This dataset contains 41 individuals and 13 variables, 2 quantitative variables are considered as illustrative, 1 qualitative variable is considered as illustrative.

1. Study of the outliers

The analysis of the graphs does not detect any outlier.

2. Inertia distribution

The inertia of the first dimensions shows if there are strong relationships between variables and suggests the number of dimensions that should be studied.

The first two dimensions of PCA express 50.09% of the total dataset inertia ; that means that 50.09% of the individuals (or variables) cloud total variability is explained by the plane. This percentage is relatively high and thus the first plane well represents the data variability. This value is greater than the reference value that equals 37.95%, the variability explained by this plane is thus significant (the reference value is the 0.95-quantile of the inertia percentages distribution obtained by simulating 1690 data tables of equivalent size on the basis of a normal distribution).

From these observations, it should be better to also interpret the dimensions greater or equal to the third one.

Figure 2 - Decomposition of the total inertia on the components of the PCA

An estimation of the right number of axis to interpret suggests to restrict the analysis to the description of the first 3 axis. These axis present an amount of inertia greater than those obtained by the 0.95-quantile of random distributions (64.14% against 51.54%). This observation suggests that only these axis are carrying a real information. As a consequence, the description will stand to these axis.

3. Description of the plane 1:2

Figure 3.1 - Individuals factor map (PCA) The labeled individuals are those with the higher contribution to the plane construction.

The Wilks test p-value indicates which variable factors are the best separated on the plane (i.e.Â which one explain the best the distance between individuals).

Competition
0.366311 

There only is one possible qualitative variable to illustrate the distance between individuals : Competition.

Figure 3.2 - Individuals factor map (PCA) The labeled individuals are those with the higher contribution to the plane construction. The individuals are coloured after their category for the variable Competition.

Figure 3.3 - Variables factor map (PCA) The variables in black are considered as active whereas those in blue are illustrative. The labeled variables are those the best shown on the plane.

Figure 3.4 - Qualitative factor map (PCA) The labeled factors are those the best shown on the plane.

The dimension 1 opposes individuals such as Karpov, Sebrle, Clay and Macey (to the right of the graph, characterized by a strongly positive coordinate on the axis) to individuals such as BOURGUIGNON, Uldal, Lorenzo, NOOL and Karlivans (to the left of the graph, characterized by a strongly negative coordinate on the axis).

The group in which the individuals Karpov, Sebrle, Clay and Macey stand (characterized by a positive coordinate on the axis) is sharing :

• high values for the variables Points, High.jump, Discus, Shot.put and Long.jump (variables are sorted from the strongest).
• low values for the variables 400m, 110m.hurdle, Rank and 100m (variables are sorted from the weakest).

The group in which the individuals BOURGUIGNON, Uldal, Lorenzo, NOOL and Karlivans stand (characterized by a negative coordinate on the axis) is sharing :

• high values for the variables 110m.hurdle, 100m and Rank (variables are sorted from the strongest).
• low values for the variables Discus, High.jump, Points and Shot.put (variables are sorted from the weakest).

Note that the variable Points is highly correlated with this dimension (correlation of 0.91). This variable could therefore summarize itself the dimension 1.

The dimension 2 opposes individuals such as Casarsa, YURKOV and Parkhomenko (to the top of the graph, characterized by a strongly positive coordinate on the axis) to individuals such as Warners, Drews and WARNERS (to the bottom of the graph, characterized by a strongly negative coordinate on the axis).

The group in which the individuals Casarsa, YURKOV and Parkhomenko stand (characterized by a positive coordinate on the axis) is sharing :

• high values for the variable 400m.
• low values for the variable Long.jump.

The group in which the individuals Warners, Drews and WARNERS stand (characterized by a negative coordinate on the axis) is sharing :

• high values for the variable Pole.vault.
• low values for the variable 110m.hurdle.

