A quel groupe puis-je m’identifier ?

Objectif :

• A partir de groupes définis, trouver à quel groupe pourraient appartenir un nouveau groupe

A quel groupe puis-je m’identifier ?

• Groupes de 50 personnes
• 100 groupes
• Distributions normales

Etape 01 : les données

n <- 50
nGp <- 100
pop <- lapply(1:nGp, function(i){
  rnorm(n, 
    mean = sample(1:100, size = 1), 
    sd = sample(seq(from = 0, to = 10, by = 0.1), size = 1))
})

Etape 02 : représenter les données

boxplot(pop)

Etape 03 : décrire les données

sapply(pop, summary)

##              [,1]     [,2]     [,3]     [,4]      [,5]      [,6]     [,7]
## Min.     74.27455 41.11207 10.51831 51.51460 -9.485134  2.205377 30.54648
## 1st Qu.  83.33520 52.55579 16.92646 63.08290  4.752595 14.559844 50.81628
## Median   93.23222 57.74860 20.35526 66.98194  8.477465 19.585493 55.34405
## Mean     92.50879 57.73765 19.65232 69.16426  8.529659 18.146881 56.33546
## 3rd Qu.  99.06913 63.28232 22.53829 77.16588 13.033607 21.937279 63.97840
## Max.    115.37264 75.38764 26.08747 88.51441 24.254558 28.372826 73.45121
##             [,8]     [,9]    [,10]    [,11]      [,12]    [,13]     [,14]
## Min.    39.82701 -4.40990 31.79166 53.84383 -1.5831872 43.97055  9.836463
## 1st Qu. 41.57272 12.30906 37.44946 73.08766  0.1659421 61.71282 17.613859
## Median  42.25140 16.09588 40.53007 76.30242  1.1216168 67.83055 20.791146
## Mean    42.15184 17.09736 40.49761 77.06892  1.0945679 67.32473 20.381091
## 3rd Qu. 42.81346 22.72888 42.52557 80.66331  1.9192584 72.66031 23.419859
## Max.    43.44890 31.91827 51.84156 97.85022  4.1807842 84.88119 26.131053
##            [,15]    [,16]    [,17]    [,18]     [,19]    [,20]    [,21]
## Min.    15.70053 13.95568 12.49993 17.48163  67.39836 -3.34799 63.89002
## 1st Qu. 17.30777 28.01764 23.00571 23.60668  83.93691 11.17089 70.63725
## Median  18.08473 35.63813 29.80744 25.63882  89.04872 16.30886 74.10600
## Mean    17.97583 33.86398 29.18532 25.62256  88.02511 16.82275 75.43848
## 3rd Qu. 18.53114 39.14303 34.08772 27.33074  91.67314 23.46190 81.15941
## Max.    20.74906 49.14577 49.86168 31.42873 115.54756 33.48232 87.92778
##            [,22]      [,23]    [,24]     [,25]    [,26]    [,27]    [,28]
## Min.    69.85000 -0.1201301 23.78250  2.383489 37.90611 23.96825 67.53885
## 1st Qu. 74.37086  8.2632439 34.14930 12.552133 50.42490 31.49375 67.84511
## Median  75.60125 11.5868893 39.21405 18.038248 55.67086 32.85521 68.00230
## Mean    75.62291 12.1298801 39.47404 20.037921 56.92244 32.99340 68.00424
## 3rd Qu. 77.21834 15.7016081 45.14006 28.818943 63.72125 34.16805 68.12582
## Max.    80.96398 26.3976589 64.75705 41.232607 74.72656 39.69630 68.46742
##            [,29]    [,30]    [,31]    [,32]    [,33]    [,34]     [,35]
## Min.    31.94556 74.46386 16.60784 57.36436 33.63507 24.22916  77.81789
## 1st Qu. 40.65000 79.12245 27.89577 65.96129 33.82867 26.74899  88.64357
## Median  43.08247 79.67629 32.30916 69.32935 33.95502 28.19739  95.51371
## Mean    43.32592 79.78298 31.79538 68.96408 33.98200 28.09012  94.28414
## 3rd Qu. 45.70162 81.20425 36.19240 72.65306 34.11959 29.43702 100.44883
## Max.    57.66245 83.95869 49.81348 76.87017 34.48944 31.61683 106.06234
##            [,36]    [,37]    [,38]     [,39]     [,40]    [,41]    [,42]
## Min.    72.97127 75.40996 18.44928 -1.504092  8.809089 66.22203 55.10230
## 1st Qu. 75.31868 79.08686 29.03002  9.015879 11.444627 77.54721 72.07808
## Median  76.94935 80.87946 33.37887 13.652560 12.886191 81.39526 75.91544
## Mean    77.07971 80.81642 33.67202 14.245349 13.258347 81.44181 76.35867
## 3rd Qu. 78.73486 82.15555 39.11431 19.177594 15.452840 84.94125 82.54334
## Max.    81.30722 85.51239 47.10848 31.964640 18.191620 94.35255 90.52245
##            [,43]     [,44]     [,45]    [,46]    [,47]    [,48]     [,49]
## Min.    28.66968  8.266537  9.589925 51.24352 42.42727 40.73821  75.73359
## 1st Qu. 40.50334 16.303574 28.946084 65.76329 44.31876 40.94764  90.23626
## Median  46.33773 19.042430 32.188966 70.59745 45.23721 41.04342  92.91563
## Mean    45.88431 18.802507 32.503189 69.85132 45.29923 41.04934  