moRe R examples - TTests, etc
R introduction - week #4, class #1 for Fall 2014


  1. Some wow graphics to show you up front what R can do to help you visualize the patterns in your data:
    > demo()
       
    > demo(package = .packages(all.available = TRUE))
    >
    > 
    > demo(graphics)
    
    
            demo(graphics)
            ---- ~~~~~~~~
    
    Type     to start : 
    
  2. ls() lists the contents of your workspace.
    > ls()
     [1] "b"            "bmi"          "bp.obese"     "c"            "caesar.shoe" 
     [6] "coking"       "d"            "daily.intake" "energy"       "fake.trypsin"
    [11] "heart.rate"   "hh"           "ht"           "ht2"          "IgM"         
    [16] "intake"       "juul"         "LETTERS"      "m"            "wt"          
    [21] "x"            "xbar"    
    
  3. Using sequences, concatenate, etc.
    > myVector<-c(11,22.2,33,44,55,66)
      
    > myVector2 <- c(1.3, 1.4, 1.6, 1.75, 1.9, 2.1)
      
    > seq(1,40,2)
     [1]  1  3  5  7  9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
        
    > c<-seq(11,30,2)
    > c
     [1] 11 13 15 17 19 21 23 25 27 29
        
    > d<-seq(1,20)
    > d
     [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
       
    > d*2-1
     [1]  1  3  5  7  9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
       
    > letters
     [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r" "s" "t" "u" "v"
    [23] "w" "x" "y" "z"
    
    
    
  4. Postional arguments and named argument. pch is the NAME of an argument. Postional matching is used on 1st plot, both positional and named actual argument approach is used on the 2nd plot, and finally the 3rd plot uses only named actual arguments.
    > 
    > plot(myVector,myVector2)
    > 
    > plot(myVector,myVector2,pch=8)
         
    > plot(pch=3,y=myVector2,x=myVector)
    
    
  5. Pages 83-84 of Peter Dalgaard Introductory Statistics with R - daily energy intake in kJ for 11 women.
    > daily.intake <- c(5260,5470,5640,6180,6390,6515,6805,7515,7515,8230,8770)
    
    > mean(daily.intake)
    [1] 6753.636
    
    > sd(daily.intake)
    [1] 1142.123
    
    > quantile(daily.intake)
      0%  25%  50%  75% 100% 
    5260 5910 6515 7515 8770 
    
    > t.test(daily.intake,mu=7725)
    
            One Sample t-test
    
    data:  daily.intake 
    t = -2.8208, df = 10, p-value = 0.01814
    alternative hypothesis: true mean is not equal to 7725 
    95 percent confidence interval:
     5986.348 7520.925 
    sample estimates:
    mean of x 
     6753.636 
    
    
  6. How do you get the data frames that are used in many of the R tutorials and that are used in the Peter Dalgaard book for all examples?
    > library(ISwR)
    
                    energy, intake and juul are three of the many data sets in the ISwR library.
                    ------  ------     ----
    
  7. Two-sample t test - daily energy expenditure comparisons - lean versus obese women study.
    > data(energy)
    > attach(energy)
    > energy
       expend stature
    1    9.21   obese
    2    7.53    lean
    3    7.48    lean
    4    8.08    lean
    5    8.09    lean
    6   10.15    lean
    7    8.40    lean
    8   10.88    lean
    9    6.13    lean
    10   7.90    lean
    11  11.51   obese
    12  12.79   obese
    13   7.05    lean
    14  11.85   obese
    15   9.97   obese
    16   7.48    lean
    17   8.79   obese
    18   9.69   obese
    19   9.68   obese
    20   7.58    lean
    21   9.19   obese
    22   8.11    lean
    
    > t.test(expend~stature)
    
            Welch Two Sample t-test
    
    data:  expend by stature 
    t = -3.8555, df = 15.919, p-value = 0.001411
    alternative hypothesis: true difference in means is not equal to 0 
    95 percent confidence interval:
     -3.459167 -1.004081 
    sample estimates:
     mean in group lean mean in group obese 
               8.066154           10.297778 
    
    > t.test(expend~stature, var.equal=T)
    
            Two Sample t-test
    
    data:  expend by stature 
    t = -3.9456, df = 20, p-value = 0.000799
    alternative hypothesis: true difference in means is not equal to 0 
    95 percent confidence interval:
     -3.411451 -1.051796 
    sample estimates:
     mean in group lean mean in group obese 
               8.066154           10.297778 
    
    
  8. Are the group variances the same? Using the var.test R function to test the equal variances assumption. Section 4.4 of Dalgaard book. Comparison of variances.
    > var.test(expend~stature)
    
            F test to compare two variances
    
    data:  expend by stature 
    F = 0.7844, num df = 12, denom df = 8, p-value = 0.6797
    alternative hypothesis: true ratio of variances is not equal to 1 
    95 percent confidence interval:
     0.1867876 2.7547991 
    sample estimates:
    ratio of variances 
              0.784446 
    