4. Description of the dimension 3

Figure 4.1 - Individuals factor map (PCA) The labeled individuals are those with the higher contribution to the plane construction.

The Wilks test p-value indicates which variable factors are the best separated on the plane (i.e.Â which one explain the best the distance between individuals).

Competition
0.496903 

There only is one possible qualitative variable to illustrate the distance between individuals : Competition.

Figure 4.2 - Individuals factor map (PCA) The labeled individuals are those with the higher contribution to the plane construction. The individuals are coloured after their category for the variable Competition.

Figure 4.3 - Variables factor map (PCA) The variables in black are considered as active whereas those in blue are illustrative. The labeled variables are those the best shown on the plane.

Figure 4.4 - Qualitative factor map (PCA) The labeled factors are those the best shown on the plane.

The dimension 3 opposes individuals such as KARPOV, Korkizoglou, Terek and CLAY (to the right of the graph, characterized by a strongly positive coordinate on the axis) to individuals such as ZSIVOCZKY, Barras, Zsivoczky, McMULLEN, Macey, Bernard and Smith (to the left of the graph, characterized by a strongly negative coordinate on the axis).

The group in which the individuals KARPOV, Korkizoglou, Terek and CLAY stand (characterized by a positive coordinate on the axis) is sharing :

• high values for the variable 1500m.
• low values for the variable Javeline.

The group in which the individuals ZSIVOCZKY, Barras, Zsivoczky, McMULLEN, Macey, Bernard and Smith stand (characterized by a negative coordinate on the axis) is sharing :

• low values for the variables 1500m and Pole.vault (variables are sorted from the weakest).

5. Classification

Figure 5 - Ascending Hierachical Classification of the individuals. The classification made on individuals reveals 4 clusters.

The cluster 1 is made of individuals such as YURKOV, MARTINEAU, NOOL, BOURGUIGNON, Parkhomenko, Lorenzo, Karlivans, Uldal and Casarsa. This group is characterized by :

• high values for the variables 100m, 110m.hurdle, 400m and Rank (variables are sorted from the strongest).
• low values for the variables Shot.put, Long.jump and Points (variables are sorted from the weakest).

The cluster 2 is made of individuals such as WARNERS, Warners, Nool, Averyanov, Drews and Korkizoglou. This group is characterized by :

• high values for the variables Pole.vault and 1500m (variables are sorted from the strongest).
• low values for the variables 100m and Javeline (variables are sorted from the weakest).

The cluster 3 is made of individuals such as Macey. This group is characterized by :

• low values for the variables 1500m and Pole.vault (variables are sorted from the weakest).

The cluster 4 is made of individuals such as Sebrle, Clay and Karpov. This group is characterized by :

• high values for the variables Points, Long.jump, Discus, Shot.put, Javeline and High.jump (variables are sorted from the strongest).
• low values for the variables 110m.hurdle, Rank, 400m and 100m (variables are sorted from the weakest).

Annexes

dimdesc(res, axes = 1:3)
$Dim.1$Dim.1$quanti correlation p.value Points 0.9561543 2.099191e-22 Long.jump 0.7418997 2.849886e-08 Shot.put 0.6225026 1.388321e-05 High.jump 0.5719453 9.362285e-05 Discus 0.5524665 1.802220e-04 Rank -0.6705104 1.616348e-06 400m -0.6796099 1.028175e-06 110m.hurdle -0.7462453 2.136962e-08 100m -0.7747198 2.778467e-09$Dim.2
$Dim.2$quanti
correlation      p.value
Discus      0.6063134 2.650745e-05
Shot.put    0.5983033 3.603567e-05
400m        0.5694378 1.020941e-04
1500m       0.4742238 1.734405e-03
High.jump   0.3502936 2.475025e-02
Javeline    0.3169891 4.344974e-02
Long.jump  -0.3454213 2.696969e-02

