A 2 J table has ordinal response. Let F j|i = 1|i + ..... +

A 2 × J table has ordinal response. Let F_j|i= Ï€_1|i+ ..... + Ï€_j|i. When F_j|2‰¤ F_j|1for j = 1,......, J, the conditional distribution in row 2 is stochastically higher than the one in row 1. Consider the cumulative odds ratios

Show that log θ_j > 0 for all j is equivalent to row 2 being stochastically higher than row 1. Explain why row 2 is then more likely than row 1 to have observations at the high end of the ordinal scale.

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F1/(1 - F) Fj2/(1 - Fj2)" j = 1..., J - 1.