
时刻已到，决战已近，
前线的军情吃紧，
骄横的爱德华在统兵入侵——
带来锁链，带来奴役！
谁愿卖国求荣？
谁愿爬进懦夫的坟茔？
谁卑鄙到宁做奴隶偷生？——
让他走，让他逃避！
谁愿将苏格兰国王和法律保护，
拔出自由之剑来痛击、猛舞？
谁愿生作自由人，死作自由魂？——
让他来，跟我出击！
凭被压迫者的苦难采起誓，
凭你们受奴役的子孙来起誓，
我们决心流血到死——
但他们必须自由！
打倒骄横的篡位者！
死一个敌人，少一个暴君！
多一次攻击，添一分自由！
动手——要不就断头！
袁可嘉译
①这是彭斯所作爱国诗中最著名的一首，写的是苏格兰
国王罗伯特·布鲁斯在大破英国侵略军的班诺克本一役
(1314)之前向部队所作的号召。首先发表在1794年6月的
《纪事晨报》。
诗中所提的华莱士是一位十三世纪的英格兰民族英雄，
也曾大败英军。但后来为奸人出卖，被执处死。爱德华指
英王爱德华二世。
彭斯一直念念不忘为苏格兰民族独立而斗争的志士，
写此诗时爱国热情尤其澎湃。不仅如此，他还借古讽今，
曾经明白写信告诉朋友说：启发他写这首诗的不止是古代
那场“光荣的争取自由的斗争”，而还有“在时间上却不
是那么遥远的同类性质的斗争”，即法国大革命，当时正
方兴未艾，在苏格兰的彼岸如火如荼地展开。
我的心儿在高原①
我的心儿在高原，我的心不在这儿，
我的心儿在高原，迫遂着鹿儿。
追逐着野鹿，跟踪着獐儿；
我的心儿在高原，不管我上哪儿，
别了啊高原，别了啊北国，
英雄的家乡，可敬的故国，
不管我上哪儿漂荡，我上哪儿遨游，
我永远爱着高原的山丘。
别了啊，高耸的积雪的山岳，
别了啊，山下的溪壑和翠谷，
别了啊，森林和枝檀纵横的树林，
别了啊，急川和洪流的轰鸣，
我的心儿在高原，我的心不在这儿，
我的心儿在高原，追逐着鹿儿，
追逐着野鹿，跟踪着獐儿，
我的心儿在高原，不管我上哪儿。
袁可嘉译
①苏格兰北部地区。
Robert Burns
Born in Alloway, Scotland, on January 25, 1759, Robert Burns was the first of William and Agnes Burnes' seven children. His father, a tenant farmer, educated his children at home. Burns also attended one year of mathematics schooling and, between 1765 and 1768, he attended an "adventure" school established by his father and John Murdock. His father died in bankruptcy in 1784, and Burns and his brother Gilbert took over farm. This hard labor later contributed to the heart trouble that Burns' suffered as an adult.
At the age of fifteen, he fell in love and shortly thereafter he wrote his first poem. As a young man, Burns pursued both love and poetry with uncommon zeal. In 1785, he fathered the first of his fourteen children. His biographer, DeLancey Ferguson, had said, "it was not so much that he was conspicuously sinful as that he sinned conspicuously." Between 1784 and 1785, Burns also wrote many of the poems collected in his first book, Poems, Chiefly in the Scottish Dialect, which was printed in 1786 and paid for by subscriptions. This collection was an immediate success and Burns was celebrated throughout England and Scotland as a great "peasant-poet."
In 1788, he and his wife, Jean Armour, settled in Ellisland, where Burns was given a commission as an excise officer. He also began to assist James Johnson in collecting folk songs for an anthology entitled The Scots Musical Museum. Burns' spent the final twelve years of his life editing and imitating traditional folk songs for this volume and for Select Collection of Original Scottish Airs. These volumes were essential in preserving parts of Scotland's cultural heritage and include such well-known songs as "My Luve is Like a Red Red Rose" and "Auld Land Syne." Robert Burns died from heart disease at the age of thirty-seven. On the day of his death, Jean Armour gave birth to his last son, Maxwell.
Most of Burns' poems were written in Scots. They document and celebrate traditional Scottish culture, expressions of farm life, and class and religious distinctions. Burns wrote in a variety of forms: epistles to friends, ballads, and songs. His best-known poem is the mock-heroic Tam o' Shanter. He is also well known for the over three hundred songs he wrote which celebrate love, friendship, work, and drink with often hilarious and tender sympathy. Even today, he is often referred to as the National Bard of Scotland.
外部链接：彭斯官方网：http://www.robertburns.org/
英国诗人 。1759年1月25日生于苏格兰艾尔郡阿洛韦镇的一个佃农家庭，1796年7月21日卒于邓弗里斯。自幼家境贫寒，未受过正规教育，靠自学获得多方面的知识。最优秀的诗歌作品产生于1785～1790年 ，收集在诗集《主要以苏格兰方言而写的诗》中。诗集体现了诗人一反当时英国诗坛的新古典主义诗风，从地方生活和民间文学中汲取营养，为诗歌创作带来了新鲜的活力，形成了他诗歌创作的基本特色。以虔诚的感情歌颂大自然及乡村生活；以入木三分的犀利言辞讽刺教会及日常生活中人们的虚伪。诗集使彭斯一举成名，被称为天才的农夫。后应邀到爱丁堡，出入于上流社会的显贵中间。但发现自己高傲的天性和激进思想与上流社会格格不入，乃返回故乡务农。一度到苏格兰北部高原地区游历，后来当了税务官，一边任职一边创作。
彭斯的诗歌作品多使用苏格兰方言，并多为抒情短诗，如歌颂爱情的名篇《我的爱人像朵红红的玫瑰》和抒发爱国热情的《苏格兰人》等。他还创作了不少讽刺诗（如《威利长老的祈祷》），诗札（如《致拉布雷克书》）和叙事诗（如《两只狗》和《快活的乞丐》）。作品表达了平民阶级的思想感情，同情下层人民疾苦，同时以健康、自然的方式体现了追求“美酒、女人和歌”的快乐主义人生哲学。彭斯富有敏锐的幽默感。对苏格兰乡村生活的生动描写使他的诗歌作品具有民族特色和艺术魅力。
除诗歌创作外，彭斯还收集整理大量的苏格兰民间歌谣，编辑出版了6卷本的《苏格兰音乐总汇》和8卷本的《原始的苏格兰歌曲选集》。其中《友谊地久天长》不仅享誉苏格兰，而且闻名世界。
在地球的各个角落，在亲朋的离别或是会议的告别仪式，人们以各种不同语言齐唱《友谊地久天长》(Auld Lang Syne，又名《骊歌》)，朋友们紧紧挽着手，歌唱永不相忘的友谊。它驱走了人们离别的哀愁，使人们满怀激情各奔前程。这首家喻户晓的苏格兰民歌的词作者，即是著名的民族诗人罗伯特·彭斯(Robert Burns，1759－1796)。
彭斯出生在一个贫苦农民家庭，以租地耕种为生。幼时在苏格兰家乡附近上小学。不久校长离去，父亲请老师来家教学。老师认为彭斯兄弟不比年长的同学差。父亲晚上教他们文法及神学。12岁时彭斯二兄弟又轮流去离家四英里的村落上学，14岁在学习英语之余，开始学习法文。
彭斯15岁时成为父亲身边主要的劳动力，驾驭马匹在土墩及洼地上耕作。劳动极为艰辛。虽数次更换土地租耕，因土地贫瘠，收获仍然不佳。劳动之余，彭斯爱读苏格兰诗人申斯通(Shenstone，1714-1793)、蒲柏（Pope，1688-1744）及弗格森（Fergusson 1750-1774）的作品，也浏览苏格兰小说家麦肯齐(MacKenzie，1745-1831)的书。他希望能成为苏格兰艾尔郡(Ayrshire)的诗人，歌唱故乡的山河。
1784年他的父亲去世，全家迁去莫斯吉尔（Mossgiel)，耕作收获并无好转。幸而他的主要用苏格兰方言写的诗集得以出版并迅即获得成功，爱丁堡的出版商又很快为之再版。编辑文学杂志的麦肯齐在评论中称赞这位庄稼汉是位诗歌天才。
于是在爱丁堡，彭斯穿起深色大衣、浅背心、皱边的衬衫，足登鹿皮鞋或长靴，过起出入文学集会及酒馆的双重生活。
彭斯在爱丁堡生活及游历苏格兰一段时期后，仍回乡务农。1788年他考取税务局职员，除了在农田干活外，还要每周在马背上驰骋200英里去上班。执法时，他不放过大鱼，但对贫穷者则手下留情。他为了全力做好税务局的工作，1791年放弃农活迁往邓弗里斯（Dumfries），在那儿度过了他的最后的岁月。
彭斯写了大量的抒情诗，还写讽刺诗及叙事诗。他也喜爱歌曲，有敏锐的音乐耳朵，对节奏有良好的反应。他把最后十年的精力，主要放在为二个丛刊的整理及收集民歌上，使濒临失传的三百多首民歌得以保存下来。
1796年他患了风湿性关节炎及心脏病，于同年7月21日英年早逝。前来送葬的多达二万人。
当年彭斯出生并度过了七年童年的茅屋，位于艾尔郡的阿洛韦镇(Alloway)，现由彭斯纪念碑信托基金机构管理。与茅屋相连接的红瓦顶、前面为长廊及花园的博物馆，为信托机构理事会于1920年所扩建。1994年该理事会重铺稻草屋顶，再建18世纪的菜园及石堤。这就是现在世界著名的彭斯茅舍。
彭斯雕像位于艾尔市中心。从市中心附近坐开往杜恩河老桥(Auld Brig O’Doon)的公共汽车，在终点老桥前一站下车，即见到茅草顶的白色平房，木制的门窗是深棕色的。门上方的黑色纪念板上写着“彭斯茅舍”，接着是“罗伯特·彭斯—艾尔郡诗人”及他的生卒年月。进门后先是谷仓，然后是牛棚及马厩。依稀传来牲畜的叫声，蜡制的耕牛旁还有几只母鸡在啄食谷粒。起居室中以蜡像布置一家人当时融洽的情景。父亲在烛光下读《圣经》，母亲抱着妹妹坐在对面，弟弟坐在一边，彭斯则光着脚站在一旁专心听讲。一个小妹妹躺在摇篮里。厨房里熏黑的炉灶还生着火，彭斯出生的床即在厨房内。布置一如当年。幼年时母亲在这里教孩子们唱苏格兰民歌，姨母则介绍给他们大量有关鬼怪神仙的故事和歌曲。“彭斯茅屋”对崇拜彭斯的人来说是圣地，但也是当年贫苦农家家居生活的写照。
彭斯长期生活在农村，从事繁重的农活。地主的剥削，加上土地的贫瘠，欠收、负债、迁居……使他常常过着没有温饱的生活。但他热爱生活，对劳动人民有深厚的感情。在《两只狗》这首诗里，通过两只分属贫富人家的狗之间的对话，描绘了地主家的骄奢淫逸。贫穷的佃户虽然耕作及劳动辛苦，但同欢共乐聚在一起。而这两家的狗能够融洽相处，成为人类不公平生活的鲜明对照。
诗人也理解农民对牲口的深厚感情。他在《新年早晨老农向老马麦琪致辞》一诗中，回顾了老马一生的辛劳后，写道：“我将在留下的麦地上面，把你的缰绳系好，不用费大力气，你就在那边舒舒畅畅吃个饱。”
与彭斯茅屋相通连的彭斯博物馆，收藏了彭斯珍贵的手稿、他的包括早期版本的作品、有关的画像等，有些收藏品来自美国、加拿大甚至南非。
大展览室介绍他一生的劳动、写作和生活。以图片的形式，配合他的诗句、信件或日记，生动地叙述了他当年的经历。这里还展出了他的怀表、记事本、墨水瓶、鼻烟壶，两把柄上刻有“R.B.”的手枪，以及当税务员测酒用的长棒，也展有1786年版的主要用苏格兰方言写的诗集。笔者自然记得寻找《友谊地久天长》的原稿，它原来出自彭斯于1788年写给友人的一封信中。
第二室展出数幅著名的油画。《羊杂宴》描绘彭斯夫妇款待客人的场景。彭斯喜欢这种热闹场面。另有一组四幅的版画，描绘他的作品《汤姆·奥桑特的故事》(Tam o’Shanter)，彭斯这部根据民间传说写的长诗，讲的是汤姆深夜回家途中遇鬼的故事。他去除了传说中迷信的成分，以喜剧形式讲魔法，寓有深意。同时，它也把儿时听到的传说，与故乡阿罗韦他幼时熟悉的界标、陈旧的教堂、古老的石桥和石冢等联系起来，具有沧桑感和神秘感。
离开这里步行一里，抵达老杜恩河桥，彭斯纪念碑即位于附近的山丘上。这座希腊式建筑由爱丁堡著名建筑师设计，1823年完成，耗资3247镑。登上这座台式纪念碑，可眺望杜恩河及卡里克山(Carrick Hill)的优美景色。纪念碑的基座建有展览室，展出15种外国文字的彭斯著作。在附近花园里，还建有一个雕像室，内有三座《汤姆·奥桑特的故事》中的人物雕像，真人大小，造型风趣。
归途中于老杜恩河老桥公共汽车站，见到一家大百货公司，里面的多种商品以彭斯命名。如果时间合适(回到艾尔的公共汽车每小时一班)，还可看一看介绍彭斯的记录影片。
在他住过的基尔马诺克（Kilmarnock）及邓弗里斯也建有彭斯博物馆、雕像或纪念碑，欧文（lrving）也有他的雕像。甚至远在加拿大和澳大利亚，也有他的纪念碑。位于苏格兰首府爱丁堡的“三作家博物馆”介绍了彭斯、司各特(Walter Scott，1771-1832)及斯蒂文森(Robert L.Stevenson， 1850-1894)的生平，也值得一去。
在彭斯的故乡苏格兰，有数千个彭斯联谊会，苏格兰各地每年都庆祝他的生日。
如此广受故乡人民爱戴的诗人，在世界上也不多见。因为除了长期生活在农村并写出描绘故乡及朴直人民的诗歌外，身受民族压迫的他十分热爱苏格兰，并热情歌颂民主及自由。
在彭斯的青年时代，先后爆发了美国独立战争和法国大革命。他关心世界政治及苏格兰祖国的命运。他写的《华盛顿将军生辰颂》，赞扬美国人民的独立斗争。在法国大革命的影响下，他写了《自由树》和《苏格兰人》两首著名长诗。《自由树》声言有了法兰西这棵自由树，人类将变得平等，世界将获得和平。《苏格兰人》重温历史，以颂扬早年民族英雄华莱士等人的事迹来激励人民：
谁愿为苏格兰国君和法律，
奋力把自由之剑拔出？
生为自由人，死为自由魂，
让他跟我前进！
彭斯是人民的诗人，也是为自由而斗争的战士。这颗明亮的星，永远闪耀在苏格兰的上空，也永远闪耀在爱好和平与友谊的人们心中。
【作品选译】
一朵红红的玫瑰 【英文朗诵：下载地址】
啊，我的爱人象朵红红的玫瑰，
六月里迎风初开，
啊，我的爱人象支甜甜的曲子，
奏得合拍又和谐。
我的好姑娘，多么美丽的人儿！
请看我，多么深挚的爱情！
亲爱的，我永远爱你，
纵使大海干涸水流尽。
纵使大海千涸水流尽，
太阳将岩石烧作灰尘，
亲爱的，我永远爱你，
只要我一息犹存。
珍重吧，我唯一的爱人，
珍重吧，让我们暂时别离，
但我定要回来，
哪怕千里万里！
王佐良译
往昔的时光
老朋友哪能遗忘，
哪能不放在心上？
老朋友哪能遗忘，
还有往昔的时光？
为了往昔的时光，老朋友，
为了往昔的时光，
再干一杯友情的酒，
为了往昔的时光，
你来痛饮一大杯，
我也买酒来相陪。
干一杯友情的酒又何妨？
为了往昔的时光。
我们曾邀游山岗，
到处将野花拜访。
但以后走上疲惫的旅程，
逝去了往昔的时光！
我们曾赤脚瞠过河流，
水声笑语里将时间忘。
如今大海的怒涛把我们隔开，
逝去了往昔的时光！
忠实的老友，伸出你的手，
让我们握手聚一堂，
再来痛饮—杯欢乐酒，
为了往昔的时光！
王佐良译
给我开门，哦！
曲调：轻轻地开门
哦，开门，纵使你对戬无情，
也表一点怜悯，哦。
你虽变了心，我仍忠于糟．
哦，给我开门，哦。
风吹我苍白的双颊，好冷！
但冷不过你对我的心，哦．
冰霜使我心血凝冻，
也没你给我的痛深，哦。
残月沉落白水中，
时间也随我沉落，哦。
假朋友，变心人，永别不再逢！
我决不再采烦渎，哦。
她把门儿大敞开，
见了平地上苍白的尸体，哦，
只喊了一声“爱’就倒在尘埃，
从此再也不起，哦。
王佐良译
走过麦田来
（合唱）啊，珍尼是可怜的人儿，
珍尼哭得悲哀。
她拖着长裙，
走过麦田来。
