SOLUTION OF EX. 1 - Wood
60 68 69 56 20 12 55 47 48 61 62 21 54 22 40 30 37 38 46 18 13 64 65 67 27 63 71 7 72 19 36 5 26 6
14 39 31 70 29 8
23 32 42 58 57 24 53 43 51 1
41 28 66 50 33 35 45 44 15 52 3 4 16 2
34 49 59 9 10 17 11 25
0510152025
Dendogram − Euclidean distance − Ward method
From the dendogram we choose: 4 clusters Description of the clusters:
• means of the variables in the groups (original and standardized variables)
n_units carcar corflo faggra ileopa liqsty maggra nyssyl ostvir oxyarb pingla quenig quemic symtin 1 24 4.92 2.62 11.50 6.08 4.67 6.04 1.21 5.75 1.29 2.17 0.5 4.58 0.67 2 10 1.00 3.20 7.10 15.90 7.80 2.90 2.00 13.20 3.50 0.80 1.2 5.30 0.60 3 23 8.43 1.83 6.91 5.61 11.48 2.96 1.09 7.26 0.57 5.52 1.7 4.65 7.61 4 15 18.40 1.20 4.60 5.13 8.33 2.53 2.87 1.93 0.20 0.73 5.0 10.33 1.47
n_units carcar corflo faggra ileopa liqsty maggra nyssyl ostvir oxyarb pingla quenig quemic symtin 1 24 -0.39 0.23 0.76 -0.18 -0.55 0.83 -0.19 -0.12 0.07 -0.14 -0.56 -0.31 -0.39 2 10 -0.85 0.50 -0.19 1.54 -0.04 -0.38 0.17 1.10 1.06 -0.46 -0.28 -0.14 -0.40 3 23 0.02 -0.16 -0.23 -0.26 0.56 -0.36 -0.25 0.13 -0.26 0.66 -0.09 -0.29 0.75 4 15 1.17 -0.46 -0.73 -0.34 0.05 -0.52 0.58 -0.74 -0.42 -0.48 1.23 1.04 -0.26
• dispersion in the clusters
mean_within_dist max_within_dist within_var
[1,] 2.45 3.91 6.50
[2,] 2.99 7.16 11.03
[3,] 3.40 4.78 12.11
[4,] 2.72 4.28 7.85
• the between variance percentage is 29.21 Comments
- The groups are not well separated (can be read from the small between variance percentage).
- Group 4 has most extremes values of the variables.
Group 2 has outliers.
Groups 2 e 3 are more disperse than the other two groups.
Group sparsity can be seen in the dendogram: the larger the length parameter the sparser the cluster.
- From the means of the variables in the groups (standardized variables) we observe that:
groups 1 and 3 do not have large prevalence of any species (no group mean is higher than one);
some prevalence of faggra (0.76) and maggra (0.83) are in the first group, and of symtin (0.75) in the third group;
in the second group there is the largest presence of ileopa (1.54), ostvir (1.10) and oxyarb (1.06) and some carflo (0.50);
in the fourth group there is the largest presence of carcar (1.17), quenig (1.23 ) and quemic (1.04), and some nyssyl (0.58).
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