ETSUMath Department Colloquium Got

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ETSU-Math Department ColloquiumGot ?

• Edith Seier
• 10/31/05
• If you wish go to
• http//www.etsu.edu/math/seier/Rtalk.htm

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• What is R?
• What can we do with R?
• How to work with R
• Who can use R?
• Who really needs R?
• Learning R.
• Should we teach R at ETSU?

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What is R ?

• Its developers (Robert Gentleman and Ross,
  Statistics Department of the University of
  Auckland) define it as an environment in which
  statistical techniques are implemented. The
  programming language R started as a free teaching
  version of the S language (developed by Chambers,
  Becker and Wilks at Bell Laboratories), it is
  considered a dialect of S and in 1995 was put in
  the public domain. (The commercial version of S
  of use in the academia is S-Plus)
• New packages of functions are being created and
  its development is an international effort. All
  the information about the R project is available
  from
• 
  http//www.r-project.org
• Its use in advanced statistical topics,
  bioinformatics and biostatistics is constantly
  growing and
• It is free!!!
• Notes.-
• There are versions for Mac, Windows Linux
• It can be linked to C or Fortran for
  computationally intensive tasks
• The language has some affinities to Lisp
  (Lisp-Stat?) and APL

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Where can we get R?

• The web page shown at the right is
• http//www.r-project.org
• There we can find
• The basic program
• Additional packages of functions
• Manuals in several languages

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What can we do with R?

• Basic statistical calculations and graphs
• Write functions that are not included in
  commercial statistical software.
• Use it to teach upper division/graduate courses
  when we want the students to be aware of the
  steps needed to solve a problem instead of using
  a totally menu (point and click) menu driven
  program. (at least some times)
• To use packages written in R for specialized
  areas such as spatial statistics, survival
  analysis, microarray data analysis, generalized
  linear models, etcetera.

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How to work with R

• Using R
• To start data entry
• Operations, transformations.
• Descriptive statistics graphs
• More graphs and calculations
• Writing our own functions in R
• Interactive Statistics with R (Motoya Machida
  TNTechU)
• Using packages in R

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Starting and entering data

• 1)Once you have downloaded R from
• http//www.r-project.org
• click on the icon

• You can
• Use data sets that come with R, data()
• Type your own data
• Read ascii data files
• Import data from other software
• Generate random numbers and sequences

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Typing data in R

• Decide the name of the object where you will
  store the data
• name lt- c( , , , , )
• Example Cigarette consumption per capita in 1930
  (Freeman et al (1970) Statistics )
• Categorical data
• countrylt-c("Australia" , "Canada", Denmark"
  ,"Finland", England" , "Island" , Netherlands"
  , Norway",
• Sweden", "Switzerland", USA" )
• Numerical data
• cigarettelt-c(480,500,380,1100,1100,230,490,250,300
  ,510,1300)
• Labels for the data
• If you want to put labels to the data use the
  command names.
• names(cigarette)lt-country
• Now type cigarettes to see the data, in the
  screen you will see
• Australia Canada Denmark Finland England
  Island Netherland
• 480 500 380 1100
  1100 230 490
• Norway Sweden Switzerland USA
• 250 300 510 1300

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Generating data

• a) Sequences
• ilt-seq(0,10,by2) will create the sequence
• 0,2,4,6,8,10
• b) Evaluating functions. First we need to create
  the argument of the function
• tlt-seq(0,60,by0.01)
• Y lt-cos(t)
• c) Generating random numbers
• xlt-rnorm(500)

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Operations, transformations

• The arithmetic operations are done with the usual
  symbols - / . For example, if we want to
  convert weights in pounds into kilos
  weightklweightlb/2.2
• Some useful transformations are
• exp( ) , for power
• log( ) for natural logarithms
• log10( ) for base 10 logarithms
• Trigonometric functions
• sin(), cos(), tan(), asin(), atan(), acos()

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Descriptive statisticstasamortlt-c(180,150,170,350
,460,60,240,90,110,250,200)

• gt length(tasamort)
• 1 11
• gt sum(tasamort)
• 1 2260
• gt mean(tasamort)
• 1 205.4545
• gt median(tasamort)
• 1 180
• gt sd(tasamort)
• 1 117.2488
• gt var(tasamort)
• 1 13747.27

gt quantile(tasamort,0.5) 50 180 gt
min(tasamort) 1 60 gt max(tasamort) 1
460 summary(tasamort) Min. 1st Qu. Median
Mean 3rd Qu. Max. 60.0 130.0 180.0
205.5 245.0 460.0 cor(x,y)
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Statistical graphs and plots of functions
hist(variable)
plot(cigarette,deathrate) abline(67.56 , 0.22844)
boxplot(variable)
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• Among the graphs for which R has commands are
• Practically all the graphs from Multivariate
  Analysis
• Mosaic graphs (for categorical variables)
• Smoothing in regression
• Time series plots
• Plots from Microarray data analysis
• If in the menu of R we click on Help, and then
  Search help and write plot, a list of graphs in
  R will appear.
• In the next slide we have copied and pasted the
  plot displays from R .screenshots in
  http//www.r-project.org

