Viiie: Ordered Categories, Disordered Thresholds

When the experts all agree, it doesn’t necessarily follow that the converse is true. When the experts don’t agree, the average person has no business thinking about it. B. Russell

The experts don’t agree on the topic of reversed thresholds and I’ve been thinking about it anyway. But I may be even less lucid than usual.

The categories, whether rating scale or partial credit, are always ordered: 0 always implies less than 1; 1 always implies less than 2; 2 always implies less than 3 . . . The concentric circle for k on the archery target is always inside (smaller thus harder to hit) than the circle for k-1. In baseball, you can’t get to second without touching first first. The transition points, or thresholds, might or might not be ordered in the data. Perhaps the circle for k-1 is so close in diameter to k that it is almost impossible to be inside k-1 without being inside k. Category k-1 might be very rarely observed, unless you have very sharp arrows and very consistent archers. Perhaps four-base hits actually require less of the aspect than three-base.

Continue . . . Ordered categories, disordered thresholds

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