## Tmax Hypothesis testing [Nonparametrics]

Dear Mittyri,

I hope that I can fully understand what you mean, so I hope that I can repeat your point of view with my own words:

1. The meaning of the value of P should be stated in the hypothesis of my Protocol and set a significant level α, which I assume here α = 0.05 .

2. For the Tmax test, I can use any test method for ordinal data as long as there is scientific evidence.

3. If I use the method of the paper to test Tmax, only the "3.2 treatment test" is meaningful when the P value of the "3.1 sequence test" sequence effect is >0.05. such as,
Scene 1: P value of sequence effect = 0.6, P value of treatment effect = 0.6
Scene 2: P value of sequence effect = 0.6, P value of treatment effect = 0.01
Scene 3: P value of sequence effect = 0.01, P value of treatment effect = 0.6
Scene 4: P value of sequence effect = 0.01, P value of treatment effect = 0.01
Among the above four scenarios, only the treatment effect of scene 1 is not significantly different.
Only the therapeutic effects of Scene 2 are significantly different,
Scene 3 and Scene 4 cannot determine whether the treatment effect is significantly different.

4. If I use the paper method to test Tmax, and if the P value of the "3.1 Sequence Test" sequence effect is <0.05, then I should use the "3.4 Treatment & Residual (simultaneous) test" instead of "3.2 treatment test".

5. I must assume that there is no significant difference between the sequence effect and the pairing effect before the "Wilcoxon signed rank test" method can be used.

6. Does it mean that the method in the paper as a whole is more extensive than the data applied by the "Wilcoxon signed rank test". In other words, the method in the paper has fewer assumptions than the "Wilcoxon signed rank test". Kind regards,
0521 Ing. Helmut Schütz 