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• R can be use to do statistical calculations
  related to
• Test of hypotheses
• Analysis of Variance and Covariance
• Probability Distributions
• Tests for two-way tables (Chi-cuadrado, McNemar
  etc.)
• Multiple regression
• Calculation of sample size
• Logistic regression
• Survival analysis
• All these topics are explained in
• Dalgaard, P.(2002)Introductory Statistics with
  R Springer Verlag.
• There are also several manuals and other books on
  specific topics such as Linear Models,
  Bioinformatics, etcetera. Also some general
  methods books have instructions in R. For
  example
• Heiberger Holland (2004) Statistical Analysis
  and Data Display, An Intermediate Course with
  Examples in S-Plus, R, and SAS. Springer Verlag
  
• In http//www.r-project.org you can find manuals
  and tutorials that can be downloaded for free
  (not only in English but in some other languages)

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Writing our own functions in R Example
calculating a confidence interval for the mean
absolute deviation

• In a sample, MAD is calculated as the average of
  the distances of the values to the median.
• In Bonett Seier (2003), Confidence Intervals
  for Mean Absolute Deviations The American
  Statistical Association, Vol 57 4 the following
  formula for the confidence interval for the
  population mean absolute deviation was derived

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Once we have copied and pasted the function citau
into R, we simply write citau(x,1.96) To
calculate the CI for the data in x
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• In Bonett, D.G. and Seier, E. (2005) 
  Confidence Interval for a Coefficient of
  Dispersion in Non-normal Distributions.
  Biometrical Journal 47  (5) pp 1-5, we included
  the following program to calculate the Confidence
  interval for COD we were defining in the paper
• CODCIlt-function(x,z)mdmedian(x) mmean(x)
  vvar(x) taumean(abs(x-md))
• del(m-md)/tau nlength(x) cn/(n-1)
  gamv/(tau2)
• codtau/median(x)a1round(((n1)/2)-sqrt(n))
  a2n-a11
• sxsort(x) l1log(sxa1) u1log(sxa2)
  se1(u1-l1)/4 se2sqrt((gam(del2)-1)/n)
• fmsqrt(1/(4n(se12)))covtm(m-md)/(2nfmtau)
  ksqrt(se12se22-2covtm)/(se1se2)
• b1round((n1)/2-kzsqrt(n/4))
  b1round((n1)/2-kzsqrt(n/4)) b2n-b11
• l1log(sxb1) u1log(sxb2)
  l2log(ctau)-kzse2 u2log(ctau)kzse2
• ll1exp(l2-u1) ul1exp(u2-l1) cilt-
  c(ll1,cod,ul1) ci

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The output of a function could be a plot.
Example periodogram

• this function calculates the periodogram and
  displays its graph
• perioplotlt-function(x)
• adjxx-mean(x) substracts the mean of
  the series
• tffft(adjx) calculates
  FFT nflength(tf) n2nf/21 decides
  the number of frequencies
• pritflt-tfc(1n2) takes the elements of
  the FFT
• intensitylt-(abs(pritf2))/nf calculates the
  ordinates of periodogram
• nyquist1/2 pfreqlt-seq(0,nf/2,by1)
  preparation for frequencies
• freqlt-pfreq/(length(pfreq)-1)nyquist
  calculates frequencies
• plot(freq,intensity,type"l")
• After reading a data set, for example sunspots,
  we type
• perioplot(sunspots)

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Things I am still avoiding in R

• Loops (it can be done..) but there are ways to
  get around that sometimes by using
  matrices.Example

estspeclt-function(au) Mlt-length(au)
counts how many autocorrelations (M) we
read jlt-seq(1,M,by1) creates sub-indexes
j1M lam0.5(1cos(jpi/M)) calculates
Tukeys weights wlt-seq(0,pi,bypi/50)
calculates angular frequencies lact(lam)au
multiplies each weight by the corresponding
autocorrelation flt-function(j,w) cos(jw)
zlt-outer(j,w,f)
calculates cos j w for all values of w and
j szlt-lacz obtains the
sum of weights correlations cos
jw hlt-(1/(2pi))(12sz) calculates
h(w) plot(w,h ,type"l",mainEstimated spectral
density )
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A user friendly version for teaching STATS
without writing commands

