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Statistics: An Introduction using R

Computer software is an essential tool for many statistical modelling and data analysis techniques, aiding in the implementation of large data sets in order to obtain useful results. R is one of the most powerful and flexible statistical software packages available, and enables the user to apply a wide variety of statistical methods ranging from simple regression to generalized linear modelling. Statistics: An Introduction using R is a clear and concise introductory textbook to statistical analysis using this powerful and free software, and follows on from the success of the author's previous best-selling title Statistical Computing.
* Features step-by-step instructions that assume no mathematics, statistics or programming background, helping the non-statistician to fully understand the methodology.
* Uses a series of realistic examples, developing step-wise from the simplest cases, with the emphasis on checking the assumptions (e.g. constancy of variance and normality of errors) and the adequacy of the model chosen to fit the data.
* The emphasis throughout is on estimation of effect sizes and confidence intervals, rather than on hypothesis testing.
* Covers the full range of statistical techniques likely to be need to analyse the data from research projects, including elementary material like t-tests and chi-squared tests, intermediate methods like regression and analysis of variance, and more advanced techniques like generalized linear modelling.
* Includes numerous worked examples and exercises within each chapter.
* Accompanied by a website featuring worked examples, data sets, exercises and solutions:

http://www.imperial.ac.uk/bio/research/crawley/statistics

Statistics: An Introduction using R is the first text to offer such a concise introduction to a broad array of statistical methods, at a level that is elementary enough to appeal to a broad range of disciplines. It is primarily aimed at undergraduate students in medicine, engineering, economics and biology - but will also appeal to postgraduates who have not previously covered this area, or wish to switch to using R.

This little cottage, now hideously decorated by the carpet company which resides within, is one of the oldest buildings in Crawley. From the front there are so many silly advertising flags it's hard to see, but it's really more interesting round the back, where it's ancient roots show through in the form of half-timbering.

The cottage, known as Buckswood, was built in 1495 and extended later in its life. Farmland which surrounded the cottage was built on in the 1960s as Crawley's new town continued to expand. By some miracle it has survived, perhaps thanks to the Cheals family which once owned an extensive horticultural nursery in the town. The cottage sits almost surrounded by their garden centre, now called Squires.

More carpet offcuts. And the tardis. Why they had to put that in such a prominent place I don't know. It appears in the webcam too -I think the vicar should ask for it to be moved to somewhere less prominent. It is afterall right outside his front door and study window. I'm pretty sure that soon someone is going to be caught on the web cam going in or out.....LOL!

The high-level language of R is recognized as one of the most powerful and flexible statistical software environments, and is rapidly becoming the standard setting for quantitative analysis, statistics and graphics. R provides free access to unrivalled coverage and cutting-edge applications, enabling the user to apply numerous statistical methods ranging from simple regression to time series or multivariate analysis.
Building on the success of the author’s bestselling Statistics: An Introduction using R, The R Book is packed with worked examples, providing an all inclusive guide to R, ideal for novice and more accomplished users alike. The book assumes no background in statistics or computing and introduces the advantages of the R environment, detailing its applications in a wide range of disciplines.
Provides the first comprehensive reference manual for the R language, including practical guidance and full coverage of the graphics facilities.
Introduces all the statistical models covered by R, beginning with simple classical tests such as chi-square and t-test.
Proceeds to examine more advance methods, from regression and analysis of variance, through to generalized linear models, generalized mixed models, time series, spatial statistics, multivariate statistics and much more.
The R Book is aimed at undergraduates, postgraduates and professionals in science, engineering and medicine. It is also ideal for students and professionals in statistics, economics, geography and the social sciences.

