Stat 141  Nov 3        Two-sample(treatment/control)inference:
t-test, nonparametric alternatives (Mann-Whiney, Duckworth) SW Ch 7.
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> #2-sample example 7.7 table 7.5 ancy.dat (con't 11/1)
$ancy
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.   sd
   5.80    7.40   11.00   11.01   13.00   19.50   4.72
$control
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.   sd
   9.60   12.40   16.60   15.91   19.93   21.20   4.78
> t.test(height~group)
        Welch Two Sample t-test
data:  height by group 
t = -1.9939, df = 12.783, p-value = 0.06795
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:   -10.2146719   0.4182434 
sample estimates:   mean in group ancy mean in group control 
                          11.01429              15.91250 
> # p-value .068 consistent with CI 95% including 0, CI for ancy-control
> #recreates by hand calc in SW 228-229, df Welch df SW eq 7.1
> qt(.975, 12.8)      [1] 2.163805
> # matches SW p.229 "t-multiplier" in CI or critical value for test statistic

> #for the old-fashioned "pooled" solution, original 2-sample t
> t.test(height~group, var.equal = TRUE)
        Two Sample t-test
data:  height by group 
t = -1.9919, df = 13, p-value = 0.06781
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:   -10.2106670   0.4142385 
sample estimates:    mean in group ancy mean in group control 
                         11.01429              15.91250 

> # see also hypothesis tests SW pp.238-9, p-values 237-8, TypeI,II errors 252-4

> # directional hypoth ex, feeding lambs niacin (you don't want it even if MD says)
> # SW lamb data (ex7.20,7.22) not available, so go to rats sniffing glue 
   tuolene ex 7.9-7.11 etc; mtb analysis p. 262
> glue = read.table(file="D:\\stat141\\toluene.dat", header = T)
> tapply(NE.conc, group, sort)
$control                          $Toluene                              
[1] 385 387 412 502 535           [1] 431 523 543 549 564 635
> t.test(NE.conc ~group, alt = "less")
        Welch Two Sample t-test
data:  NE.conc by group 
t = -2.3447, df = 8.451, p-value = 0.02272
alternative hypothesis: true difference in means is less than 0 
95 percent confidence interval:   -Inf -20.52321 
sample estimates:   mean in group control mean in group Toluene 
                             444.2000              540.8333 
> # matches Minitab on SW p.262, modulo sign

> # t-test assumptions; tissue inflamation exp.281, 
              log-transform then parametric t-test
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Nonparametric Alternatives: Can you (should you) do arithmetic on the data?
> #Wilcoxon-Mann-Whitney SW sec 7.11 p.288      # soil respiration 7.17 p.289
> soil = read.table(file="D:\\stat141\\soil.dat", header = T) 
> tapply(co2,group,sort)
$gap                               $growth                        
[1]  6 13 14 15 16 18 22 29        [1]  17  20  22  64 170 190 315
> # do duckworth c=9, reject? ( >= 7 -> .05, >= 10 -> .01); 
                    reject with p-value close to .01
> wilcox.test(co2~group)
        Wilcoxon rank sum test with continuity correction
data:  co2 by group 
W = 6.5, p-value = 0.01500
alternative hypothesis: true mu is not equal to 0 
Warning message:
cannot compute exact p-value with ties in: wilcox.test.default(x = c(13, 16, 15, 18, 14, 6, 29, 22), y = c(17,  
> # compare: SW contortions pp.290-292; R-wilcox easier, 
         Duckworth even easier and agrees.
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> # Brogan-Kutner liver data--repeated measures analysis of variance

> bkdat = read.table(file="D:\\stat141\\brogkutrow.dat", header = T)
> # c4 method (1 = selective, 2=nonselective); c2 pre (urea synthesis); c3 post                   
> attach(bkdat)
> imp = post - pre
> tapply(imp,method,sort)
$"1"  [1] -6 -6 -5 -3 -3 -3 12 20
$"2"  [1] -24 -18 -18 -18 -18 -15 -14 -11  -8  -7  -6  -4   4

> t.test(imp~method)
        Welch Two Sample t-test
data:  imp by method 
t = 3.1743, df = 12.271, p-value = 0.007806
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
  4.044203 21.609643 
sample estimates:    mean in group 1 mean in group 2 
                            0.75000       -12.07692 
> # improvement diifers by methods--treatment by occasions interaction

> # t-test for equal var assumption equiv to repeated measures
> # in repeated measures analysis of variance 3.37^2 is F-statistic F(1,19)
> t.test(imp~method, var.equal = TRUE)
        Two Sample t-test
data:  imp by method 
t = 3.3709, df = 19, p-value = 0.003209
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
  4.862645 20.791201 
sample estimates:
mean in group 1 mean in group 2 
        0.75000       -12.07692 

                 pre,post description
> tapply(pre, method, summary)
$"1"
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  35.00   39.75   44.00   46.38   51.25   66.00 
$"2"
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  32.00   36.00   42.00   43.54   50.00   63.00 

> tapply(post, method, summary)
$"1"
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  35.00   41.25   47.00   47.13   54.25   60.00 
$"2"
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  14.00   18.00   32.00   31.46   36.00   67.00 

> # Duckworth BK improvement c = 10 + 2 = 12, p < .01