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Hands-on Introduction to R 3 2 1 0 1 2 3 Why Leaning Programing? • We live in oceans of data. Computers are essential to record and help analyse it. • Competent scientists speak C/C++, Java, MATLAB, Python, Perl, R and/or Mathematica • Data collection and analysis very important in Forensic Science since NAS 2009 • Using the above languages, codes can easily be made available for review/discovery Getting a computer to do anything useful • All machines understand is on/off! • • • • High/low voltage High/low current High/low charge 1/0 binary digits (bits) • To make a computer do anything, you have to speak machine language to it: 000000 00001 00010 00110 00000 100000 Add 1 and 2. Store the result.Wikipedia Getting a computer to do anything useful • Machine language is not intuitive and can vary a great deal over designs • The basic operations operations however are the same, e.g.: • • • • Move data here Combine these values Store this data Etc. • “Human readable” language for basic machine operations: assembly language Getting a computer to do anything useful • Assembly is still cumbersome for (most) humans 10110000 01100001 MOV AL, 61h A machine encoding Assembly Move the number 97 over to “storage area” AL Getting a computer to do anything useful • Better yet is a more “Englishy”, “high-level” language • Enter: C, C++, Fortran, Java, … • Higher level languages like these are translated (“compiled”) to machine language • Not exactly true for Java, but it’s something analogous… Getting a computer to do anything useful • Even more “Englishy” and “high-level” are interpreted languages • Enter: R MATLAB, Perl, Python, Mathematica, Maple, … • The “code” of these languages are “interpreted” as commands by a program that is already running • They make many assumptions behind the scenes • Much easier to program with • Much slower than compiled languages Why ? • R is not a black box! • Codes available for review; totally transparent! • R maintained by a professional group of statisticians, and computational scientists • From very simple to state-of-the-art procedures available • Very good graphics for exhibits and papers • R is extensible (it is a full scripting language) • Coding/syntax similar to Python and MATLAB • Easy to link to C/C++ routines Why ? • Where to get information on R : • R: http://www.r-project.org/ • Just need the base • RStudio: http://rstudio.org/ • A great IDE for R • Work on all platforms • Sometimes slows down performance… • CRAN: http://cran.r-project.org/ • Library repository for R • Click on Search on the left of the website to search for package/info on packages Finding our way around R/RStudio Handy Commands: • Basic Input and Output Numeric input x <- 4 variables: store information :Assignment operator x <- “text goes in quotes” Text (character) input Handy Commands: • Get help on an R command: • If you know the name: ?command name • ?plot brings up html on plot command • If you don’t know the name: • Use Google (my favorite) • ??key word Handy Commands: • R is driven by functions: func(arguement1, argument2) function name input to function goes in parenthesis function returns something; gets dumped into x x <- func(arg1, arg2) Handy Commands: • Input from Excel • Save spreadsheet as a CSV file • Use read.csv function • Needs the path to the file Mac e.g.: "/Users/npetraco/latex/papers/data.csv” Windows e.g.: “C:\Users\npetraco\latex\papers\data.csv” *Exercise: basicIO.R Handy Commands: • Matrices: X • X[,1] returns column 1 of matrix X • X[3,] returns row 3 of matrix X • Handy functions for data frames and matrices: • dim, nrow, ncol, rbind, cbind • User defined functions syntax: • func.name <- function(arguements) { do something return(output) } • To use it: func.name(values) First Thing: Look at your Data o Explore the Glass dataset of the mlbench package 14 13 12 11 Na 15 16 17 • Source (load) all_data_source.R • *visualize_with_plots.r • Scatter plots: plot any two variables against each other 1.515 1.520 1.525 RI 1.530 First Thing: Look at your Data • Pairs plots: do many scatter plots at once 1 2 3 4 5 6 73 74 75 0 4 5 6 70 71 72 Si 12 14 16 0 1 2 3 K 6 8 10 Ca 70 71 72 73 74 75 6 8 10 12 14 16 First Thing: Look at your Data • Histograms: “bin” a variable and plot frequencies 60 50 Percent of Total 40 30 20 10 0 1.510 1.515 1.520 1.525 RI 1.530 1.535 First Thing: Look at your Data • Histograms conditioned on other variables: use lattice package 1.5101.5151.5201.5251.5301.535 5 6 7 80 60 40 RIs Conditioned on glass group membership Percent of Total 20 0 1 2 3 80 60 40 20 0 1.5101.5151.5201.5251.5301.535 1.5101.5151.5201.5251.5301.535 RI First Thing: Look at your Data • Probability density plots: also needs lattice 200 Density 150 100 50 0 1.510 1.515 1.520 1.525 RI 1.530 1.535 First Thing: Look at your Data • Empirical Probability Distribution plots: also called empirical cumulative density 1.0 Empirical CDF 0.8 0.6 0.4 0.2 0.0 1.515 1.520 1.525 RI 1.530 1.535 First Thing: Look at your Data • Box and Whiskers plots: range possible outliers possible outliers 25th-%tile 1st-quartile 1.5188 1.5189 median 50th-%tile 1.5190 RI 75th-%tile 3rd-quartile 1.5191 1.5192 Visualizing Data • Note the relationship: First Thing: Look at your Data • Box and Whiskers plots: 60 40 values values 5 0 20 0 Al Ba Ca Fe K Mg Na Box-Whiskers plots for actual variable values RI Si Al Ba Ca Fe K Mg Na RI Box-Whiskers plots for scaled variable values Si Confidence Intervals • A confidence interval (CI) gives a range in which a true population parameter may be found. • Specifically, (1 – a)×100% CIs for a parameter, constructed from a random sample (of a given sample size), will contain the true value of the parameter approximately (1 – a)×100% of the time. • Different from tolerance and prediction intervals Confidence Intervals • Caution: IT IS NOT CORRECT to say that there a (1 - a)×100% probability that the true value of a parameter is between the bounds of any given CI. Take a sample. Compute a CI. Here 90% of the CIs contain the true value of the parameter Graphical representation of 90% CIs is for a parameter: true value of parameter Confidence Intervals • Construction of a CI for a mean depends on: • Sample size n s • Standard error for means sx n • Level of confidence 1-a • a is significance level • Use a to compute tc-value • (1-a )×100% CI for population mean using a sample average and standard error is: x tc sx , x tc sx Confidence Intervals • Compute a 99% confidence interval for the mean using this sample set: Fragment # Fragment nD 1 1.52005 2 1.52003 3 1.52001 4 1.52004 5 1.52000 6 1.52001 7 1.52008 8 1.52011 9 1.52008 10 1.52008 11 1.52008 x 1.52005 s 0.0004 sx 0.0001 α 0.01 (a/2=0.005) tc = 3.17 Putting this together: [1.52005 - (3.17)(0.00001), 1.52005 + (3.17)(0.00001)] 99% CI for sample = [1.52002, 1.52009] *Try out confidence_intervals.R