Hodgeman County Study, part 9 of 12

Discriminant analysis

Table 3. Within-group covariance matrices for cumulative sandstone thickness.

	Group	UJ	LJ	K	Ch
23	UJ	1532.1
	LJ	344.6	615.9
	K	-224.3	186.3	692.7
	Ch	606.2	146.5	59.6	2312.4
26	UJ	317.1
	LJ	53.2	490.8
	K	127.3	140.5	965.0
	Ch	-204.6	-17.9	-444.3	1543.1
36	UJ	436.8
	LJ	317.6	1336.4
	K	-73.1	214.0	330.7
	Ch	-91.2	-176.3	21.3	511.1
65	UJ	254.9
	LJ	57.3	329.8
	K	-30.2	42.4	96.7
	Ch	44.1	115.4	79.6	765.4
81	UJ	148.5
	LJ	29.6	155.8
	K	5.7	45.5	138.8
	Ch	-39.7	29.8	97.1	616.5

Table 4 shows a 97% agreement between Ward's method clusters and the groups based on the posterior probabilities of membership. The group sizes are in the bottom line. Although they are slightly different than the corresponding cluster sizes, we will keep the cluster labels to avoid cluttering the exposition.

Table 4. Resubstitution summary

	Group
Cluster	23	26	36	65	81
23	23	0	0	0	0
26	0	25	0	1	0
36	0	0	33	1	2
65	0	0	0	65	0
81	0	2	0	1	78
Total	23	27	33	68	80

Considering that in this case the relative cluster sizes in the sampling are a good approximation to the true relative sizes, one should use the relative proportions in Table 2 as estimates for the a priori group probabilities.

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