可怜的人儿，走过麦田来，
走过麦田来，
她拖着长裙
走过麦田来。
如果一个他碰见一个她，
走过麦田来，
如果一个他吻了一个她，
她何必哭起来？
如果一个他碰见一个她
走过山间小道，
如果一个他吻了一个她，
别人哪用知道！
（合唱）啊，珍尼是可怜的人儿，
珍尼哭得悲哀。
她拖着长裙，
走过麦田来。
王佐良译
如果你站在冷风里
呵，如果你站在冷风里，
一人在草地，在草地，
我的小屋会挡住凶恶的风，
保护你，保护你。
如果灾难象风暴袭来，
落在你头上，你头上，
我将用胸脯温暖你，
一切同享，一切同当。
如果我站在可怕的荒野，
天黑又把路迷，把路迷，
就是沙漠也变成天堂，
只要有你，只要有你。
如果我是地球的君王，
宝座我们共有，我们共有，
我的王冠上有一粒最亮的珍珠——
它是我的王后，我的王后。
王佐良译
选自《彭斯诗选》，人民文学出版社(1959)
苏格兰人①
跟华莱士流过血的苏格兰人，
随布鲁斯作过战的苏格兰人，
起来！倒在血泊里也成——
要不就夺取胜利！
时刻已到，决战已近，
前线的军情吃紧，
骄横的爱德华在统兵入侵——
带来锁链，带来奴役！
谁愿卖国求荣？
谁愿爬进懦夫的坟茔？
谁卑鄙到宁做奴隶偷生？——
让他走，让他逃避！
谁愿将苏格兰国王和法律保护，
拔出自由之剑来痛击、猛舞？
谁愿生作自由人，死作自由魂？——
让他来，跟我出击！
凭被压迫者的苦难采起誓，
凭你们受奴役的子孙来起誓，
我们决心流血到死——
但他们必须自由！
打倒骄横的篡位者！
死一个敌人，少一个暴君！
多一次攻击，添一分自由！
动手——要不就断头！
袁可嘉译
①这是彭斯所作爱国诗中最著名的一首，写的是苏格兰
国王罗伯特·布鲁斯在大破英国侵略军的班诺克本一役
(1314)之前向部队所作的号召。首先发表在1794年6月的
《纪事晨报》。
诗中所提的华莱士是一位十三世纪的英格兰民族英雄，
也曾大败英军。但后来为奸人出卖，被执处死。爱德华指
英王爱德华二世。
彭斯一直念念不忘为苏格兰民族独立而斗争的志士，
写此诗时爱国热情尤其澎湃。不仅如此，他还借古讽今，
曾经明白写信告诉朋友说：启发他写这首诗的不止是古代
那场“光荣的争取自由的斗争”，而还有“在时间上却不
是那么遥远的同类性质的斗争”，即法国大革命，当时正
方兴未艾，在苏格兰的彼岸如火如荼地展开。
我的心儿在高原①
我的心儿在高原，我的心不在这儿，
我的心儿在高原，迫遂着鹿儿。
追逐着野鹿，跟踪着獐儿；
我的心儿在高原，不管我上哪儿，
别了啊高原，别了啊北国，
英雄的家乡，可敬的故国，
不管我上哪儿漂荡，我上哪儿遨游，
我永远爱着高原的山丘。
别了啊，高耸的积雪的山岳，
别了啊，山下的溪壑和翠谷，
别了啊，森林和枝檀纵横的树林，
别了啊，急川和洪流的轰鸣，
我的心儿在高原，我的心不在这儿，
我的心儿在高原，追逐着鹿儿，
追逐着野鹿，跟踪着獐儿，
我的心儿在高原，不管我上哪儿。
袁可嘉译
①苏格兰北部地区。
Tuesday, January 19, 2010
Bonferroni correction in SPSS
ANOVA with SPSS
Never, ever, run any statistical test without performing EDA first!
What's wrong with t-tests?
Nothing, except ...
If you want to compare three or more groups using t-tests with the usual 0.05 level of significance, you would have to compare the three groups pairwise (A to B, A to C, B to C), so the chance of getting the wrong result would be:
1 - (0.95 x 0.95 x 0.95) = 14.3%
If you wanted to compare four or more groups, the chance of getting the wrong result would be (0.95)6 = 26%, and for five groups, 40%. Not good, is it? So we use ANOVA. Never perform multiple t-tests: Anyone on this module discovered performing multiple t-tests when they should use ANOVA will be shot!
ANalysis Of VAriance (ANOVA) is such an important statistical method that it would be easy to spend a whole module on this test alone. Like the t-test, ANOVA is a parametric test which assumes:
•data is numerical data representing samples from normally distributed populations
•the variances of the groups are "similar"
•the sizes of the groups are "similar"
•the groups should be independent
so it's important to carry out EDA before starting AVOVA! In fact, ANOVA is quite a robust procedure, so as long as the groups are similar, the test is normally reliable.
ANOVA tests the null hypothesis that the means of all the groups being compared are equal, and produces a statistic called F which is equivalent to the t-statistic from a t-test. But there's a catch. If the means of all the groups tested by ANOVA are equal, fine. But if the result tells us to reject the null hypothesis, we still don't know which of the means differ. We solve this problem by performing what is known as a "post hoc" (after the event) test.
Reminder:
•Independent variable: Variables which are experimentally manipulated by an investigator are called independent variables.
•Dependent variable: Variables which are measured are called dependent variables (because they are presumed to depend on the value of the independent variable).
ANOVA jargon:
•Way = an independent variable, so a one-way ANOVA has one independent variable, two-way ANOVA has two independent variables, etc. Simple ANOVA tests the hypothesis that means from two or more samples are equal (drawn from populations with the same mean). Student's t-test is actually a particular application of one-way ANOVA (two groups compared).
•Factor = a test or measurement. Single-factor ANOVA tests whether the means of the groups being compared are equal and returns a yes/no answer, two-factor ANOVA simultaneously tests two or more factors, e.g. tumour size after treatment with different drugs and/or radiotherapy (drug treatment is one factor and radiotherapy is another). So, "factor" and "way" are alternative terms for the same thing (inpependent variables).
•Repeated measures: Used when members of a sample are measured under different conditions. As the sample is exposed to each condition, the measurement of the dependent variable is repeated. Using standard ANOVA is not appropriate because it fails to take into account correlation between the repeated measures, violating the assumption of independence. This approach can be used for several reasons, e.g. where research requires repeated measures, such as longitudinal research which measures each sample member at each of several ages - age is a repeated factor. This is comparable to a paired t-test.
The array of options for different ANOVA tests in SPSS is confusing, so I'll go through the most important bits using some examples.
One-Way / Single-Factor ANOVA:
Data:
Pain Scores for Analgesics
Drug: Pain Score:
Diclofenac 0, 35, 31, 29, 20, 7, 43, 16
Ibuprophen 30, 40, 27, 25, 39, 15, 30, 45
Paracetamol 16, 33, 25, 32, 21, 54, 57, 19
Asprin 55, 58, 56, 57, 56, 53, 59, 55
Since it would be unethical to withhold pain relief, there is no control group and we are just interested in knowing whether one drug performs better (lower pain score) than another, so we need to perform a one-way/single-factor ANOVA.
We enter this data into SPSS using dummy values (1, 2, 3, 4) for the drugs so this numeric data can be used in the ANOVA:
It's always a good idea to enter descriptive labels for data into the Variable View window, or the output is difficult to interpret!
EDA (Analyzer: Descriptive Statistics: Explore) shows that the data is normally distributed, so we can proceed with the ANOVA:
Analyze: Compare Means: One-Way ANOVA
Dependent variable: Pain Score
Factor: Drug:
•SPSS allows many different post hoc tests. Click Post Hoc and select the Tukey and Games-Howell tests.
◦The Tukey test is powerful and widely accepted, but is parametric in that it assumes that the population variances are equal. It also assumes that the sample sizes are equal. If this is not the case, you should use Gabriel's procedure, or if the sizes are very different, use Hochberg's GT2.
◦Games-Howell does not assume population variances are equal or that sample sizes are equal, so is a good alternative if this turns out to be the case.
•Click Options and select Homogeneity of Variance Test, Brown-Forsythe and Welch. The homogeneity of variance test is important since this is an assumption of ANOVA, but if this assumption turns out to be broken, the Brown-Forsythe and Welch options will display alternative versions of the F statistic which means you may still be able to use the result.
•Click OK to run the tests.
Output:
Test of Homogeneity of Variances: Pain Levene Statistic df1 df2 Sig.
4.837 3 28 .008
The significance value for homogeneity of variances is <.05, so the variances of the groups are significantly different. Since this is an assumption of ANOVA, we need to be very careful in interpreting the outcome of this test:
ANOVA: Pain
Sum of Squares df Mean Square F Sig.
Between Groups 4956.375 3 1652.125 11.967 .000
Within Groups 3865.500 28 138.054
Total 8821.875 31
This is the main ANOVA result. The significance value comparing the groups (drugs) is <.05, so we could reject the null hypothesis (there is no difference in the mean pain scores with the four drugs). However, since the variances are significantly different, this might be the wrong answer. Fortunately, the Welch and Brown-Forsythe statistics can still be used in these circumstances:
Robust Tests of Equality of Means: Pain
Statistic df1 df2 Sig.
