1. Importer les données

decath <- read.table("https://r-stat-sc-donnees.github.io/decathlon.csv", sep=";", dec=".", header=TRUE, row.names=1, check.names=FALSE)

2 et 3. Construire la Classification Ascendante Hiérarchique

set.seed(123)
classe <- kmeans(scale(decath[,1:10]), centers = 4, nstart = 100)
classe

K-means clustering with 4 clusters of sizes 12, 13, 3, 13

Cluster means:
        100m    Longueur       Poids    Hauteur       400m     110m H     Disque     Perche    Javelot      1500m
1 -0.2713911 -0.06847836  0.11372756  0.3635437 -0.3949090 -0.2543941  0.1073831 -0.9020594  0.2519080 -0.7024505
2  1.0222463 -0.80958444 -0.43964769 -0.3362115  0.9594995  0.9463002 -0.3152426 -0.2467371 -0.1518058  0.2708137
3 -1.5260343  1.92792930  1.65317910  1.2722886 -1.2972738 -1.1781827  1.7272523  0.2550157  1.4378164  0.0869614
4 -0.4195697  0.42788847 -0.04683446 -0.2929723 -0.2955972 -0.4395866 -0.1824770  1.0205576 -0.4125285  0.3575341

Clustering vector:
     Sebrle        Clay      Karpov       Macey     Warners   Zsivoczky       Hernu        Nool     Bernard    Schwarzl 
          3           3           3           1           4           1           1           4           1           4 
  Pogorelov  Schoenbeck      Barras       Smith   Averyanov    Ojaniemi     Smirnov          Qi       Drews Parkhomenko 
          4           4           1           1           4           1           1           1           4           2 
      Terek       Gomez        Turi     Lorenzo   Karlivans Korkizoglou       Uldal     Casarsa      SEBRLE        CLAY 
          4           1           2           2           2           2           2           2           4           4 
     KARPOV     BERNARD      YURKOV     WARNERS   ZSIVOCZKY    McMULLEN   MARTINEAU       HERNU      BARRAS        NOOL 
          4           4           2           4           1           1           2           2           2           2 
BOURGUIGNON 
          2 

Within cluster sum of squares by cluster:
[1]  55.90563 100.18299  12.62547  73.25410
 (between_SS / total_SS =  39.5 %)

Available components:

[1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss" "betweenss"    "size"        
[8] "iter"         "ifault"      

4. Caractériser les classes

decath.comp <- cbind.data.frame(decath,classe=factor(classe$cluster))

library(FactoMineR)
catdes(decath.comp, num.var = 14)

Link between the cluster variable and the quantitative variables
================================================================
                Eta2      P-value
Points     0.7959632 7.543476e-13
Perche     0.6072763 1.213468e-07
100m       0.5935880 2.263340e-07
Longueur   0.5526927 1.290912e-06
400m       0.5006104 9.468719e-06
110m.H     0.4773576 2.150925e-05
Classement 0.3481185 1.114882e-03
Poids      0.2723874 7.667540e-03
Disque     0.2703340 8.052236e-03
Javelot    0.2368840 1.746553e-02
Hauteur    0.2256861 2.241818e-02
1500m      0.2139786 2.895804e-02

Description of each cluster by quantitative variables
=====================================================
$`1`
          v.test Mean in category Overall mean sd in category Overall sd      p.value
1500m  -2.893339       270.825000   279.024878      5.8957039 11.5300118 0.0038117012
Perche -3.715512         4.511667     4.762439      0.1635967  0.2745887 0.0002027925

$`2`
              v.test Mean in category Overall mean sd in category  Overall sd      p.value
100m        4.460054        11.266923     10.99805      0.1819292   0.2597956 8.193887e-06
400m        4.186290        50.723077     49.61634      1.0359268   1.1392975 2.835507e-05
110m.H      4.128702        15.052308     14.60585      0.3659583   0.4660000 3.648172e-05
Classement  3.196166        17.923077     12.12195      7.7604673   7.8217805 1.392670e-03
Longueur   -3.532212         7.003846      7.26000      0.2492308   0.3125193 4.120991e-04
Points     -4.463711      7655.076923   8005.36585    189.9592918 338.1839416 8.055212e-06

$`3`
              v.test Mean in category Overall mean sd in category   Overall sd      p.value
Points      4.242103       8812.66667  8005.365854    68.78145745 338.18394159 2.214348e-05
Longueur    3.468581          7.87000     7.260000     0.06480741   0.31251927 5.232144e-04
Disque      3.107539         50.16000    44.325610     1.19668988   3.33639725 1.886523e-03
Poids       2.974272         15.84000    14.477073     0.46568945   0.81431175 2.936847e-03
Javelot     2.586808         65.25667    58.316585     6.87867397   4.76759315 9.686955e-03
Hauteur     2.289003          2.09000     1.976829     0.02449490   0.08785906 2.207917e-02
110m.H     -2.119695         14.05000    14.605854     0.06531973   0.46599998 3.403177e-02
Classement -2.299627          2.00000    12.121951     0.81649658   7.82178048 2.146935e-02
400m       -2.333955         48.12000    49.616341     0.98634004   1.13929751 1.959810e-02
100m       -2.745523         10.59667    10.998049     0.18080069   0.25979560 6.041458e-03

$`4`
         v.test Mean in category Overall mean sd in category Overall sd      p.value
Perche 4.452686         5.046154     4.762439      0.1763536  0.2745887 8.480264e-06