Six Patients Were Each Given Four Different Pain Killers and Asked

Essay

Six patients were each given four different pain killers and asked to rate each pain killer's effectiveness in reducing pain on a scale of 1 to 10. A Friedman $\mathrm { F } _ { \mathrm { r } ^ { - } }$ test was performed on the results. A printout is shown below.

Friedman Test: Response versus Treatment blocked by Patient $$\mathrm { S } = 18.00 \mathrm { DF } = 3 \mathrm { P } = 0.000$$
$\begin{array} { l r r r } & & \text { Est } & \text { Sum of } \\ \text { Treatment } & \text { N } & \text { Median } & \text { Ranks } \\ 1 & 6 & 7.500 & 24.0 \\ 2 & 6 & 4.500 & 12.0 \\ 3 & 6 & 6.000 & 18.0 \\ 4 & 6 & 2.500 & 6.0 \end{array}$
Grand median $= 5.125$ Is there evidence that at least two of the treatment probability distributions differ in location? Explain.