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

A 2 Ã— 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

F1/(1 - F) Fj2/(1 - Fj2)

Show that log Î¸_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.

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

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