In a SAS k-means clustering workflow using PROC HPCLUS, the pseudo-F statistic (Calinski-Harabasz index) is computed across k=2 through k=10. The pseudo-F values are: k=3: 482, k=4: 716, k=5: 698, k=6: 534. Which k value does the pseudo-F criterion suggest?
Select an answer to reveal the explanation.
Short Explanation
Here's the deal — you pick k=4 because the pseudo-F (Calinski-Harabasz) statistic is highest there, and a higher value means better-defined clusters.
Full Explanation
The correct choice is k=4 because the pseudo-F (Calinski-Harabasz) statistic measures the ratio of between-cluster variance to within-cluster variance. A higher value indicates better-defined clusters. The maximum pseudo-F of 716 occurs at k=4, suggesting that 4 clusters provides the best cluster separation relative to within-cluster compactness. The option selecting k=3 because the pseudo-F increases before this value is wrong because k=3 has a lower pseudo-F than k=4. The options selecting k=6 because the pseudo-F stabilizes after this value and k=5 because the elbow in pseudo-F occurs between k=4 and k=5 are wrong because the peak is clearly at k=4.