94.11833
## 3rd Qu. 48.85887 21.406758 37.328034 74.05780 46.28037 41.16381  98.89802
## Max.    64.89066 27.078648 45.125743 84.51853 48.69292 41.37083 110.04642
##            [,50]    [,51]     [,52]    [,53]    [,54]    [,55]    [,56]
## Min.    72.19371 47.08320  5.843809 23.24171 76.01956 64.53420 75.87063
## 1st Qu. 76.53513 51.47010 11.109107 34.69115 78.12038 67.20677 83.58648
## Median  78.23400 54.02012 13.120852 38.10162 79.18228 69.09531 85.85647
## Mean    78.69425 53.92487 12.897704 38.25233 79.15450 68.92603 85.99863
## 3rd Qu. 81.07206 56.15974 15.006183 41.13943 80.05598 70.43969 88.53392
## Max.    85.88088 61.64621 21.345184 55.12616 82.97535 74.63982 96.13358
##            [,57]    [,58]     [,59]    [,60]      [,61]     [,62]    [,63]
## Min.    16.46748 49.31525  8.244332 37.90116 -13.062476  7.673774 10.74179
## 1st Qu. 27.95751 61.03602 15.417630 44.67511   1.513024 23.280079 20.15796
## Median  30.30655 64.05867 18.295184 46.87221   8.478660 29.395095 26.62788
## Mean    30.91192 63.34817 17.827994 47.64034   7.118449 27.802139 27.11730
## 3rd Qu. 34.20251 66.82747 20.288719 50.86462  12.695027 32.827843 32.00161
## Max.    46.80932 76.57914 25.776123 58.49302  24.321064 45.551174 47.24304
##            [,64]    [,65]    [,66]    [,67]    [,68]     [,69]     [,70]
## Min.    70.37959 43.37915 77.50433 43.77913 26.99672 -3.245807  6.138395
## 1st Qu. 76.95552 52.15621 80.77736 45.90505 31.69321 10.385275 29.850240
## Median  80.49960 56.51624 82.99084 46.96613 33.11523 15.715719 34.331273
## Mean    81.14849 56.14681 82.74775 47.10493 32.93626 15.892090 34.623805
## 3rd Qu. 85.04069 60.16015 84.66824 48.32735 34.48897 22.668719 41.085935
## Max.    94.96785 67.00158 87.97203 50.96757 39.21208 35.298977 50.171641
##            [,71]    [,72]      [,73]    [,74]    [,75]    [,76]      [,77]
## Min.    69.28467 58.30810 -0.7326249 87.10431 58.69201 56.15496 -4.8602545
## 1st Qu. 77.80982 68.91630  0.4322190 88.48094 65.98719 69.03077 -0.4447333
## Median  83.20737 73.53151  0.8909348 88.98854 70.23056 75.17714  2.7280315
## Mean    82.42989 73.61040  0.9452913 88.95936 69.69550 74.81451  2.3374694
## 3rd Qu. 86.36791 78.14595  1.4869933 89.40539 73.97882 80.75281  4.4515909
## Max.    98.21118 89.57022  2.5935564 90.81138 81.45795 99.64282 12.3568984
##             [,78]    [,79]    [,80]     [,81]    [,82]    [,83]    [,84]
## Min.     8.793126 59.34966 20.64557  49.25742 18.05349 52.48212 50.61240
## 1st Qu. 13.482894 71.75751 34.41775  62.00592 31.84040 54.25176 54.37005
## Median  14.930894 77.35098 40.65897  70.54196 34.89323 55.18971 57.45812
## Mean    15.052009 78.13520 39.94949  69.57612 34.29960 55.00171 57.06489
## 3rd Qu. 16.461798 85.87440 46.79284  75.70962 37.79724 55.60239 59.65307
## Max.    21.210132 95.84775 57.57749 101.15411 42.50945 57.49413 63.37048
##            [,85]    [,86]     [,87]     [,88]     [,89]    [,90]    [,91]
## Min.    57.77537  1.53875  3.280604  7.065647  72.07917 45.34979 48.11738
## 1st Qu. 72.91066 12.32080  7.275619 18.428937  88.70797 51.90430 60.04798
## Median  76.93317 15.42794 10.536672 22.084266  92.82872 54.01856 63.36352
## Mean    76.67846 15.22894 10.107486 23.457491  93.45831 54.50736 63.93132
## 3rd Qu. 80.02784 18.68804 12.052999 29.263871  97.74667 58.00593 69.27779
## Max.    94.08730 28.53188 18.482194 39.928435 109.34908 61.87895 84.77513
##              [,92]    [,93] [,94]     [,95]    [,96]    [,97]      [,98]
## Min.     0.9813135 17.42242    39  73.67990 32.91484 44.89180 -0.8624545
## 1st Qu. 22.9850115 22.76290    39  89.20920 38.27538 47.24763 19.1049867
## Median  30.6753043 26.29405    39  95.56547 40.01796 49.71747 24.8336584
## Mean    29.9325315 26.09769    39  96.26551 40.34509 49.57400 24.4787201
## 3rd Qu. 38.1140260 28.75250    39 103.71395 42.60574 51.54693 31.3240109
## Max.    53.8630574 35.37350    39 123.61204 47.40077 56.16270 40.8092275
##            [,99]   [,100]
## Min.    67.63364 10.45588
## 1st Qu. 78.65218 25.42939
## Median  87.08379 32.79963
## Mean    84.92311 31.79787
## 3rd Qu. 90.10277 38.30566
## Max.    99.44517 52.16478