Welch 32.064 3 12.171 .000
Brown-Forsythe 11.967 3 18.889 .000
The significance value of these are both <.05, so we still reject the null hypothesis. However, this result does not tell us which drugs are responsible for the difference, so we need the post hoc test results:
Multiple Comparisons
Dependent Variable: Pain
(I) Drug (J) Drug Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
Tukey HSD 1 2 -8.750 5.875 .457 -24.79 7.29
3 -9.500 5.875 .386 -25.54 6.54
4 -33.500(*) 5.875 .000 -49.54 -17.46
2 1 8.750 5.875 .457 -7.29 24.79
3 -.750 5.875 .999 -16.79 15.29
4 -24.750(*) 5.875 .001 -40.79 -8.71
3 1 9.500 5.875 .386 -6.54 25.54
2 .750 5.875 .999 -15.29 16.79
4 -24.000(*) 5.875 .002 -40.04 -7.96
4 1 33.500(*) 5.875 .000 17.46 49.54
2 24.750(*) 5.875 .001 8.71 40.79
3 24.000(*) 5.875 .002 7.96 40.04
Games-Howell 1 2 -8.750 6.176 .513 -27.05 9.55
3 -9.500 7.548 .602 -31.45 12.45
4 -33.500(*) 5.194 .001 -50.55 -16.45
2 1 8.750 6.176 .513 -9.55 27.05
3 -.750 6.485 .999 -20.09 18.59
4 -24.750(*) 3.471 .001 -36.03 -13.47
3 1 9.500 7.548 .602 -12.45 31.45
2 .750 6.485 .999 -18.59 20.09
4 -24.000(*) 5.558 .014 -42.26 -5.74
4 1 33.500(*) 5.194 .001 16.45 50.55
2 24.750(*) 3.471 .001 13.47 36.03
3 24.000(*) 5.558 .014 5.74 42.26
* The mean difference is significant at the .05 level.
The Tukey test relies on homogeneity of variance, so we ignore these results. The Games-Howell post-hoc test does not rely on homogeneity of variance (this is why we used two different post-hoc tests) and so can be used. SPSS kindly flags (*) which differences are significant!
Result: Drug 4 (Asprin) produces significantly different result from the other three drugs:
Formal Reporting: When we report the outcome of an ANOVA, we cite the value of the F ratio and give the number of degrees of freedom, outcome (in a neutral fashion) and significance value. So in this case:
There is a significant difference between the pain scores for asprin and the other three drugs tested, F(3,28) = 11.97, p < .05.
Two-Factor ANOVA
Do anti-cancer drugs have different effects in males and females?
Data:
Drug: cisplatin vinblastine 5-fluorouracil
Gender:
Female Male Female Male Female Male
Tumour
Size: 65 50 70 45 55 35
70 55 65 60 65 40
60 80 60 85 70 35
60 65 70 65 55 55
60 70 65 70 55 35
55 75 60 70 60 40
60 75 60 80 50 45
50 65 50 60 50 40
We enter this data into SPSS using dummy values for the drugs (1, 2, 3) and genders (1,2) so the coded data can be used in the ANOVA:
It's always a good idea to enter descriptive labels for data into the Variable View window, or the output is difficult to interpret!
EDA (Analyze: Descriptive Statistics: Explore) shows that the data is normally distributed, so we can proceed with the ANOVA:
Analyze: General Linear Model: Univariate
Dependent variable: Tumour Diameter
Fixed Factors: Gender, Drug:
Also select:
Post Hoc: Tukey and Games-Howell:
Options:
Display Means for: Gender, Drug, Gender*Drug
Descriptive Statistics
Homogeneity tests:
Output:
Levene's Test of Equality of Error Variances(a)
Dependent Variable: Diameter F df1 df2 Sig.
1.462 5 42 .223
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a Design: Intercept+Gender+Drug+Gender * Drug
The significance result for homogeneity of variance is >.05, which shows that the error variance of the dependent variable is equal across the groups, i.e. the assumption of the ANOVA test has been met.
Tests of Between-Subjects Effects
Dependent Variable: Diameter Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 3817.188(a) 5 763.438 10.459 .000
Intercept 167442.188 1 167442.188 2294.009 .000
Gender 42.188 1 42.188 .578 .451
Drug 2412.500 2 1206.250 16.526 .000
Gender * Drug 1362.500 2 681.250 9.333 .000
Error 3065.625 42 72.991
Total 174325.000 48
Corrected Total 6882.813 47
a R Squared = .555 (Adjusted R Squared = .502)
The highlighted values are significant (<.05), but there is no effect of gender (p = 0.451). Again, this does not tell us which drugs behave differently, so again we need to look at the post hoc tests:
Multiple Comparisons
Dependent Variable: Diameter
(I) Drug (J) Drug Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
Tukey HSD cisplatin vinblastine -1.25 3.021 .910 -8.59 6.09
5-flourouracil 14.38(*) 3.021 .000 7.04 21.71
vinblastine cisplatin 1.25 3.021 .910 -6.09 8.59
5-flourouracil 15.63(*) 3.021 .000 8.29 22.96
5-flourouracil cisplatin -14.38(*) 3.021 .000 -21.71 -7.04
vinblastine -15.63(*) 3.021 .000 -22.96 -8.29
Games-Howell cisplatin vinblastine -1.25 3.329 .925 -9.46 6.96
5-flourouracil 14.38(*) 3.534 .001 5.64 23.11
vinblastine cisplatin 1.25 3.329 .925 -6.96 9.46
5-flourouracil 15.63(*) 3.699 .001 6.50 24.75
5-flourouracil cisplatin -14.38(*) 3.534 .001 -23.11 -5.64
vinblastine -15.63(*) 3.699 .001 -24.75 -6.50
Based on observed means.
* The mean difference is significant at the .05 level.
In this example, we can use the Tukey or Games-Howell results. Again, SPSS helpfully flags which results have reached statistical significance. We already know from the main ANOVA table that the effect of gender is not significant, but the post hoc tests show which drugs produce significantly different outcomes.
Formal Reporting: When we report the outcome of an ANOVA, we cite the value of the F ratio and give the number of degrees of freedom, outcome (in a neutral fashion) and significance value. So in this case:
There is a significant difference between the tumour diameter for 5-flourouracil and the other two drugs tested, F(5,47) = 10.46, p < .05.
Repeated Measures ANOVA
Remember that one of the assumptions of ANOVA is independence of the groups being compared. In lots of circumstances, we want to test the same thing repeatedly, e.g:
•Patients with a chronic disease after 3, 6 and 12 months of drug treatment
•Repeated sampling from the same location, e.g. spring, summer, autumn and winter
•etc
This type of study reduces variability in the data and so increases the power to detect effects, but violates the assumption of independence, so as with the paired t-test, we need to use a special form of ANOVA called repeated measures. In a parametric test, the assumption that the relationship between pairs of groups is equal is called "sphericity". Violating sphericity means that the F statistic cannot be compared to the normal tables of F, and so software cannot calculate a significance value. SPSS includes a procedure called Mauchly's test which tells us if the assumption of sphericity has been violated:
•If Mauchly’s test statistic is significant (i.e. p 0.05) we conclude that the condition of sphericity has not been met.
•If, Mauchly’s test statistic is nonsignificant (i.e. p >.05) it is reasonable to conclude that the variances of differences are not significantly different.
If Mauchly’s test is significant then we cannot trust the F-ratios produced by SPSS unless we apply a correction (which, fortunately, SPSS helps us to do).
One-Way Repeated Measures ANOVA
i.e. one independent variable, e.g. pain score after surgery:
Patient1 Patient2 Patient3
1 3 1
2 5 3
4 6 6
5 7 4
5 9 1
6 10 3
This data can be entered directly into SPSS. Note that each column represents a repeated measures variable (patients in this case). There is no need for a coding variable (as with between-group designs, above):
It's always a good idea to enter descriptive labels for data into the Variable View window, or the output is difficult to interpret! Next:
Analyze: General Linear Model: Repeated Measures
Within-Subject factor name: Patient
Number of Levels: 3 (because there are 3 patients)
Click Add, then Define (factors):
There are no proper post hoc tests for repeated measures variables in SPSS. However, via the Options button, you can use the paired t-test procedure to compare all pairs of levels of the independent variable, and then apply a Bonferroni correction to the probability at which you accept any of these tests. The resulting probability value should be used as the criterion for statistical significance. A ‘Bonferroni correction’ is achieved by dividing the probability value (usually 0.05) by the number of tests conducted, e.g. if we compare all levels of the independent variable of these data, we make three comparisons and so the appropriate significance level is 0.05/3 = 0.0167. Therefore, we accept t-tests as being significant only if they have a p value <0.0167.
Output:
Mauchly's Test of Sphericity Within Subjects Effect Mauchly's W Approx. Chi-Square df Sig. Epsilon
Greenhouse-Geisser Huynh-Feldt Lower-bound
patient .094 9.437 2 .009 .525 .544 .500
Mauchly’s test is significant (p <.05) so we conclude that the assumption of sphericity has not been met.
Tests of Within-Subjects Effects Source
Type III Sum of Squares df Mean Square F Sig.
patient Sphericity Assumed 44.333 2 22.167 8.210 .008
Greenhouse-Geisser 44.333 1.050 42.239 8.210 .033
Huynh-Feldt 44.333 1.088 40.752 8.210 .031
Lower-bound 44.333 1.000 44.333 8.210 .035
Error(patient) Sphericity Assumed 27.000 10 2.700
Greenhouse-Geisser 27.000 5.248 5.145
Huynh-Feldt 27.000 5.439 4.964
Lower-bound 27.000 5.000 5.400
Because the significance values are <.05, we conclude that there was a significant difference between the three patients, but this test does not tell us which patients differed from each other. The next issue is which of the three corrections to use. Going back to Mauchly's test:
•If epsilon is >0.75, use the Huynh-Feldt correction.
•If epsilon is <0.75, or nothing is known about sphericity at all, use the Greenhouse-Geisser correction.
•In this example, the epsilon values from Mauchly's test values are 0.525 and 0.544, both <0.75, so we use the Greenhouse-Geisser corrected values. Using this correction, F is still significant because its p value is 0.033, which is <.05.
Post Hoc Tests:
Pairwise Comparisons (I) patient (J) patient Mean Difference (I-J) Std. Error Sig.(a) 95% Confidence Interval for Difference(a)
Lower Bound Upper Bound
1 2 -2.833(*) .401 .003 -4.252 -1.415
3 .833 .946 1.000 -2.509 4.176
2 1 2.833(*) .401 .003 1.415 4.252
3 3.667 1.282 .106 -.865 8.199
3 1 -.833 .946 1.000 -4.176 2.509
2 -3.667 1.282 .106 -8.199 .865
Based on estimated marginal means
* The mean difference is significant at the .05 level.
a Adjustment for multiple comparisons: Bonferroni.
Formal reporting:
Mauchly’s test indicated that the assumption of sphericity had been violated (chi-square = 9.44, p <.05), therefore degrees of freedom were corrected using Greenhouse-Geisser estimates of sphericity (epsilon = 0.53). The results show that the pain scores of the three patients differed significantly, F(1.05, 5.25) = 8.21, p <.05. Post hoc tests revealed that although the pain score of Patient2 was significantly higher than that of than Patient1 (p<.001), Patient3's score was not significantly differently from either of the other patients (both p>.05).
Two-Way Repeated Measures ANOVA
i.e. two independent variables:
In a study of the best way to keep fields free of weeds for an entire growing season, a farmer treated test plots in 10 fields with either five different concentrations of weedkiller (independent variable 1) or five different length blasts with a flamethrower (independent variable 2). At the end of they growing season, the number of weeds per square metre were counted. To exclude bias (e.g. pre-existing seedbank in the soil), the following year, the farmer repeated the experiment but this time the treatments the fields received were reversed:
Treatment: Weedkiller Flamethrower
Severity: 1 2 3 4 5 1 2 3 4 5
Field1 10 15 18 22 37 9 13 13 18 22
Field2 10 18 10 42 60 7 14 20 21 32
Field3 7 11 28 31 56 9 13 24 30 35
Field4 9 19 36 45 60 7 14 9 20 25
Field5 15 14 29 33 37 14 13 20 22 29
Field6 14 13 26 26 49 5 12 17 16 33
Field7 9 12 19 37 48 5 15 12 17 24
Field8 9 18 22 31 39 13 13 14 17 17
Field9 12 14 24 28 53 12 13 21 19 22
Field10 7 11 21 23 45 12 14 20 21 29
SPSS Data View:
It's always a good idea to enter descriptive labels for data into the Variable View window, or the output is difficult to interpret:
Analyze: General Linear Model: Repeated Measures
Define Within Subject Factors (remember, "factor" = test or treatment):
Treatment, (2 treatments, weedkiller or flamethrower) (SPSS only allows 8 characters for the name)
Severity (5 different severities):
Click Define and define Within Subject Variables:
As above, there are no post hoc tests for repeated measures ANOVA in SPSS, but via the Options button, we can apply a Bonferroni correction to the probability at which you accept any of the tests:
Output:
Mauchly's Test of Sphericity(b)
Measure: MEASURE_1 Within Subjects Effect Mauchly's W Approx. Chi-Square df Sig. Epsilon
Greenhouse-Geisser Huynh-Feldt Lower-bound
treatmen 1.000 .000 0 . 1.000 1.000 1.000
severity .092 17.685 9 .043 .552 .740 .250
treatmen * severity .425 6.350 9 .712 .747 1.000 .250
The outcome of Mauchly’s test is significant (p <.05) for the severity of treatment, so we need to correct the F-values for this, but not for the treatments themselves.