• Interactive Statistics with R developed by
• Motoya Machida, Math Department, Tennessee
  Technological University
• http//www.math.tntech.edu/ISR/index.html

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Packages in RExample Microarray data analysis

• The package DNAMR and DNAMRWeb developed by
  J.Cabrera at Rutgers University can be found in.
  At the left there is a program
• http//www.rci.rutgers.edu/cabrera/DNAMR/
• The graph at the right was obtained with
  DNAMRWeb for clustering the most important genes
  for the Kahn data (each row is a gene and each
  column is a microarray)

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Other Packages of functions written in R

• nlme Linear and nonlinear
  mixed effects models
• nnet Feed-forward Neural
  Networks and Multinomial
• Log-Linear Models
• rpart Recursive Partitioning
• spatial Functions for Kriging and
  Point Pattern
• Analysis
• splines Regression Spline
  Functions and Classes
• stats The R Stats Package
• stats4 Statistical functions
  using S4 classes
• survival Survival analysis,
  including penalised
• likelihood.
• tcltk Tcl/Tk Interface
• tools Tools for Package
  Development
• utils The R Utils Package

• Packages in library 'C/PROGRA1/R/rw2001/library'
  
• base The R Base Package
• boot Bootstrap R (S-Plus)
  Functions (Canty)
• class Functions for
  Classification
• cluster Functions for clustering
  (by Rousseeuw et al.)
• datasets The R Datasets Package
• foreign Read Data Stored by
  Minitab, S, SAS, SPSS,
• Stata, Systat, ...
• graphics The R Graphics Package
• grDevices The R Graphics Devices
  and Support for Colours
• and Fonts
• grid The Grid Graphics Package
• KernSmooth Functions for kernel
  smoothing for Wand
• Jones (1995)
• lattice Lattice Graphics
• MASS Main Package of Venables
  and Ripley's MASS
• methods Formal Methods and
  Classes
• mgcv GAMs with GCV smoothness
  estimation and GAMMs
• by REML/PQL

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Who can use R?

• Anybody who wants to have a free statistical
  software at home or the office
• Schools that can not afford to buy licenses of
  statistical software
• When we teach courses outside campus in places
  without the software we have in campus for
  instance to teachers (I prefer R to Excel)
• Statisticians to write programs to do
  calculations that are not included in commercial
  software

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Who really needs R?

• If we are in an area of Statistics that has been
  developed more in R than in commercial software
  (spatial statistics etc.)
• People working in Bioinformatics, Microarray
  data analysis etc.

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• Will R push out commercial
• statistical software?
• Probably not in general but its use will increase
  in the academic environment.
• Minitab is user friendly for classroom use in
  Intro STATS courses but R could be an option for
  schools that can not afford to have MTB.
• People in social sciences are too used to SPSS.
• SAS has very good data management options for
  large data sets so probably in the big
  corporations SAS will prevail but in the academic
  environment R could be an option for advanced
  courses (SAS is quite expensive) .
• At least for a few years R probably will be used
  in environments with statistical sophistication
  and with some programming knowledge statistics
  departments of universities and research
  institutes until more user friendly versions are
  developed. Maybe the commercial software will
  take a turn more into the business world and R
  will take more of the academic/research world.

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Should we teach R at ETSU?

• Yes!! Maybe not in Math 1530 but we could
  introduce it in upper division courses. Why?
• Students planning for a grad school in
  Statistics, Bioinformatics, Biostatistics,
  Biomath would benefit from it.
• They would benefit of being able to work at home
  without buying or renting a statistical program.
• They would get familiar with an object oriented
  programming language
• Programming is good for you ? ! Why? Because you
  really have to understand a problem before
  writing a program to solve it

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Learning R

• There are several free manuals uploaded in the
  page of the R project
• http//www.r-project.org
• Books about R
• Introductory Statistics with R Peter Dalgaard
• Statistical Analysis and Data Display- An
  Intermediate Course with Examples in S-Plus, R
  and SAS
• A Handbook of Statistical Analysis using
  R-Everitt Hothorn (to appear in 2006)
• Bioinformatics for R Wiley 2006
• There is a tutorial in
• http//www.etsu.edu/math/seier/R.htm
• In Module 1 we give the basic commands to do
  calculations and graphs, the reader can search
  for more information using the HELP of R.
• In Module 2 we will learn how to write functions,
  i.e. we will learn how to program in R.
• You are welcome to use it.

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• Now we will browse the manual. Then we can Open R
  ( it is already installed in Room 205)
• see some demos
• and try some of the commands in
• http//www.etsu.edu/math/seier/commandsRtalk.doc