Etape 04 : comparer les données au nouveau groupe

gpX <- rnorm(n, mean = sample(10:90, size = 1))

pVal <- sapply(seq_along(pop), function(i){
  t.test(pop[[i]], gpX)$p.value
})

Etape 04

print(pVal)

##   [1]  1.087959e-41  1.646748e-27  5.079033e-30  7.094909e-34  7.896289e-28
##   [6]  3.872232e-23  8.218039e-24  5.699681e-71  1.730054e-18  1.484822e-17
##  [11]  2.284253e-39 2.674042e-109  3.474662e-30  7.612653e-30  3.134918e-84
##  [16]  1.115497e-01  1.537108e-02  9.090876e-21  1.092932e-44  3.597364e-16
##  [21]  2.250106e-44  6.224367e-81  2.183300e-30  6.577542e-08  1.448756e-11
##  [26]  2.513007e-24  3.328544e-02  1.420885e-81  2.922155e-21  3.568480e-95
##  [31]  7.881194e-01  5.248666e-52  2.410746e-17  1.187231e-19  2.924962e-47
##  [36]  1.226315e-86  7.713655e-89  1.063311e-01  5.145153e-22  8.694204e-54
##  [41]  8.734644e-52  2.199933e-38  2.161229e-17  4.449288e-29  6.705225e-01
##  [46]  4.881124e-40  7.284265e-69  8.056842e-49  3.642935e-49  2.356343e-65
##  [51]  1.067576e-46  1.859700e-46  6.571694e-09 1.776109e-114  1.142892e-78
##  [56]  2.413145e-63  1.516422e-01  2.220043e-40  3.913366e-34  7.419041e-30
##  [61]  3.861871e-26  3.793047e-04  2.735982e-04  2.033973e-51  9.394562e-34
##  [66]  1.914585e-84  7.310208e-65  3.191945e-02  4.587557e-18  5.187672e-02
##  [71]  2.259249e-48  5.163131e-41 8.017722e-115 2.077612e-139  7.491900e-45
##  [76]  1.818352e-34  3.193734e-52  3.464206e-50  4.039301e-37  2.488598e-07
##  [81]  1.979453e-31  3.212374e-03 1.540289e-103  2.216188e-51  7.408088e-42
##  [86]  5.732546e-28  9.925191e-46  1.545947e-10  3.515424e-48  1.396626e-40
##  [91]  2.899752e-33  1.768632e-01  8.366198e-13  4.840279e-42  1.234693e-43
##  [96]  1.117498e-23  3.098613e-46  7.785154e-07  4.981490e-44  8.307696e-01