Tests of Within-Subjects Effects Source
Type III Sum of Squares df Mean Square F Sig.
treatmen Sphericity Assumed 1730.560 1 1730.560 34.078 .000
Greenhouse-Geisser 1730.560 1.000 1730.560 34.078 .000
Huynh-Feldt 1730.560 1.000 1730.560 34.078 .000
Lower-bound 1730.560 1.000 1730.560 34.078 .000
Error(treatmen) Sphericity Assumed 457.040 9 50.782
Greenhouse-Geisser 457.040 9.000 50.782
Huynh-Feldt 457.040 9.000 50.782
Lower-bound 457.040 9.000 50.782
severity Sphericity Assumed 9517.960 4 2379.490 83.488 .000
Greenhouse-Geisser 9517.960 2.209 4309.021 83.488 .000
Huynh-Feldt 9517.960 2.958 3217.666 83.488 .000
Lower-bound 9517.960 1.000 9517.960 83.488 .000
Error(severity) Sphericity Assumed 1026.040 36 28.501
Greenhouse-Geisser 1026.040 19.880 51.613
Huynh-Feldt 1026.040 26.622 38.541
Lower-bound 1026.040 9.000 114.004
treatmen * severity Sphericity Assumed 1495.240 4 373.810 20.730 .000
Greenhouse-Geisser 1495.240 2.989 500.205 20.730 .000
Huynh-Feldt 1495.240 4.000 373.810 20.730 .000
Lower-bound 1495.240 1.000 1495.240 20.730 .001
Error(treatmen*severity) Sphericity Assumed 649.160 36 18.032
Greenhouse-Geisser 649.160 26.903 24.129
Huynh-Feldt 649.160 36.000 18.032
Lower-bound 649.160 9.000 72.129
Since there was no violation of sphericity, we can look at the comparison of the two treatments without any correction. The significance value shows (0.000) that there was a significant difference between the two treatments, but does not tell us which treatments produced this effect.
The output also tells us the effect of the severity of treatments, but remember there was a violation of sphericity here, so we must look at the corrected F-ratios. All of the corrected values are highly significant and so we can use the Greenhouse-Geisser corrected values as these are the most conservative.
Pairwise Comparisons (I) severity (J) severity Mean Difference (I-J) Std. Error Sig.(a) 95% Confidence Interval for Difference(a)
Lower Bound Upper Bound
1 2 -4.200(*) .895 .011 -7.502 -.898
3 -10.400(*) 1.190 .000 -14.790 -6.010
4 -16.200(*) 1.764 .000 -22.709 -9.691
5 -27.850(*) 2.398 .000 -36.698 -19.002
2 1 4.200(*) .895 .011 .898 7.502
3 -6.200(*) 1.521 .028 -11.810 -.590
4 -12.000(*) 1.280 .000 -16.723 -7.277
5 -23.650(*) 2.045 .000 -31.197 -16.103
3 1 10.400(*) 1.190 .000 6.010 14.790
2 6.200(*) 1.521 .028 .590 11.810
4 -5.800 1.690 .075 -12.036 .436
5 -17.450(*) 2.006 .000 -24.852 -10.048
4 1 16.200(*) 1.764 .000 9.691 22.709
2 12.000(*) 1.280 .000 7.277 16.723
3 5.800 1.690 .075 -.436 12.036
5 -11.650(*) 1.551 .000 -17.373 -5.927
5 1 27.850(*) 2.398 .000 19.002 36.698
2 23.650(*) 2.045 .000 16.103 31.197
3 17.450(*) 2.006 .000 10.048 24.852
4 11.650(*) 1.551 .000 5.927 17.373
* The mean difference is significant at the .05 level.
a Adjustment for multiple comparisons: Bonferroni.
This shows that there was only one pair for which there was no significant difference: 40% weedkiller followed by 2 minutes flame thrower, and 2 minutes flame thrower followed by 40% weedkiller. The differences for all the other pairs are significant. It does not matter if the farmer uses weedkiller or a flamethrower, but how much weedkiller and how long a burst of flame does make a difference to weed control.
Formal report:
There was a significant main effect of the type of treatment, F(1, 9) = 34.08, p < .001.
There was a significant main effect of the severity of treatment, F(2.21, 19.88) = 83.49, p <.001.
Never, ever, run any statistical test without performing EDA first!
What's wrong with t-tests?
Nothing, except ...
If you want to compare three or more groups using t-tests with the usual 0.05 level of significance, you would have to compare the three groups pairwise (A to B, A to C, B to C), so the chance of getting the wrong result would be:
1 - (0.95 x 0.95 x 0.95) = 14.3%
If you wanted to compare four or more groups, the chance of getting the wrong result would be (0.95)6 = 26%, and for five groups, 40%. Not good, is it? So we use ANOVA. Never perform multiple t-tests: Anyone on this module discovered performing multiple t-tests when they should use ANOVA will be shot!
ANalysis Of VAriance (ANOVA) is such an important statistical method that it would be easy to spend a whole module on this test alone. Like the t-test, ANOVA is a parametric test which assumes:
•data is numerical data representing samples from normally distributed populations
•the variances of the groups are "similar"
•the sizes of the groups are "similar"
•the groups should be independent
so it's important to carry out EDA before starting AVOVA! In fact, ANOVA is quite a robust procedure, so as long as the groups are similar, the test is normally reliable.
ANOVA tests the null hypothesis that the means of all the groups being compared are equal, and produces a statistic called F which is equivalent to the t-statistic from a t-test. But there's a catch. If the means of all the groups tested by ANOVA are equal, fine. But if the result tells us to reject the null hypothesis, we still don't know which of the means differ. We solve this problem by performing what is known as a "post hoc" (after the event) test.
Reminder:
•Independent variable: Variables which are experimentally manipulated by an investigator are called independent variables.
•Dependent variable: Variables which are measured are called dependent variables (because they are presumed to depend on the value of the independent variable).
ANOVA jargon:
•Way = an independent variable, so a one-way ANOVA has one independent variable, two-way ANOVA has two independent variables, etc. Simple ANOVA tests the hypothesis that means from two or more samples are equal (drawn from populations with the same mean). Student's t-test is actually a particular application of one-way ANOVA (two groups compared).
•Factor = a test or measurement. Single-factor ANOVA tests whether the means of the groups being compared are equal and returns a yes/no answer, two-factor ANOVA simultaneously tests two or more factors, e.g. tumour size after treatment with different drugs and/or radiotherapy (drug treatment is one factor and radiotherapy is another). So, "factor" and "way" are alternative terms for the same thing (inpependent variables).
•Repeated measures: Used when members of a sample are measured under different conditions. As the sample is exposed to each condition, the measurement of the dependent variable is repeated. Using standard ANOVA is not appropriate because it fails to take into account correlation between the repeated measures, violating the assumption of independence. This approach can be used for several reasons, e.g. where research requires repeated measures, such as longitudinal research which measures each sample member at each of several ages - age is a repeated factor. This is comparable to a paired t-test.
The array of options for different ANOVA tests in SPSS is confusing, so I'll go through the most important bits using some examples.
One-Way / Single-Factor ANOVA:
Data:
Pain Scores for Analgesics
Drug: Pain Score:
Diclofenac 0, 35, 31, 29, 20, 7, 43, 16
Ibuprophen 30, 40, 27, 25, 39, 15, 30, 45
Paracetamol 16, 33, 25, 32, 21, 54, 57, 19
Asprin 55, 58, 56, 57, 56, 53, 59, 55
Since it would be unethical to withhold pain relief, there is no control group and we are just interested in knowing whether one drug performs better (lower pain score) than another, so we need to perform a one-way/single-factor ANOVA.
We enter this data into SPSS using dummy values (1, 2, 3, 4) for the drugs so this numeric data can be used in the ANOVA:
It's always a good idea to enter descriptive labels for data into the Variable View window, or the output is difficult to interpret!
EDA (Analyzer: Descriptive Statistics: Explore) shows that the data is normally distributed, so we can proceed with the ANOVA:
Analyze: Compare Means: One-Way ANOVA
Dependent variable: Pain Score
Factor: Drug:
•SPSS allows many different post hoc tests. Click Post Hoc and select the Tukey and Games-Howell tests.
◦The Tukey test is powerful and widely accepted, but is parametric in that it assumes that the population variances are equal. It also assumes that the sample sizes are equal. If this is not the case, you should use Gabriel's procedure, or if the sizes are very different, use Hochberg's GT2.
◦Games-Howell does not assume population variances are equal or that sample sizes are equal, so is a good alternative if this turns out to be the case.
•Click Options and select Homogeneity of Variance Test, Brown-Forsythe and Welch. The homogeneity of variance test is important since this is an assumption of ANOVA, but if this assumption turns out to be broken, the Brown-Forsythe and Welch options will display alternative versions of the F statistic which means you may still be able to use the result.
•Click OK to run the tests.
Output:
Test of Homogeneity of Variances: Pain Levene Statistic df1 df2 Sig.
4.837 3 28 .008
The significance value for homogeneity of variances is <.05, so the variances of the groups are significantly different. Since this is an assumption of ANOVA, we need to be very careful in interpreting the outcome of this test:
ANOVA: Pain
Sum of Squares df Mean Square F Sig.
Between Groups 4956.375 3 1652.125 11.967 .000
Within Groups 3865.500 28 138.054
Total 8821.875 31
This is the main ANOVA result. The significance value comparing the groups (drugs) is <.05, so we could reject the null hypothesis (there is no difference in the mean pain scores with the four drugs). However, since the variances are significantly different, this might be the wrong answer. Fortunately, the Welch and Brown-Forsythe statistics can still be used in these circumstances:
Robust Tests of Equality of Means: Pain
Statistic df1 df2 Sig.
Welch 32.064 3 12.171 .000
Brown-Forsythe 11.967 3 18.889 .000
The significance value of these are both <.05, so we still reject the null hypothesis. However, this result does not tell us which drugs are responsible for the difference, so we need the post hoc test results:
Multiple Comparisons
Dependent Variable: Pain
(I) Drug (J) Drug Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
Tukey HSD 1 2 -8.750 5.875 .457 -24.79 7.29
3 -9.500 5.875 .386 -25.54 6.54
4 -33.500(*) 5.875 .000 -49.54 -17.46
2 1 8.750 5.875 .457 -7.29 24.79
3 -.750 5.875 .999 -16.79 15.29
4 -24.750(*) 5.875 .001 -40.79 -8.71
3 1 9.500 5.875 .386 -6.54 25.54
2 .750 5.875 .999 -15.29 16.79
4 -24.000(*) 5.875 .002 -40.04 -7.96
4 1 33.500(*) 5.875 .000 17.46 49.54
2 24.750(*) 5.875 .001 8.71 40.79
3 24.000(*) 5.875 .002 7.96 40.04
Games-Howell 1 2 -8.750 6.176 .513 -27.05 9.55
3 -9.500 7.548 .602 -31.45 12.45
4 -33.500(*) 5.194 .001 -50.55 -16.45
2 1 8.750 6.176 .513 -9.55 27.05
3 -.750 6.485 .999 -20.09 18.59
4 -24.750(*) 3.471 .001 -36.03 -13.47
3 1 9.500 7.548 .602 -12.45 31.45
2 .750 6.485 .999 -18.59 20.09
4 -24.000(*) 5.558 .014 -42.26 -5.74
4 1 33.500(*) 5.194 .001 16.45 50.55
2 24.750(*) 3.471 .001 13.47 36.03
3 24.000(*) 5.558 .014 5.74 42.26
* The mean difference is significant at the .05 level.
The Tukey test relies on homogeneity of variance, so we ignore these results. The Games-Howell post-hoc test does not rely on homogeneity of variance (this is why we used two different post-hoc tests) and so can be used. SPSS kindly flags (*) which differences are significant!
Result: Drug 4 (Asprin) produces significantly different result from the other three drugs:
Formal Reporting: When we report the outcome of an ANOVA, we cite the value of the F ratio and give the number of degrees of freedom, outcome (in a neutral fashion) and significance value. So in this case:
There is a significant difference between the pain scores for asprin and the other three drugs tested, F(3,28) = 11.97, p < .05.
Two-Factor ANOVA
Do anti-cancer drugs have different effects in males and females?
Data:
Drug: cisplatin vinblastine 5-fluorouracil
Gender:
Female Male Female Male Female Male
Tumour
Size: 65 50 70 45 55 35
70 55 65 60 65 40
60 80 60 85 70 35
60 65 70 65 55 55
60 70 65 70 55 35
55 75 60 70 60 40
60 75 60 80 50 45
50 65 50 60 50 40
We enter this data into SPSS using dummy values for the drugs (1, 2, 3) and genders (1,2) so the coded data can be used in the ANOVA:
It's always a good idea to enter descriptive labels for data into the Variable View window, or the output is difficult to interpret!
EDA (Analyze: Descriptive Statistics: Explore) shows that the data is normally distributed, so we can proceed with the ANOVA:
Analyze: General Linear Model: Univariate
Dependent variable: Tumour Diameter
Fixed Factors: Gender, Drug:
Also select:
Post Hoc: Tukey and Games-Howell:
Options:
Display Means for: Gender, Drug, Gender*Drug
Descriptive Statistics
Homogeneity tests:
Output:
Levene's Test of Equality of Error Variances(a)
Dependent Variable: Diameter F df1 df2 Sig.
1.462 5 42 .223
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a Design: Intercept+Gender+Drug+Gender * Drug
The significance result for homogeneity of variance is >.05, which shows that the error variance of the dependent variable is equal across the groups, i.e. the assumption of the ANOVA test has been met.
