I am using Fligner and Pollicello's robust rank-order (RRO) test to detect differences in central tendency between two samples.

The data comes from experimental economics simulations.

I would greatly appreciate your help with two issues I am facing with the right-tail critical values for the RRO test.

For ease of exposition, in both my questions I will assume that my data samples both have only 3 points, that is m=3, n=3.

The right-tail critical values of the RRO for m=3, n=3 are: 2.347 (significance 10%); and +infinity (significance 5%).

So, for instance, if the result of the test is 5.314, we conclude that the first samples is greater than the second sample at the 10% level (0.05<p<0.10). Instead, if the result of the test is 0.978, we conclude that the difference between the two samples is not significant at the 10% level (p>0.10).

**(1) How to interpret the result of the test, when it is close to a finite critical value.**

For example, if the result of the test is 2.3471001, is it safe to conclude that the first samples is greater than the second sample at the 10% level (0.05<p<0.10)?

Or if the result of the test is 2.3469899, is it safe to conclude that the difference between the two samples is not significant at the 10% level (p>0.10)?

**(2) How to interpret the result of the test when it is not finite.**

For example, if the result of the test is +infinity, is it safe to conclude that the first samples is greater than the second sample at the 5% level (p=0.05)?

Thanks in advance for your time, I appreciate it.