Etape 05 : rep. graph.

myCol <- vector(mode = "character", length = nGp)
myCol[pVal >= 0.05] <- "green"
myCol[pVal < 0.05] <- "red"
print(myCol)

##   [1] "red"   "red"   "red"   "red"   "red"   "red"   "red"   "red"  
##   [9] "red"   "red"   "red"   "red"   "red"   "red"   "red"   "green"
##  [17] "red"   "red"   "red"   "red"   "red"   "red"   "red"   "red"  
##  [25] "red"   "red"   "red"   "red"   "red"   "red"   "green" "red"  
##  [33] "red"   "red"   "red"   "red"   "red"   "green" "red"   "red"  
##  [41] "red"   "red"   "red"   "red"   "green" "red"   "red"   "red"  
##  [49] "red"   "red"   "red"   "red"   "red"   "red"   "red"   "red"  
##  [57] "green" "red"   "red"   "red"   "red"   "red"   "red"   "red"  
##  [65] "red"   "red"   "red"   "red"   "red"   "green" "red"   "red"  
##  [73] "red"   "red"   "red"   "red"   "red"   "red"   "red"   "red"  
##  [81] "red"   "red"   "red"   "red"   "red"   "red"   "red"   "red"  
##  [89] "red"   "red"   "red"   "green" "red"   "red"   "red"   "red"  
##  [97] "red"   "red"   "red"   "green"

Etape 05 : rep. graph.

par(mar = c(2, 2, 1, 1))
boxplot(pop, col = myCol)

Etape 05 : rep. graph.

sapply(pop, mean)

##   [1] 92.5087917 57.7376467 19.6523199 69.1642605  8.5296589 18.1468806
##   [7] 56.3354565 42.1518379 17.0973552 40.4976081 77.0689191  1.0945679
##  [13] 67.3247306 20.3810907 17.9758262 33.8639804 29.1853213 25.6225618
##  [19] 88.0251089 16.8227493 75.4384754 75.6229080 12.1298801 39.4740395
##  [25] 20.0379212 56.9224423 32.9934017 68.0042382 43.3259187 79.7829803
##  [31] 31.7953788 68.9640787 33.9820016 28.0901238 94.2841369 77.0797094
##  [37] 80.8164231 33.6720218 14.2453495 13.2583470 81.4418101 76.3586704
##  [43] 45.8843138 18.8025067 32.5031886 69.8513200 45.2992255 41.0493431
##  [49] 94.1183273 78.6942464 53.9248745 12.8977044 38.2523312 79.1545006
##  [55] 68.9260333 85.9986300 30.9119177 63.3481740 17.8279944 47.6403413
##  [61]  7.1184492 27.8021385 27.1173014 81.1484870 56.1468075 82.7477498
##  [67] 47.1049335 32.9362617 15.8920902 34.6238046 82.4298873 73.6104029
##  [73]  0.9452913 88.9593587 69.6955048 74.8145136  2.3374694 15.0520092
##  [79] 78.1352046 39.9494910 69.5761188 34.2996025 55.0017138 57.0648949
##  [85] 76.6784633 15.2289401 10.1074864 23.4574914 93.4583143 54.5073599
##  [91] 63.9313221 29.9325315 26.0976855 39.0000000 96.2655137 40.3450937
##  [97] 49.5740041 24.4787201 84.9231056 31.7978664

Etape 05 : rep. graph.

order(sapply(pop, mean))

##   [1]  73  12  77  61   5  87  23  52  40  39  78  86  69  20   9  59  15
##  [18]   6  44   3  25  14  88  98  18  93  63  62  34  17  92  57  31 100
##  [35]  45  68  27  38  16  33  82  70  53  94  24  80  96  10  48   8  29
##  [52]  47  43  67  60  97  51  90  83  65   7  26  84   2  58  91  13  28
##  [69]  55  32   4  81  75  46  72  76  21  22  42  85  11  36  79  50  54
##  [86]  30  37  64  41  71  66  99  56  19  74   1  89  49  35  95

Etape 05 : rep. graph.

popOrder <- pop[order(sapply(pop, mean))]
myColOrder <- myCol[order(sapply(pop, mean))]

Etape 05 : rep. graph.

boxplot(popOrder, col = myColOrder)