Tests of Between-Subjects Effects
Dependent Variable: Diameter Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 3817.188(a) 5 763.438 10.459 .000
Intercept 167442.188 1 167442.188 2294.009 .000
Gender 42.188 1 42.188 .578 .451
Drug 2412.500 2 1206.250 16.526 .000
Gender * Drug 1362.500 2 681.250 9.333 .000
Error 3065.625 42 72.991
Total 174325.000 48
Corrected Total 6882.813 47
a R Squared = .555 (Adjusted R Squared = .502)
The highlighted values are significant (<.05), but there is no effect of gender (p = 0.451). Again, this does not tell us which drugs behave differently, so again we need to look at the post hoc tests:
Multiple Comparisons
Dependent Variable: Diameter
(I) Drug (J) Drug Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
Tukey HSD cisplatin vinblastine -1.25 3.021 .910 -8.59 6.09
5-flourouracil 14.38(*) 3.021 .000 7.04 21.71
vinblastine cisplatin 1.25 3.021 .910 -6.09 8.59
5-flourouracil 15.63(*) 3.021 .000 8.29 22.96
5-flourouracil cisplatin -14.38(*) 3.021 .000 -21.71 -7.04
vinblastine -15.63(*) 3.021 .000 -22.96 -8.29
Games-Howell cisplatin vinblastine -1.25 3.329 .925 -9.46 6.96
5-flourouracil 14.38(*) 3.534 .001 5.64 23.11
vinblastine cisplatin 1.25 3.329 .925 -6.96 9.46
5-flourouracil 15.63(*) 3.699 .001 6.50 24.75
5-flourouracil cisplatin -14.38(*) 3.534 .001 -23.11 -5.64
vinblastine -15.63(*) 3.699 .001 -24.75 -6.50
Based on observed means.
* The mean difference is significant at the .05 level.
In this example, we can use the Tukey or Games-Howell results. Again, SPSS helpfully flags which results have reached statistical significance. We already know from the main ANOVA table that the effect of gender is not significant, but the post hoc tests show which drugs produce significantly different outcomes.
Formal Reporting: When we report the outcome of an ANOVA, we cite the value of the F ratio and give the number of degrees of freedom, outcome (in a neutral fashion) and significance value. So in this case:
There is a significant difference between the tumour diameter for 5-flourouracil and the other two drugs tested, F(5,47) = 10.46, p < .05.
Repeated Measures ANOVA
Remember that one of the assumptions of ANOVA is independence of the groups being compared. In lots of circumstances, we want to test the same thing repeatedly, e.g:
•Patients with a chronic disease after 3, 6 and 12 months of drug treatment
•Repeated sampling from the same location, e.g. spring, summer, autumn and winter
•etc
This type of study reduces variability in the data and so increases the power to detect effects, but violates the assumption of independence, so as with the paired t-test, we need to use a special form of ANOVA called repeated measures. In a parametric test, the assumption that the relationship between pairs of groups is equal is called "sphericity". Violating sphericity means that the F statistic cannot be compared to the normal tables of F, and so software cannot calculate a significance value. SPSS includes a procedure called Mauchly's test which tells us if the assumption of sphericity has been violated:
•If Mauchly’s test statistic is significant (i.e. p 0.05) we conclude that the condition of sphericity has not been met.
•If, Mauchly’s test statistic is nonsignificant (i.e. p >.05) it is reasonable to conclude that the variances of differences are not significantly different.
If Mauchly’s test is significant then we cannot trust the F-ratios produced by SPSS unless we apply a correction (which, fortunately, SPSS helps us to do).
One-Way Repeated Measures ANOVA
i.e. one independent variable, e.g. pain score after surgery:
Patient1 Patient2 Patient3
1 3 1
2 5 3
4 6 6
5 7 4
5 9 1
6 10 3
This data can be entered directly into SPSS. Note that each column represents a repeated measures variable (patients in this case). There is no need for a coding variable (as with between-group designs, above):
It's always a good idea to enter descriptive labels for data into the Variable View window, or the output is difficult to interpret! Next:
Analyze: General Linear Model: Repeated Measures
Within-Subject factor name: Patient
Number of Levels: 3 (because there are 3 patients)
Click Add, then Define (factors):
There are no proper post hoc tests for repeated measures variables in SPSS. However, via the Options button, you can use the paired t-test procedure to compare all pairs of levels of the independent variable, and then apply a Bonferroni correction to the probability at which you accept any of these tests. The resulting probability value should be used as the criterion for statistical significance. A ‘Bonferroni correction’ is achieved by dividing the probability value (usually 0.05) by the number of tests conducted, e.g. if we compare all levels of the independent variable of these data, we make three comparisons and so the appropriate significance level is 0.05/3 = 0.0167. Therefore, we accept t-tests as being significant only if they have a p value <0.0167.
Output:
Mauchly's Test of Sphericity Within Subjects Effect Mauchly's W Approx. Chi-Square df Sig. Epsilon
Greenhouse-Geisser Huynh-Feldt Lower-bound
patient .094 9.437 2 .009 .525 .544 .500
Mauchly’s test is significant (p <.05) so we conclude that the assumption of sphericity has not been met.
Tests of Within-Subjects Effects Source
Type III Sum of Squares df Mean Square F Sig.
patient Sphericity Assumed 44.333 2 22.167 8.210 .008
Greenhouse-Geisser 44.333 1.050 42.239 8.210 .033
Huynh-Feldt 44.333 1.088 40.752 8.210 .031
Lower-bound 44.333 1.000 44.333 8.210 .035
Error(patient) Sphericity Assumed 27.000 10 2.700
Greenhouse-Geisser 27.000 5.248 5.145
Huynh-Feldt 27.000 5.439 4.964
Lower-bound 27.000 5.000 5.400
Because the significance values are <.05, we conclude that there was a significant difference between the three patients, but this test does not tell us which patients differed from each other. The next issue is which of the three corrections to use. Going back to Mauchly's test:
•If epsilon is >0.75, use the Huynh-Feldt correction.
•If epsilon is <0.75, or nothing is known about sphericity at all, use the Greenhouse-Geisser correction.
•In this example, the epsilon values from Mauchly's test values are 0.525 and 0.544, both <0.75, so we use the Greenhouse-Geisser corrected values. Using this correction, F is still significant because its p value is 0.033, which is <.05.
Post Hoc Tests:
Pairwise Comparisons (I) patient (J) patient Mean Difference (I-J) Std. Error Sig.(a) 95% Confidence Interval for Difference(a)
Lower Bound Upper Bound
1 2 -2.833(*) .401 .003 -4.252 -1.415
3 .833 .946 1.000 -2.509 4.176
2 1 2.833(*) .401 .003 1.415 4.252
3 3.667 1.282 .106 -.865 8.199
3 1 -.833 .946 1.000 -4.176 2.509
2 -3.667 1.282 .106 -8.199 .865
Based on estimated marginal means
* The mean difference is significant at the .05 level.
a Adjustment for multiple comparisons: Bonferroni.
Formal reporting:
Mauchly’s test indicated that the assumption of sphericity had been violated (chi-square = 9.44, p <.05), therefore degrees of freedom were corrected using Greenhouse-Geisser estimates of sphericity (epsilon = 0.53). The results show that the pain scores of the three patients differed significantly, F(1.05, 5.25) = 8.21, p <.05. Post hoc tests revealed that although the pain score of Patient2 was significantly higher than that of than Patient1 (p<.001), Patient3's score was not significantly differently from either of the other patients (both p>.05).
Two-Way Repeated Measures ANOVA
i.e. two independent variables:
In a study of the best way to keep fields free of weeds for an entire growing season, a farmer treated test plots in 10 fields with either five different concentrations of weedkiller (independent variable 1) or five different length blasts with a flamethrower (independent variable 2). At the end of they growing season, the number of weeds per square metre were counted. To exclude bias (e.g. pre-existing seedbank in the soil), the following year, the farmer repeated the experiment but this time the treatments the fields received were reversed:
Treatment: Weedkiller Flamethrower
Severity: 1 2 3 4 5 1 2 3 4 5
Field1 10 15 18 22 37 9 13 13 18 22
Field2 10 18 10 42 60 7 14 20 21 32
Field3 7 11 28 31 56 9 13 24 30 35
Field4 9 19 36 45 60 7 14 9 20 25
Field5 15 14 29 33 37 14 13 20 22 29
Field6 14 13 26 26 49 5 12 17 16 33
Field7 9 12 19 37 48 5 15 12 17 24
Field8 9 18 22 31 39 13 13 14 17 17
Field9 12 14 24 28 53 12 13 21 19 22
Field10 7 11 21 23 45 12 14 20 21 29
SPSS Data View:
It's always a good idea to enter descriptive labels for data into the Variable View window, or the output is difficult to interpret:
Analyze: General Linear Model: Repeated Measures
Define Within Subject Factors (remember, "factor" = test or treatment):
Treatment, (2 treatments, weedkiller or flamethrower) (SPSS only allows 8 characters for the name)
Severity (5 different severities):
Click Define and define Within Subject Variables:
As above, there are no post hoc tests for repeated measures ANOVA in SPSS, but via the Options button, we can apply a Bonferroni correction to the probability at which you accept any of the tests:
Output:
Mauchly's Test of Sphericity(b)
Measure: MEASURE_1 Within Subjects Effect Mauchly's W Approx. Chi-Square df Sig. Epsilon
Greenhouse-Geisser Huynh-Feldt Lower-bound
treatmen 1.000 .000 0 . 1.000 1.000 1.000
severity .092 17.685 9 .043 .552 .740 .250
treatmen * severity .425 6.350 9 .712 .747 1.000 .250
The outcome of Mauchly’s test is significant (p <.05) for the severity of treatment, so we need to correct the F-values for this, but not for the treatments themselves.
Tests of Within-Subjects Effects Source
Type III Sum of Squares df Mean Square F Sig.
treatmen Sphericity Assumed 1730.560 1 1730.560 34.078 .000
Greenhouse-Geisser 1730.560 1.000 1730.560 34.078 .000
Huynh-Feldt 1730.560 1.000 1730.560 34.078 .000
Lower-bound 1730.560 1.000 1730.560 34.078 .000
Error(treatmen) Sphericity Assumed 457.040 9 50.782
Greenhouse-Geisser 457.040 9.000 50.782
Huynh-Feldt 457.040 9.000 50.782
Lower-bound 457.040 9.000 50.782
severity Sphericity Assumed 9517.960 4 2379.490 83.488 .000
Greenhouse-Geisser 9517.960 2.209 4309.021 83.488 .000
Huynh-Feldt 9517.960 2.958 3217.666 83.488 .000
Lower-bound 9517.960 1.000 9517.960 83.488 .000
Error(severity) Sphericity Assumed 1026.040 36 28.501
Greenhouse-Geisser 1026.040 19.880 51.613
Huynh-Feldt 1026.040 26.622 38.541
Lower-bound 1026.040 9.000 114.004
treatmen * severity Sphericity Assumed 1495.240 4 373.810 20.730 .000
Greenhouse-Geisser 1495.240 2.989 500.205 20.730 .000
Huynh-Feldt 1495.240 4.000 373.810 20.730 .000
Lower-bound 1495.240 1.000 1495.240 20.730 .001
Error(treatmen*severity) Sphericity Assumed 649.160 36 18.032
Greenhouse-Geisser 649.160 26.903 24.129
Huynh-Feldt 649.160 36.000 18.032
Lower-bound 649.160 9.000 72.129
Since there was no violation of sphericity, we can look at the comparison of the two treatments without any correction. The significance value shows (0.000) that there was a significant difference between the two treatments, but does not tell us which treatments produced this effect.
The output also tells us the effect of the severity of treatments, but remember there was a violation of sphericity here, so we must look at the corrected F-ratios. All of the corrected values are highly significant and so we can use the Greenhouse-Geisser corrected values as these are the most conservative.
Pairwise Comparisons (I) severity (J) severity Mean Difference (I-J) Std. Error Sig.(a) 95% Confidence Interval for Difference(a)
Lower Bound Upper Bound
1 2 -4.200(*) .895 .011 -7.502 -.898
3 -10.400(*) 1.190 .000 -14.790 -6.010
4 -16.200(*) 1.764 .000 -22.709 -9.691
5 -27.850(*) 2.398 .000 -36.698 -19.002
2 1 4.200(*) .895 .011 .898 7.502
3 -6.200(*) 1.521 .028 -11.810 -.590
4 -12.000(*) 1.280 .000 -16.723 -7.277
5 -23.650(*) 2.045 .000 -31.197 -16.103
3 1 10.400(*) 1.190 .000 6.010 14.790
2 6.200(*) 1.521 .028 .590 11.810
4 -5.800 1.690 .075 -12.036 .436
5 -17.450(*) 2.006 .000 -24.852 -10.048
4 1 16.200(*) 1.764 .000 9.691 22.709
2 12.000(*) 1.280 .000 7.277 16.723
3 5.800 1.690 .075 -.436 12.036
5 -11.650(*) 1.551 .000 -17.373 -5.927
5 1 27.850(*) 2.398 .000 19.002 36.698
2 23.650(*) 2.045 .000 16.103 31.197
3 17.450(*) 2.006 .000 10.048 24.852
4 11.650(*) 1.551 .000 5.927 17.373
* The mean difference is significant at the .05 level.
a Adjustment for multiple comparisons: Bonferroni.
This shows that there was only one pair for which there was no significant difference: 40% weedkiller followed by 2 minutes flame thrower, and 2 minutes flame thrower followed by 40% weedkiller. The differences for all the other pairs are significant. It does not matter if the farmer uses weedkiller or a flamethrower, but how much weedkiller and how long a burst of flame does make a difference to weed control.