The high-level language of R is recognized as one of the most powerful and flexible statistical software environments, and is rapidly becoming the standard setting for quantitative analysis, statistics and graphics. R provides free access to unrivalled coverage and cutting-edge applications, enabling the user to apply numerous statistical methods ranging from simple regression to time series or multivariate analysis.
Building on the success of the author’s bestselling Statistics: An Introduction using R, The R Book is packed with worked examples, providing an all inclusive guide to R, ideal for novice and more accomplished users alike. The book assumes no background in statistics or computing and introduces the advantages of the R environment, detailing its applications in a wide range of disciplines.
Provides the first comprehensive reference manual for the R language, including practical guidance and full coverage of the graphics facilities.
Introduces all the statistical models covered by R, beginning with simple classical tests such as chi-square and t-test.
Proceeds to examine more advance methods, from regression and analysis of variance, through to generalized linear models, generalized mixed models, time series, spatial statistics, multivariate statistics and much more.
The R Book is aimed at undergraduates, postgraduates and professionals in science, engineering and medicine. It is also ideal for students and professionals in statistics, economics, geography and the social sciences.


Excerpts from Chapter 4 of The R Book
Chapter 4: Level Set Trees and Code
Learn how to make a volume plot and a barycenter plot, and calculate level set trees with the algorithm LeafsFirst, which is implemented in function ``leafsfirst''. This function takes as an argument a piecewise constant function object.
The multimodal 2D example

(Click on image to enlarge)
We consider the density shown in the 2D three-modal density, and calculate first a piecewise constant function object representing this function, and then calculate the level set tree.
N<-c(35,35) # size of the grid pcf<-sim.data(N=N,type="mulmod") # piecewise constant function lst.big<-leafsfirst(pcf) # level set tree
We may make the volume plot with the command ''plotvolu(lst)''. However, it is faster first to prune the level set tree, and then plot the reduced level set tree. Function ''treedisc'' takes as the first argument a level set tree, as the second argument the original piecewise constant function, and the 3rd argument ''ngrid'' gives the number of levels in the pruned level set tree. We try the number of levels ngrid=100.
lst<-treedisc(lst.big,pcf,ngrid=100)
Now we may make a volume plot with the function ''plotvolu''.
plotvolu(lst)
We draw barycenter plots with the function ''plotbary''.
plotbary(lst,coordi=2) # 2nd coordinate
Note: We may find the number and the location of the modes with the ''modecent'' function, which takes as argument a level set tree. Function ''locofmax'' takes as argument a piecewise constant function and calculates the location of the maximum.
modecent(lst) locofmax(pcf)
The 3D tetrahedron example

(Click on image to enlarge)
We consider the 3-dimensional example. The calculation is much more time consuming this time.
N<-c(32,32,32) # the size of the grid pcf<-sim.data(N=N,type="tetra3d") # piecewise constant function lst.big<-leafsfirst(pcf) # level set tree lst<-treedisc(lst.big,pcf,ngrid=200) # pruned level set tree plotvolu(lst,modelabel=FALSE) # volume plot plotvolu(lst,cutlev=0.010,ptext=0.00045,colo=TRUE) # zooming coordi<-1 # coordinate, coordi = 1, 2, 3 plotbary(lst,coordi=coordi,ptext=0.0006) # barycenter plot
This time we have used parameter ''cutlev'' to make a zoomed volume plot. When this parameter is given, then only the part of the level set tree is shown which is above the value ''cutlev''. Typically it is better to zoom in to the volume plot by cutting the tails of the volume function away. This is achieved by the parameter ''xlim''. We may us for example the following command to make a ``vertically zoomed'' volume plot.
plotvolu(lst,xlim=c(140,220),ptext=0.00045, colo=TRUE,modelabel=FALSE)
Additional parameters which we have used are the ''modelabel'', which is used to suppress the plotting of the mode labels, ''ptext'', which lifts the mode labels with the given amount, and ''colo'', which colors the graph of the volume function to make a comparison with the barycenter plots easier.
The 4D pentahedron example

(Click on image to enlarge)
We consider the 4-dimensional example.
N<-c(16,16,16,16) pcf<-sim.data(N=N,type="penta4d") lst.big<-leafsfirst(pcf) lst<-treedisc(lst.big,pcf,ngrid=100) plotvolu(lst,modelabel=F) # volume plot plotvolu(lst,cutlev=0.0008,ptext=0.00039,colo=TRUE) # zooming coordi<-1 # coordinate, coordi = 1, 2, 3, 4 plotbary(lst,coordi=coordi,ptext=0.0003) # barycenter plot