Can we use tests of runs to test randomness of a game?

[Bacle]

Hi, everyone:

I am trying to prepare a class for tests of randomness. I am trying to use

as output, the 6 numbers of an (actual) lottery. Would a test of runs of the

means of the winning numbers be effective here? I am thinking of selecting, say N=50

consecutive winning combinations of six numbers, first finding the total sum S_n of

each of the 50 winning combinations. I will plot the data with a histogram, to see if

it is well-behaved-enough to use the mean Mu as a measure of center, or else

(outliers, non-symmetry of plot, etc.) I will use the median M as a measure of center.


After that, I will find the median M/ mean Mu of all the 50

sums, and then I will tag a sum S_n with a '-' , if S_n< m, and with a '+' otherwise

( I think it is not too likely I will hit the actual mean, nor the median), and then

define a run as a collection of consecutive ' +' or '-' values.


Then I can use the U-statistic to test actual randomness

at a certain significance level.

Would this work?

Thanks.

 

[bpet]

The question with this approach is, what physical meaning does S_n have? (since the lotto numbers are really categorical data, just being convenient labels rather than quantities)

Perhaps instead look for evidence of numbers occurring more often than they should, e.g. with a variant of the chi-square test?

 

[Bacle]

Thanks, bpet:

I am little confused, tho, in that I have seen the test-of-runs used to test whether

birthdays are uniformly-distributed , and birthdate also seems like categorical data.

Still, your point is well-taken.