Formal report:
There was a significant main effect of the type of treatment, F(1, 9) = 34.08, p < .001.
There was a significant main effect of the severity of treatment, F(2.21, 19.88) = 83.49, p <.001.
Monday, January 18, 2010
Commands in Matlab
MATLAB常用命令大全(2009-11-15 00:19:08)
标签：matlab 多项式 位线 条件数 样条函数 校园 分类：学与得
[sizeabs 绝对值、模、字符的ASCII码值
A a
acos 反余弦
acosh 反双曲余弦
acot 反余切
acoth 反双曲余切
acsc 反余割
acsch 反双曲余割
align 启动图形对象几何位置排列工具
all 所有元素非零为真
angle 相角
ans 表达式计算结果的缺省变量名
any 所有元素非全零为真
area 面域图
argnames 函数M文件宗量名
asec 反正割
asech 反双曲正割
asin 反正弦
asinh 反双曲正弦
assignin 向变量赋值
atan 反正切
atan2 四象限反正切
atanh 反双曲正切
autumn 红黄调秋色图阵
axes 创建轴对象的低层指令
axis 控制轴刻度和风格的高层指令
B b
bar 二维直方图
bar3 三维直方图
bar3h 三维水平直方图
barh 二维水平直方图
base2dec X进制转换为十进制
bin2dec 二进制转换为十进制
blanks 创建空格串
bone 蓝色调黑白色图阵
box 框状坐标轴
break while 或for 环中断指令
brighten 亮度控制
C c
capture （3版以前）捕获当前图形
cart2pol 直角坐标变为极或柱坐标
cart2sph 直角坐标变为球坐标
cat 串接成高维数组
caxis 色标尺刻度
cd 指定当前目录
cdedit 启动用户菜单、控件回调函数设计工具
cdf2rdf 复数特征值对角阵转为实数块对角阵
ceil 向正无穷取整
cell 创建元胞数组
cell2struct 元胞数组转换为构架数组
celldisp 显示元胞数组内容
cellplot 元胞数组内部结构图示
char 把数值、符号、内联类转换为字符对象
chi2cdf 分布累计概率函数
chi2inv 分布逆累计概率函数
chi2pdf 分布概率密度函数
chi2rnd 分布随机数发生器
chol Cholesky分解
clabel 等位线标识
cla 清除当前轴
class 获知对象类别或创建对象
clc 清除指令窗
clear 清除内存变量和函数
clf 清除图对象
clock 时钟
colorcube 三浓淡多彩交叉色图矩阵
colordef 设置色彩缺省值
colormap 色图
colspace 列空间的基
close 关闭指定窗口
colperm 列排序置换向量
comet 彗星状轨迹图
comet3 三维彗星轨迹图
compass 射线图
compose 求复合函数
cond （逆）条件数
condeig 计算特征值、特征向量同时给出条件数
condest 范 -1条件数估计
conj 复数共轭
contour 等位线
contourf 填色等位线
contour3 三维等位线
contourslice 四维切片等位线图
conv 多项式乘、卷积
cool 青紫调冷色图
copper 古铜调色图
cos 余弦
cosh 双曲余弦
cot 余切
coth 双曲余切
cplxpair 复数共轭成对排列
csc 余割
csch 双曲余割
cumsum 元素累计和
cumtrapz 累计梯形积分
cylinder 创建圆柱
D d
dblquad 二重数值积分
deal 分配宗量
deblank 删去串尾部的空格符
dec2base 十进制转换为X进制
dec2bin 十进制转换为二进制
dec2hex 十进制转换为十六进制
deconv 多项式除、解卷
delaunay Delaunay 三角剖分
del2 离散Laplacian差分
demo Matlab演示
det 行列式
diag 矩阵对角元素提取、创建对角阵
diary Matlab指令窗文本内容记录
diff 数值差分、符号微分
digits 符号计算中设置符号数值的精度
dir 目录列表
disp 显示数组
display 显示对象内容的重载函数
dlinmod 离散系统的线性化模型
dmperm 矩阵Dulmage-Mendelsohn 分解
dos 执行DOS 指令并返回结果
double 把其他类型对象转换为双精度数值
drawnow 更新事件队列强迫Matlab刷新屏幕
dsolve 符号计算解微分方程
E e
echo M文件被执行指令的显示
edit 启动M文件编辑器
eig 求特征值和特征向量
eigs 求指定的几个特征值
end 控制流FOR等结构体的结尾元素下标
eps 浮点相对精度
error 显示出错信息并中断执行
errortrap 错误发生后程序是否继续执行的控制
erf 误差函数
erfc 误差补函数
erfcx 刻度误差补函数
erfinv 逆误差函数
errorbar 带误差限的曲线图
etreeplot 画消去树
串演算指令
in 跨空间串演算指令
exist 检查变量或函数是否已定义
exit 退出Matlab环境
exp 指数函数
expand 符号计算中的展开操作
expint 指数积分函数
expm 常用矩阵指数函数
expm1 Pade法求矩阵指数
expm2 Taylor法求矩阵指数
expm3 特征值分解法求矩阵指数
eye 单位阵
ezcontour 画等位线的简捷指令
ezcontourf 画填色等位线的简捷指令
ezgraph3 画表面图的通用简捷指令
ezmesh 画网线图的简捷指令
ezmeshc 画带等位线的网线图的简捷指令
ezplot 画二维曲线的简捷指令
ezplot3 画三维曲线的简捷指令
ezpolar 画极坐标图的简捷指令
ezsurf 画表面图的简捷指令
ezsurfc 画带等位线的表面图的简捷指令
F f
factor 符号计算的因式分解
feather 羽毛图
feedback 反馈连接
f 执行由串指定的函数
fft 离散Fourier变换
fft2 二维离散Fourier变换
fftn 高维离散Fourier变换
fftshift 直流分量对中的谱
fieldnames 构架域名
figure 创建图形窗
fill3 三维多边形填色图
find 寻找非零元素下标
findobj 寻找具有指定属性的对象图柄
findstr 寻找短串的起始字符下标
findsym 机器确定内存中的符号变量
finverse 符号计算中求反函数
fix 向零取整
flag 红白蓝黑交错色图阵
fliplr 矩阵的左右翻转
flipud 矩阵的上下翻转
flipdim 矩阵沿指定维翻转
floor 向负无穷取整
flops 浮点运算次数
flow Matlab提供的演示数据
fmin 求单变量非线性函数极小值点（旧版）
fminbnd 求单变量非线性函数极小值点
fmins 单纯形法求多变量函数极小值点（旧版）
fminunc 拟牛顿法求多变量函数极小值点
fminsearch 单纯形法求多变量函数极小值点
fnder 对样条函数求导
fnint 利用样条函数求积分
fnval 计算样条函数区间内任意一点的值
fnplt 绘制样条函数图形
fopen 打开外部文件
for 构成for环用
format 设置输出格式
fourier Fourier 变换
fplot 返函绘图指令
fprintf 设置显示格式
fread 从文件读二进制数据
fsolve 求多元函数的零点
full 把稀疏矩阵转换为非稀疏阵
funm 计算一般矩阵函数
funtool 函数计算器图形用户界面
fzero 求单变量非线性函数的零点
G g
gamma 函数
gammainc 不完全 函数
gammaln 函数的对数
gca 获得当前轴句柄
gcbo 获得正执行"回调"的对象句柄
gcf 获得当前图对象句柄
gco 获得当前对象句柄
geomean 几何平均值
get 获知对象属性
getfield 获知构架数组的域
getframe 获取影片的帧画面
ginput 从图形窗获取数据
global 定义全局变量
gplot 依图论法则画图
gradient 近似梯度
gray 黑白灰度
grid 画分格线
griddata 规则化数据和曲面拟合
gtext 由鼠标放置注释文字
guide 启动图形用户界面交互设计工具
H h
harmmean 调和平均值
help 在线帮助
helpwin 交互式在线帮助
helpdesk 打开超文本形式用户指南
hex2dec 十六进制转换为十进制
hex2num 十六进制转换为浮点数
hidden 透视和消隐开关
hilb Hilbert矩阵
hist 频数计算或频数直方图
histc 端点定位频数直方图
histfit 带正态拟合的频数直方图
hold 当前图上重画的切换开关
horner 分解成嵌套形式
hot 黑红黄白色图
hsv 饱和色图
I i
if-else-elseif 条件分支结构
ifft 离散Fourier反变换
ifft2 二维离散Fourier反变换
ifftn 高维离散Fourier反变换
ifftshift 直流分量对中的谱的反操作
ifourier Fourier反变换
i, j 缺省的"虚单元"变量
ilaplace Laplace反变换
imag 复数虚部
image 显示图象
imagesc 显示亮度图象
imfinfo 获取图形文件信息
imread 从文件读取图象
imwrite 把图象写成文件
ind2sub 单下标转变为多下标
inf 无穷大
info MathWorks公司网点地址
inline 构造内联函数对象
inmem 列出内存中的函数名
input 提示用户输入
inputname 输入宗量名
int 符号积分
int2str 把整数数组转换为串数组
interp1 一维插值
interp2 二维插值
interp3 三维插值
interpn N维插值
interpft 利用FFT插值
intro Matlab自带的入门引导
inv 求矩阵逆
invhilb Hilbert矩阵的准确逆
ipermute 广义反转置
isa 检测是否给定类的对象
ischar 若是字符串则为真
isequal 若两数组相同则为真
isempty 若是空阵则为真
isfinite 若全部元素都有限则为真
isfield 若是构架域则为真
isglobal 若是全局变量则为真
ishandle 若是图形句柄则为真
ishold 若当前图形处于保留状态则为真
isieee 若计算机执行IEEE规则则为真
isinf 若是无穷数据则为真
isletter 若是英文字母则为真
islogical 若是逻辑数组则为真
ismember 检查是否属于指定集
isnan 若是非数则为真
isnumeric 若是数值数组则为真
isobject 若是对象则为真
isprime 若是质数则为真
isreal 若是实数则为真
isspace 若是空格则为真
issparse 若是稀疏矩阵则为真
isstruct 若是构架则为真
isstudent 若是Matlab学生版则为真
iztrans 符号计算Z反变换
J j , K k
jacobian 符号计算中求Jacobian 矩阵
jet 蓝头红尾饱和色
jordan 符号计算中获得 Jordan标准型
keyboard 键盘获得控制权
kron Kronecker乘法规则产生的数组
L l
laplace Laplace变换
lasterr 显示最新出错信息
lastwarn 显示最新警告信息
leastsq 解非线性最小二乘问题（旧版）
legend 图形图例
lighting 照明模式
line 创建线对象
lines 采用plot 画线色
linmod 获连续系统的线性化模型
linmod2 获连续系统的线性化精良模型
linspace 线性等分向量
ln 矩阵自然对数
load 从MAT文件读取变量
log 自然对数
log10 常用对数
log2 底为2的对数
loglog 双对数刻度图形
logm 矩阵对数
logspace 对数分度向量
lookfor 按关键字搜索M文件
lower 转换为小写字母
lsqnonlin 解非线性最小二乘问题
lu LU分解
M m
mad 平均绝对值偏差
magic 魔方阵
maple &nb, sp; 运作 Maple格式指令
mat2str 把数值数组转换成输入形态串数组
material 材料反射模式
max 找向量中最大元素
mbuild 产生EXE文件编译环境的预设置指令
mcc 创建MEX或EXE文件的编译指令
mean 求向量元素的平均值
median 求中位数
menuedit 启动设计用户菜单的交互式编辑工具
mesh 网线图
meshz 垂帘网线图
meshgrid 产生"格点"矩阵
methods 获知对指定类定义的所有方法函数
mex 产生MEX文件编译环境的预设置指令
mfunlis 能被mfun计算的MAPLE经典函数列表
mhelp 引出 Maple的在线帮助
min 找向量中最小元素
mkdir 创建目录
mkpp 逐段多项式数据的明晰化
mod 模运算
more 指令窗中内容的分页显示
movie 放映影片动画
moviein 影片帧画面的内存预置
mtaylor 符号计算多变量Taylor级数展开
N n
ndims 求数组维数
NaN 非数（预定义）变量
nargchk 输入宗量数验证
nargin 函数输入宗量数
nargout 函数输出宗量数
ndgrid 产生高维格点矩阵
newplot 准备新的缺省图、轴
nextpow2 取最接近的较大2次幂
nnz 矩阵的非零元素总数
nonzeros 矩阵的非零元素
norm 矩阵或向量范数
normcdf 正态分布累计概率密度函数
normest 估计矩阵2范数
norminv 正态分布逆累计概率密度函数
normpdf 正态分布概率密度函数
normrnd 正态随机数发生器
notebook 启动Matlab和Word的集成环境
null 零空间
num2str 把非整数数组转换为串
numden 获取最小公分母和相应的分子表达式
nzmax 指定存放非零元素所需内存
O o
ode1 非Stiff 微分方程变步长解算器
ode15s Stiff 微分方程变步长解算器
ode23t 适度Stiff 微分方程解算器
ode23tb Stiff 微分方程解算器
ode45 非Stiff 微分方程变步长解算器
odefile ODE 文件模板
odeget 获知ODE 选项设置参数
odephas2 ODE 输出函数的二维相平面图
odephas3 ODE 输出函数的三维相空间图
odeplot ODE 输出函数的时间轨迹图
odeprint 在Matlab指令窗显示结果
