Bioequivalence and Bioavailability Forum

Dear All!

In the R-package randomizeBE you can control the randomness of the list by a Wald-Wolfowitz runs test as Helmut has suggested in this post .
This suggestion was aimed to avoid some 'ordered' lists beside the fact that such lists are of course obtainable by dicing, also with low probability.

Internally randomizeBE uses the sequence numbers for the runs test. The runs test is originally formulated for dichotomous input only.
It is generalized to other cases using the dichotomizing of the values via <=median and > median. See f.i. german wikipedia. The english version suggests to omit values = median. IMHO this is not appropriate here where we are dealing with sequences.

Here some observations that the randomness control does not work that good in case of more than 2 sequences.

Example: 3 sequences numbered 1, 2, 3 (substitute a character representation whatever fits your needs. F.i. latin square "ABC", "BCA" and "CAB").
The 'alternating' random lists analogous to the 2x2 case give the following results:
    list                  runs p.value
 1 2 3 1 2 3 1 2 3 1 2 3   0.2502
 1 3 2 1 3 2 1 3 2 1 3 2   0.2502
 2 1 3 2 1 3 2 1 3 2 1 3   0.0438
 2 3 1 2 3 1 2 3 1 2 3 1   0.0438
 3 1 2 3 1 2 3 1 2 3 1 2   0.2502
 3 2 1 3 2 1 3 2 1 3 2 1   0.2502
Majority of them considered as compatible with null hypothesis: sequence is random.

The ordered list on the other hand is correctly considered as 'non-random':
    list                  runs p.value
 1 1 1 1 2 2 2 2 3 3 3 3   0.0028

BTW: You needn't dicing with function RL4() until you get one of the above lists to see the runs p-value. Use the function runs.pvalue() and a numeric representation of the sequences.
Example:
rl <- rep(c(1,2,3),4)
runs.pvalue(rl)

BTW2: The runs test is implemented via normal approximation like the implementations in the R-packages tseries or lawstat. The drawback is that it by design will give only approximate p-values for such small lists as discussed here. If these approximate values are conservative or liberal I don't know.