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

The analysis of the graphs does not detect any outlier.

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.

**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*.

**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).

**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).

`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.**