odeset 创建或改写 ODE选项构架参数值
ones 全1数组
optimset 创建或改写优化泛函指令的选项参数值
orient 设定图形的排放方式
orth 值空间正交化
P p
pack 收集Matlab内存碎块扩大内存
pagedlg 调出图形排版对话框
patch 创建块对象
path 设置Matlab搜索路径的指令
pathtool 搜索路径管理器
pause 暂停
pcode 创建预解译P码文件
pcolor 伪彩图
peaks Matlab提供的典型三维曲面
permute 广义转置
pi （预定义变量）圆周率
pie 二维饼图
pie3 三维饼图
pink 粉红色图矩阵
pinv 伪逆
plot 平面线图
plot3 三维线图
plotmatrix 矩阵的散点图
plotyy 双纵坐标图
poissinv 泊松分布逆累计概率分布函数
poissrnd 泊松分布随机数发生器
pol2cart 极或柱坐标变为直角坐标
polar 极坐标图
poly 矩阵的特征多项式、根集对应的多项式
poly2str 以习惯方式显示多项式
poly2sym 双精度多项式系数转变为向量符号多项式
polyder 多项式导数
polyfit 数据的多项式拟合
polyval 计算多项式的值
polyvalm 计算矩阵多项式
pow2 2的幂
ppval 计算分段多项式
pretty 以习惯方式显示符号表达式
print 打印图形或SIMULINK模型
printsys 以习惯方式显示有理分式
prism 光谱色图矩阵
procread 向MAPLE输送计算程序
profile 函数文件性能评估器
propedit 图形对象属性编辑器
pwd 显示当前工作目录
Q q
quad 低阶法计算数值积分
quad8 高阶法计算数值积分(QUADL)
quit 推出Matlab 环境
quiver 二维方向箭头图
quiver3 三维方向箭头图
R r
rand 产生均匀分布随机数
randn 产生正态分布随机数
randperm 随机置换向量
range 样本极差
rank 矩阵的秩
rats 有理输出
rcond 矩阵倒条件数估计
real 复数的实部
reallog 在实数域内计算自然对数
realpow 在实数域内计算乘方
realsqrt 在实数域内计算平方根
realmax 最大正浮点数
realmin 最小正浮点数
rectangle 画"长方框"
rem 求余数
repmat 铺放模块数组
reshape 改变数组维数、大小
residue 部分分式展开
return 返回
ribbon 把二维曲线画成三维彩带图
rmfield 删去构架的域
roots 求多项式的根
rose 数扇形图
rot90 矩阵旋转90度
rotate 指定的原点和方向旋转
rotate3d 启动三维图形视角的交互设置功能
round 向最近整数圆整
rref 简化矩阵为梯形形式
rsf2csf 实数块对角阵转为复数特征值对角阵
rsums Riemann和
S s
save 把内存变量保存为文件
scatter 散点图
scatter3 三维散点图
sec 正割
sech 双曲正割
semilogx X轴对数刻度坐标图
semilogy Y轴对数刻度坐标图
series 串联连接
set 设置图形对象属性
setfield 设置构架数组的域
setstr 将ASCII码转换为字符的旧版指令
sign 根据符号取值函数
signum 符号计算中的符号取值函数
sim 运行SIMULINK模型
simget 获取SIMULINK模型设置的仿真参数
simple 寻找最短形式的符号解
simplify 符号计算中进行简化操作
simset 对SIMULINK模型的仿真参数进行设置
simulink 启动SIMULINK模块库浏览器
sin 正弦
sinh 双曲正弦
size 矩阵的大小
slice 立体切片图
solve 求代数方程的符号解
spalloc 为非零元素配置内存
sparse 创建稀疏矩阵
spconvert 把外部数据转换为稀疏矩阵
spdiags 稀疏对角阵
spfun 求非零元素的函数值
sph2cart 球坐标变为直角坐标
sphere 产生球面
spinmap 色图彩色的周期变化
spline 样条插值
spones 用1置换非零元素
sprandsym 稀疏随机对称阵
sprank 结构秩
spring 紫黄调春色图
sprintf 把格式数据写成串
spy 画稀疏结构图
sqrt 平方根
sqrtm 方根矩阵
squeeze 删去大小为1的"孤维"
sscanf 按指定格式读串
stairs 阶梯图
std 标准差
stem 二维杆图
step 阶跃响应指令
str2double 串转换为双精度值
str2mat 创建多行串数组
str2num 串转换为数
strcat 接成长串
strcmp 串比较
strjust 串对齐
strmatch 搜索指定串
strncmp 串中前若干字符比较
strrep 串替换
strtok 寻找第一间隔符前的内容
struct 创建构架数组
struct2cell 把构架转换为元胞数组
strvcat 创建多行串数组
sub2ind 多下标转换为单下标
subexpr 通过子表达式重写符号对象
subplot 创建子图
subs 符号计算中的符号变量置换
subspace 两子空间夹角
sum 元素和
summer 绿黄调夏色图
superiorto 设定优先级
surf 三维着色表面图
surface 创建面对象
surfc 带等位线的表面图
surfl 带光照的三维表面图
surfnorm 空间表面的法线
svd 奇异值分解
svds 求指定的若干奇异值
switch-case-otherwise 多分支结构
sym2poly 符号多项式转变为双精度多项式系数向量
symmmd 对称最小度排序
symrcm 反向Cuthill-McKee排序
syms 创建多个符号对象
T t
tan 正切
tanh 双曲正切
taylortool 进行Taylor逼近分析的交互界面
text 文字注释
tf 创建传递函数对象
tic 启动计时器
title 图名
toc 关闭计时器
trapz 梯形法数值积分
treelayout 展开树、林
treeplot 画树图
tril 下三角阵
trim 求系统平衡点
trimesh 不规则格点网线图
trisurf 不规则格点表面图 triu 上三角阵 try-catch 控制流中的Try-catch结构 type 显示M文件
U u
uicontextmenu 创建现场菜单
uicontrol 创建用户控件
uimenu 创建用户菜单
unmkpp 逐段多项式数据的反明晰化
unwrap 自然态相角
upper 转换为大写字母
V v
var 方差
varargin 变长度输入宗量
varargout 变长度输出宗量
vectorize 使串表达式或内联函数适于数组运算
ver 版本信息的获取
view 三维图形的视角控制
voronoi Voronoi多边形
vpa 任意精度（符号类）数值
W w
warning 显示警告信息
what 列出当前目录上的文件
whatsnew 显示Matlab中 Readme文件的内容
which 确定函数、文件的位置
while 控制流中的While环结构
white 全白色图矩阵
whitebg 指定轴的背景色
who 列出内存中的变量名
whos 列出内存中变量的详细信息
winter 蓝绿调冬色图
workspace 启动内存浏览器
X x , Y y , Z z
xlabel X轴名
xor 或非逻辑
yesinput 智能输入指令
ylabel Y轴名
zeros 全零数组
zlabel Z轴名
zoom 图形的变焦放大和缩小
ztrans 符号计算Z变换
标签：matlab 多项式 位线 条件数 样条函数 校园 分类：学与得
[sizeabs 绝对值、模、字符的ASCII码值
A a
acos 反余弦
acosh 反双曲余弦
acot 反余切
acoth 反双曲余切
acsc 反余割
acsch 反双曲余割
align 启动图形对象几何位置排列工具
all 所有元素非零为真
angle 相角
ans 表达式计算结果的缺省变量名
any 所有元素非全零为真
area 面域图
argnames 函数M文件宗量名
asec 反正割
asech 反双曲正割
asin 反正弦
asinh 反双曲正弦
assignin 向变量赋值
atan 反正切
atan2 四象限反正切
atanh 反双曲正切
autumn 红黄调秋色图阵
axes 创建轴对象的低层指令
axis 控制轴刻度和风格的高层指令
B b
bar 二维直方图
bar3 三维直方图
bar3h 三维水平直方图
barh 二维水平直方图
base2dec X进制转换为十进制
bin2dec 二进制转换为十进制
blanks 创建空格串
bone 蓝色调黑白色图阵
box 框状坐标轴
break while 或for 环中断指令
brighten 亮度控制
C c
capture （3版以前）捕获当前图形
cart2pol 直角坐标变为极或柱坐标
cart2sph 直角坐标变为球坐标
cat 串接成高维数组
caxis 色标尺刻度
cd 指定当前目录
cdedit 启动用户菜单、控件回调函数设计工具
cdf2rdf 复数特征值对角阵转为实数块对角阵
ceil 向正无穷取整
cell 创建元胞数组
cell2struct 元胞数组转换为构架数组
celldisp 显示元胞数组内容
cellplot 元胞数组内部结构图示
char 把数值、符号、内联类转换为字符对象
chi2cdf 分布累计概率函数
chi2inv 分布逆累计概率函数
chi2pdf 分布概率密度函数
chi2rnd 分布随机数发生器
chol Cholesky分解
clabel 等位线标识
cla 清除当前轴
class 获知对象类别或创建对象
clc 清除指令窗
clear 清除内存变量和函数
clf 清除图对象
clock 时钟
colorcube 三浓淡多彩交叉色图矩阵
colordef 设置色彩缺省值
colormap 色图
colspace 列空间的基
close 关闭指定窗口
colperm 列排序置换向量
comet 彗星状轨迹图
comet3 三维彗星轨迹图
compass 射线图
compose 求复合函数
cond （逆）条件数
condeig 计算特征值、特征向量同时给出条件数
condest 范 -1条件数估计
conj 复数共轭
contour 等位线
contourf 填色等位线
contour3 三维等位线
contourslice 四维切片等位线图
conv 多项式乘、卷积
cool 青紫调冷色图
copper 古铜调色图
cos 余弦
cosh 双曲余弦
cot 余切
coth 双曲余切
cplxpair 复数共轭成对排列
csc 余割
csch 双曲余割
cumsum 元素累计和
cumtrapz 累计梯形积分
cylinder 创建圆柱
D d
dblquad 二重数值积分
deal 分配宗量
deblank 删去串尾部的空格符
dec2base 十进制转换为X进制
dec2bin 十进制转换为二进制
dec2hex 十进制转换为十六进制
deconv 多项式除、解卷
delaunay Delaunay 三角剖分
del2 离散Laplacian差分
demo Matlab演示
det 行列式
diag 矩阵对角元素提取、创建对角阵
diary Matlab指令窗文本内容记录
diff 数值差分、符号微分
digits 符号计算中设置符号数值的精度
dir 目录列表
disp 显示数组
display 显示对象内容的重载函数
dlinmod 离散系统的线性化模型
dmperm 矩阵Dulmage-Mendelsohn 分解
dos 执行DOS 指令并返回结果
double 把其他类型对象转换为双精度数值
drawnow 更新事件队列强迫Matlab刷新屏幕
dsolve 符号计算解微分方程
E e
echo M文件被执行指令的显示
edit 启动M文件编辑器
eig 求特征值和特征向量
eigs 求指定的几个特征值
end 控制流FOR等结构体的结尾元素下标
eps 浮点相对精度
error 显示出错信息并中断执行
errortrap 错误发生后程序是否继续执行的控制
erf 误差函数
erfc 误差补函数
erfcx 刻度误差补函数
erfinv 逆误差函数
errorbar 带误差限的曲线图
etreeplot 画消去树
串演算指令
in 跨空间串演算指令
exist 检查变量或函数是否已定义
exit 退出Matlab环境
exp 指数函数
expand 符号计算中的展开操作
expint 指数积分函数
expm 常用矩阵指数函数
expm1 Pade法求矩阵指数
expm2 Taylor法求矩阵指数
expm3 特征值分解法求矩阵指数
eye 单位阵
ezcontour 画等位线的简捷指令
ezcontourf 画填色等位线的简捷指令
ezgraph3 画表面图的通用简捷指令
ezmesh 画网线图的简捷指令
ezmeshc 画带等位线的网线图的简捷指令
ezplot 画二维曲线的简捷指令
ezplot3 画三维曲线的简捷指令
ezpolar 画极坐标图的简捷指令
ezsurf 画表面图的简捷指令
ezsurfc 画带等位线的表面图的简捷指令
F f
factor 符号计算的因式分解
feather 羽毛图
feedback 反馈连接
f 执行由串指定的函数
fft 离散Fourier变换
fft2 二维离散Fourier变换
fftn 高维离散Fourier变换
fftshift 直流分量对中的谱
fieldnames 构架域名
figure 创建图形窗
fill3 三维多边形填色图
find 寻找非零元素下标
findobj 寻找具有指定属性的对象图柄
findstr 寻找短串的起始字符下标
findsym 机器确定内存中的符号变量
finverse 符号计算中求反函数
fix 向零取整
flag 红白蓝黑交错色图阵
fliplr 矩阵的左右翻转
flipud 矩阵的上下翻转
flipdim 矩阵沿指定维翻转
floor 向负无穷取整
flops 浮点运算次数
flow Matlab提供的演示数据
fmin 求单变量非线性函数极小值点（旧版）
fminbnd 求单变量非线性函数极小值点
fmins 单纯形法求多变量函数极小值点（旧版）
fminunc 拟牛顿法求多变量函数极小值点
fminsearch 单纯形法求多变量函数极小值点
fnder 对样条函数求导
fnint 利用样条函数求积分
fnval 计算样条函数区间内任意一点的值
fnplt 绘制样条函数图形
fopen 打开外部文件
for 构成for环用
format 设置输出格式
fourier Fourier 变换
fplot 返函绘图指令
fprintf 设置显示格式
fread 从文件读二进制数据
fsolve 求多元函数的零点
full 把稀疏矩阵转换为非稀疏阵