  9. The paired t test examples.
    > data(intake)
    > attach(intake)
    > intake
        pre post
    1  5260 3910
    2  5470 4220
    3  5640 3885
    4  6180 5160
    5  6390 5645
    6  6515 4680
    7  6805 5265
    8  7515 5975
    9  7515 6790
    10 8230 6900
    11 8770 7335
       
    > post - pre
     [1] -1350 -1250 -1755 -1020  -745 -1835 -1540 -1540  -725 -1330 -1435
     
     > t.test(pre, post, paired=T)
    
            Paired t-test
    
    data:  pre and post 
    t = 11.9414, df = 10, p-value = 3.059e-07
    alternative hypothesis: true difference in means is not equal to 0 
    95 percent confidence interval:
     1074.072 1566.838 
    sample estimates:
    mean of the differences 
                   1320.455 
    
    > t.test(pre, post)  # This is WRONG for above data!!!!
    
            Welch Two Sample t-test
    
    data:  pre and post 
    t = 2.6242, df = 19.92, p-value = 0.01629
    alternative hypothesis: true difference in means is not equal to 0 
    95 percent confidence interval:
      270.5633 2370.3458 
    sample estimates:
    mean of x mean of y 
     6753.636  5433.182 
    
  10. The juul data frame has 1,339 rows and 6 columns. IGF1 is Insulin-like Growth Factor. It is measured in mg/l, micrograms per liter.
    > data(juul)
       
    > attach(juul)
    
    > mean(igf1)
    [1] NA
    
    > mean(igf1,na.rm=T)
    [1] 340.168
        
    > summary(igf1)
       Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
       25.0   202.2   313.5   340.2   462.8   915.0   321.0 
    
  11. In R, the data sets NA's could be counted like this too, since TRUE is converted to 1 and FALSE is converted to 0 when we apply arithmetic operations or R functions that expect numeric input to TRUE and FALSE.
    > sum(!is.na(igf1))
    [1] 1018
      
    > sum(is.na(igf1))
    [1] 321
       
    > 1018 + 321
    [1] 1339         The juul data set is 1,339 rows and 6 columns...
    
  12. Making a variable categorical or a factor in R is often necessary.
    > summary(juul)
          age            menarche            sex             igf1      
     Min.   : 0.170   Min.   :  1.000   Min.   :1.000   Min.   : 25.0  
     1st Qu.: 9.053   1st Qu.:  1.000   1st Qu.:1.000   1st Qu.:202.2  
     Median :12.560   Median :  1.000   Median :2.000   Median :313.5  
     Mean   :15.095   Mean   :  1.476   Mean   :1.534   Mean   :340.2  
     3rd Qu.:16.855   3rd Qu.:  2.000   3rd Qu.:2.000   3rd Qu.:462.8  
     Max.   :83.000   Max.   :  2.000   Max.   :2.000   Max.   :915.0  
     NA's   : 5.000   NA's   :635.000   NA's   :5.000   NA's   :321.0  
         tanner           testvol       
     Min.   :  1.000   Min.   :  1.000  
     1st Qu.:  1.000   1st Qu.:  1.000  
     Median :  2.000   Median :  3.000  
     Mean   :  2.640   Mean   :  7.896  
     3rd Qu.:  5.000   3rd Qu.: 15.000  
     Max.   :  5.000   Max.   : 30.000  
     NA's   :240.000   NA's   :859.000  
    
    > juul$sex <- factor(juul$sex, labels=c("Male","Female"))
     
    > summary(juul)
          age            menarche           sex           igf1      
     Min.   : 0.170   Min.   :  1.000   Male  :621   Min.   : 25.0  
     1st Qu.: 9.053   1st Qu.:  1.000   Female:713   1st Qu.:202.2  
     Median :12.560   Median :  1.000   NA's  :  5   Median :313.5  
     Mean   :15.095   Mean   :  1.476                Mean   :340.2  
     3rd Qu.:16.855   3rd Qu.:  2.000                3rd Qu.:462.8  
     Max.   :83.000   Max.   :  2.000                Max.   :915.0  
     NA's   : 5.000   NA's   :635.000                NA's   :321.0      
    
  13. The IgM data set is only a single column of data, i.e. a single numeric vector or a single variable. The Serum IgM (Immunoglobulin G) level in 298 children ranging in age from 6 months to 6 years. IgM is measured in gram/liter, i.e. g/l for the units.
    > library(ISwR)
    > 
    > data(IgM)
    > 
    > stripchart(IgM,method="stack")
        
    > summary(IgM)
       Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
      0.100   0.500   0.700   0.803   1.000   4.500 
         
    > sd(IgM)
    [1] 0.4694982
    > 
    > mean(IgM)
    [1] 0.8030201