$Dim.3$Dim.3$quanti correlation p.value 1500m 0.7821428 1.554450e-09 Pole.vault 0.6917567 5.480172e-07 Javeline -0.3896554 1.179331e-02 Figure 6 - List of variables characterizing the dimensions of the analysis. res.hcpc$desc.var
$quanti.var Eta2 P-value Points 0.7438620 4.908988e-11 100m 0.6581552 9.668613e-09 Pole.vault 0.5712977 5.972228e-07 Long.jump 0.5293255 3.246949e-06 110m.hurdle 0.4455078 6.229435e-05 400m 0.4425235 6.859144e-05 Shot.put 0.2869412 5.393490e-03 Discus 0.2777274 6.745695e-03 Rank 0.2693094 8.250830e-03 1500m 0.2602251 1.022178e-02 Javeline 0.2500899 1.293207e-02 High.jump 0.2255099 2.250558e-02$quanti
$quanti$1
v.test Mean in category Overall mean sd in category
100m         4.741585        11.300833     10.99805      0.1445947
110m.hurdle  3.964894        15.060000     14.60585      0.3798903
400m         3.822084        50.686667     49.61634      1.0702051
Rank         2.667277        17.250000     12.12195      7.7041655
Shot.put    -2.100392        14.056667     14.47707      0.8698116
Long.jump   -3.406381         6.998333      7.26000      0.2586450
Points      -4.131722      7661.916667   8005.36585    196.1718882
Overall sd      p.value
100m          0.2597956 2.120526e-06
110m.hurdle   0.4660000 7.342867e-05
400m          1.1392975 1.323286e-04
Rank          7.8217805 7.646858e-03
Shot.put      0.8143118 3.569438e-02
Long.jump     0.3125193 6.583024e-04
Points      338.1839416 3.600552e-05

$quanti$2
v.test Mean in category Overall mean sd in category
Pole.vault  4.295481         5.021429     4.762439      0.1919024
1500m       2.602164       285.612857   279.024878     12.7576030
100m       -1.969217        10.885714    10.998049      0.1539812
Javeline   -2.125561        56.091429    58.316585      4.5043580
Overall sd      p.value
Pole.vault  0.2745887 1.743152e-05
1500m      11.5300118 9.263766e-03
100m        0.2597956 4.892823e-02
Javeline    4.7675931 3.353983e-02

$quanti$3
v.test Mean in category Overall mean sd in category
1500m      -2.893339       270.825000   279.024878      5.8957039
Pole.vault -3.715512         4.511667     4.762439      0.1635967
Overall sd      p.value
1500m      11.5300118 0.0038117012
Pole.vault  0.2745887 0.0002027925

$quanti$4
v.test Mean in category Overall mean sd in category
Points       4.242103       8812.66667  8005.365854    68.78145745
Long.jump    3.468581          7.87000     7.260000     0.06480741
Discus       3.107539         50.16000    44.325610     1.19668988
Shot.put     2.974272         15.84000    14.477073     0.46568945
Javeline     2.586808         65.25667    58.316585     6.87867397
High.jump    2.289003          2.09000     1.976829     0.02449490
110m.hurdle -2.119695         14.05000    14.605854     0.06531973
Rank        -2.299627          2.00000    12.121951     0.81649658
400m        -2.333955         48.12000    49.616341     0.98634004
100m        -2.745523         10.59667    10.998049     0.18080069
Overall sd      p.value
Points      338.18394159 2.214348e-05
Long.jump     0.31251927 5.232144e-04
Discus        3.33639725 1.886523e-03
Shot.put      0.81431175 2.936847e-03
Javeline      4.76759315 9.686955e-03
High.jump     0.08785906 2.207917e-02
110m.hurdle   0.46599998 3.403177e-02
Rank          7.82178048 2.146935e-02
400m          1.13929751 1.959810e-02
100m          0.25979560 6.041458e-03

attr(,"class")
[1] "catdes" "list " 

Figure 7 - List of variables characterizing the clusters of the classification.