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

Table 2 Comparison of internal and stability validity by clustering methods

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 Squares^a	255.87	384.55	292.65
Average silhouette width^b	0.14	0.17	0.09
Dunn index^b	0.27	0.20	0.19
Stability Validity Indexes
Average Proportion of Non-overlap (APN)^c	0.13	0.09	0.19
Average Distance AD^c	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

^a The lower the value of the within-cluster sum of square, the higher the extent of compactness
^b The higher the value of Dunn index and average silhouette width, the higher the extent of compactness and separation
^c For all stability indices, smaller values indicate better stability validity

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