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Table 2 Comparison of internal and stability validity by clustering methods

From: Introducing an efficient sampling method for national surveys with limited sample sizes: application to a national study to determine quality and cost of healthcare

Validity Indexes MCM-8
Model-based with eight clusters
HCM-2
Hierarchical with two clusters
HCM-8
Hierarchical with
eight clusters
(Additional scenario)
Internal Validity Indexes
 Within-clusters Sum of Squaresa 255.87 384.55 292.65
 Average silhouette widthb 0.14 0.17 0.09
 Dunn indexb 0.27 0.20 0.19
Stability Validity Indexes
 Average Proportion of Non-overlap (APN)c 0.13 0.09 0.19
 Average Distance ADc 1.11 1.37 1.24
 Average distance between means (ADM)c 0.19 0.19 0.28
 Figure of Merit (FOM)c 0.21 0.24 0.22
  1. a The lower the value of the within-cluster sum of square, the higher the extent of compactness
  2. b The higher the value of Dunn index and average silhouette width, the higher the extent of compactness and separation
  3. c For all stability indices, smaller values indicate better stability validity