funm 计算一般矩阵函数
funtool 函数计算器图形用户界面
fzero 求单变量非线性函数的零点
G g
gamma 函数
gammainc 不完全 函数
gammaln 函数的对数
gca 获得当前轴句柄
gcbo 获得正执行"回调"的对象句柄
gcf 获得当前图对象句柄
gco 获得当前对象句柄
geomean 几何平均值
get 获知对象属性
getfield 获知构架数组的域
getframe 获取影片的帧画面
ginput 从图形窗获取数据
global 定义全局变量
gplot 依图论法则画图
gradient 近似梯度
gray 黑白灰度
grid 画分格线
griddata 规则化数据和曲面拟合
gtext 由鼠标放置注释文字
guide 启动图形用户界面交互设计工具
H h
harmmean 调和平均值
help 在线帮助
helpwin 交互式在线帮助
helpdesk 打开超文本形式用户指南
hex2dec 十六进制转换为十进制
hex2num 十六进制转换为浮点数
hidden 透视和消隐开关
hilb Hilbert矩阵
hist 频数计算或频数直方图
histc 端点定位频数直方图
histfit 带正态拟合的频数直方图
hold 当前图上重画的切换开关
horner 分解成嵌套形式
hot 黑红黄白色图
hsv 饱和色图
I i
if-else-elseif 条件分支结构
ifft 离散Fourier反变换
ifft2 二维离散Fourier反变换
ifftn 高维离散Fourier反变换
ifftshift 直流分量对中的谱的反操作
ifourier Fourier反变换
i, j 缺省的"虚单元"变量
ilaplace Laplace反变换
imag 复数虚部
image 显示图象
imagesc 显示亮度图象
imfinfo 获取图形文件信息
imread 从文件读取图象
imwrite 把图象写成文件
ind2sub 单下标转变为多下标
inf 无穷大
info MathWorks公司网点地址
inline 构造内联函数对象
inmem 列出内存中的函数名
input 提示用户输入
inputname 输入宗量名
int 符号积分
int2str 把整数数组转换为串数组
interp1 一维插值
interp2 二维插值
interp3 三维插值
interpn N维插值
interpft 利用FFT插值
intro Matlab自带的入门引导
inv 求矩阵逆
invhilb Hilbert矩阵的准确逆
ipermute 广义反转置
isa 检测是否给定类的对象
ischar 若是字符串则为真
isequal 若两数组相同则为真
isempty 若是空阵则为真
isfinite 若全部元素都有限则为真
isfield 若是构架域则为真
isglobal 若是全局变量则为真
ishandle 若是图形句柄则为真
ishold 若当前图形处于保留状态则为真
isieee 若计算机执行IEEE规则则为真
isinf 若是无穷数据则为真
isletter 若是英文字母则为真
islogical 若是逻辑数组则为真
ismember 检查是否属于指定集
isnan 若是非数则为真
isnumeric 若是数值数组则为真
isobject 若是对象则为真
isprime 若是质数则为真
isreal 若是实数则为真
isspace 若是空格则为真
issparse 若是稀疏矩阵则为真
isstruct 若是构架则为真
isstudent 若是Matlab学生版则为真
iztrans 符号计算Z反变换
J j , K k
jacobian 符号计算中求Jacobian 矩阵
jet 蓝头红尾饱和色
jordan 符号计算中获得 Jordan标准型
keyboard 键盘获得控制权
kron Kronecker乘法规则产生的数组
L l
laplace Laplace变换
lasterr 显示最新出错信息
lastwarn 显示最新警告信息
leastsq 解非线性最小二乘问题（旧版）
legend 图形图例
lighting 照明模式
line 创建线对象
lines 采用plot 画线色
linmod 获连续系统的线性化模型
linmod2 获连续系统的线性化精良模型
linspace 线性等分向量
ln 矩阵自然对数
load 从MAT文件读取变量
log 自然对数
log10 常用对数
log2 底为2的对数
loglog 双对数刻度图形
logm 矩阵对数
logspace 对数分度向量
lookfor 按关键字搜索M文件
lower 转换为小写字母
lsqnonlin 解非线性最小二乘问题
lu LU分解
M m
mad 平均绝对值偏差
magic 魔方阵
maple &nb, sp; 运作 Maple格式指令
mat2str 把数值数组转换成输入形态串数组
material 材料反射模式
max 找向量中最大元素
mbuild 产生EXE文件编译环境的预设置指令
mcc 创建MEX或EXE文件的编译指令
mean 求向量元素的平均值
median 求中位数
menuedit 启动设计用户菜单的交互式编辑工具
mesh 网线图
meshz 垂帘网线图
meshgrid 产生"格点"矩阵
methods 获知对指定类定义的所有方法函数
mex 产生MEX文件编译环境的预设置指令
mfunlis 能被mfun计算的MAPLE经典函数列表
mhelp 引出 Maple的在线帮助
min 找向量中最小元素
mkdir 创建目录
mkpp 逐段多项式数据的明晰化
mod 模运算
more 指令窗中内容的分页显示
movie 放映影片动画
moviein 影片帧画面的内存预置
mtaylor 符号计算多变量Taylor级数展开
N n
ndims 求数组维数
NaN 非数（预定义）变量
nargchk 输入宗量数验证
nargin 函数输入宗量数
nargout 函数输出宗量数
ndgrid 产生高维格点矩阵
newplot 准备新的缺省图、轴
nextpow2 取最接近的较大2次幂
nnz 矩阵的非零元素总数
nonzeros 矩阵的非零元素
norm 矩阵或向量范数
normcdf 正态分布累计概率密度函数
normest 估计矩阵2范数
norminv 正态分布逆累计概率密度函数
normpdf 正态分布概率密度函数
normrnd 正态随机数发生器
notebook 启动Matlab和Word的集成环境
null 零空间
num2str 把非整数数组转换为串
numden 获取最小公分母和相应的分子表达式
nzmax 指定存放非零元素所需内存
O o
ode1 非Stiff 微分方程变步长解算器
ode15s Stiff 微分方程变步长解算器
ode23t 适度Stiff 微分方程解算器
ode23tb Stiff 微分方程解算器
ode45 非Stiff 微分方程变步长解算器
odefile ODE 文件模板
odeget 获知ODE 选项设置参数
odephas2 ODE 输出函数的二维相平面图
odephas3 ODE 输出函数的三维相空间图
odeplot ODE 输出函数的时间轨迹图
odeprint 在Matlab指令窗显示结果
odeset 创建或改写 ODE选项构架参数值
ones 全1数组
optimset 创建或改写优化泛函指令的选项参数值
orient 设定图形的排放方式
orth 值空间正交化
P p
pack 收集Matlab内存碎块扩大内存
pagedlg 调出图形排版对话框
patch 创建块对象
path 设置Matlab搜索路径的指令
pathtool 搜索路径管理器
pause 暂停
pcode 创建预解译P码文件
pcolor 伪彩图
peaks Matlab提供的典型三维曲面
permute 广义转置
pi （预定义变量）圆周率
pie 二维饼图
pie3 三维饼图
pink 粉红色图矩阵
pinv 伪逆
plot 平面线图
plot3 三维线图
plotmatrix 矩阵的散点图
plotyy 双纵坐标图
poissinv 泊松分布逆累计概率分布函数
poissrnd 泊松分布随机数发生器
pol2cart 极或柱坐标变为直角坐标
polar 极坐标图
poly 矩阵的特征多项式、根集对应的多项式
poly2str 以习惯方式显示多项式
poly2sym 双精度多项式系数转变为向量符号多项式
polyder 多项式导数
polyfit 数据的多项式拟合
polyval 计算多项式的值
polyvalm 计算矩阵多项式
pow2 2的幂
ppval 计算分段多项式
pretty 以习惯方式显示符号表达式
print 打印图形或SIMULINK模型
printsys 以习惯方式显示有理分式
prism 光谱色图矩阵
procread 向MAPLE输送计算程序
profile 函数文件性能评估器
propedit 图形对象属性编辑器
pwd 显示当前工作目录
Q q
quad 低阶法计算数值积分
quad8 高阶法计算数值积分(QUADL)
quit 推出Matlab 环境
quiver 二维方向箭头图
quiver3 三维方向箭头图
R r
rand 产生均匀分布随机数
randn 产生正态分布随机数
randperm 随机置换向量
range 样本极差
rank 矩阵的秩
rats 有理输出
rcond 矩阵倒条件数估计
real 复数的实部
reallog 在实数域内计算自然对数
realpow 在实数域内计算乘方
realsqrt 在实数域内计算平方根
realmax 最大正浮点数
realmin 最小正浮点数
rectangle 画"长方框"
rem 求余数
repmat 铺放模块数组
reshape 改变数组维数、大小
residue 部分分式展开
return 返回
ribbon 把二维曲线画成三维彩带图
rmfield 删去构架的域
roots 求多项式的根
rose 数扇形图
rot90 矩阵旋转90度
rotate 指定的原点和方向旋转
rotate3d 启动三维图形视角的交互设置功能
round 向最近整数圆整
rref 简化矩阵为梯形形式
rsf2csf 实数块对角阵转为复数特征值对角阵
rsums Riemann和
S s
save 把内存变量保存为文件
scatter 散点图
scatter3 三维散点图
sec 正割
sech 双曲正割
semilogx X轴对数刻度坐标图
semilogy Y轴对数刻度坐标图
series 串联连接
set 设置图形对象属性
setfield 设置构架数组的域
setstr 将ASCII码转换为字符的旧版指令
sign 根据符号取值函数
signum 符号计算中的符号取值函数
sim 运行SIMULINK模型
simget 获取SIMULINK模型设置的仿真参数
simple 寻找最短形式的符号解
simplify 符号计算中进行简化操作
simset 对SIMULINK模型的仿真参数进行设置
simulink 启动SIMULINK模块库浏览器
sin 正弦
sinh 双曲正弦
size 矩阵的大小
slice 立体切片图
solve 求代数方程的符号解
spalloc 为非零元素配置内存
sparse 创建稀疏矩阵
spconvert 把外部数据转换为稀疏矩阵
spdiags 稀疏对角阵
spfun 求非零元素的函数值
sph2cart 球坐标变为直角坐标
sphere 产生球面
spinmap 色图彩色的周期变化
spline 样条插值
spones 用1置换非零元素
sprandsym 稀疏随机对称阵
sprank 结构秩
spring 紫黄调春色图
sprintf 把格式数据写成串
spy 画稀疏结构图
sqrt 平方根
sqrtm 方根矩阵
squeeze 删去大小为1的"孤维"
sscanf 按指定格式读串
stairs 阶梯图
std 标准差
stem 二维杆图
step 阶跃响应指令
str2double 串转换为双精度值
str2mat 创建多行串数组
str2num 串转换为数
strcat 接成长串
strcmp 串比较
strjust 串对齐
strmatch 搜索指定串
strncmp 串中前若干字符比较
strrep 串替换
strtok 寻找第一间隔符前的内容
struct 创建构架数组
struct2cell 把构架转换为元胞数组
strvcat 创建多行串数组
sub2ind 多下标转换为单下标
subexpr 通过子表达式重写符号对象
subplot 创建子图
subs 符号计算中的符号变量置换
subspace 两子空间夹角
sum 元素和
summer 绿黄调夏色图
superiorto 设定优先级
surf 三维着色表面图
surface 创建面对象
surfc 带等位线的表面图
surfl 带光照的三维表面图
surfnorm 空间表面的法线
svd 奇异值分解
svds 求指定的若干奇异值
switch-case-otherwise 多分支结构
sym2poly 符号多项式转变为双精度多项式系数向量
symmmd 对称最小度排序
symrcm 反向Cuthill-McKee排序
syms 创建多个符号对象
T t
tan 正切
tanh 双曲正切
taylortool 进行Taylor逼近分析的交互界面
text 文字注释
tf 创建传递函数对象
tic 启动计时器
title 图名
toc 关闭计时器
trapz 梯形法数值积分
treelayout 展开树、林
treeplot 画树图
tril 下三角阵
trim 求系统平衡点
trimesh 不规则格点网线图
trisurf 不规则格点表面图 triu 上三角阵 try-catch 控制流中的Try-catch结构 type 显示M文件
U u
uicontextmenu 创建现场菜单
uicontrol 创建用户控件
uimenu 创建用户菜单
unmkpp 逐段多项式数据的反明晰化
unwrap 自然态相角
upper 转换为大写字母
V v
var 方差
varargin 变长度输入宗量
varargout 变长度输出宗量
vectorize 使串表达式或内联函数适于数组运算
ver 版本信息的获取
view 三维图形的视角控制
voronoi Voronoi多边形
vpa 任意精度（符号类）数值
W w
warning 显示警告信息
what 列出当前目录上的文件
whatsnew 显示Matlab中 Readme文件的内容
which 确定函数、文件的位置
while 控制流中的While环结构
white 全白色图矩阵
whitebg 指定轴的背景色
who 列出内存中的变量名
whos 列出内存中变量的详细信息
winter 蓝绿调冬色图
workspace 启动内存浏览器
X x , Y y , Z z
xlabel X轴名
xor 或非逻辑
yesinput 智能输入指令
ylabel Y轴名
zeros 全零数组
zlabel Z轴名
zoom 图形的变焦放大和缩小
ztrans 符号计算Z变换
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