Shufflix: Statistical Validation
Assorted statistical tests are run on output from Shufflix. The purpose is to test whether the hands generated are indeed unbiased.
The chi2 test yields a single number between zero and one, which can be taken as sort of measurement of how well the observations fit with the theoretically predicted results. Large numbers (close to 1) denote a good fit while small numbers (close to 0) denote a bad fit. A statistical test like this is often taken to be accepted at the 95% confidence level if the chi2 number is greater than 0.05. Note, however, that the distribution of the chi2 statistic follows a uniform distribution between 0 and 1, so that one true result out of 20 is expected to be less than 0.05.
The statistical tests can be criticized for using one sample to generate several different statistics, since these different observations cannot be completely independent of each other. For the time being, that will not be helped.
|Test name||Test description||chi2 statistic||observations||spreadsheet|
|n-pat||Pattern of North's hand, e.g. 5-5-2-1, 4-4-4-1. 4-4-3-2 is most likely.||
|d7-patt||Taking groups of four consecutive boards, who gets the 7, e.g. NNSW, EWEW. All patterns are equally likely.||
|hcp||How many high card points does a randomly selected hand on each board have, e.g. 16 hcp, 3 hcp. 10 hcp is the most likely outcome.||
|8-card||Number of 8-cards suits held by West per 1000 hands. The typical value is around 4.||
|void-hst||Number of boards with a void per runs of 36 boards. The typical value is 6 or 7.||void-hst.txt|
|sa-c2||Who gets the A and the 2, e.g. E-E or N-S. All 16 combinations are about equally likely, but combinations where the same hand gets both are a little less likely than those where different hands are involved.||
|di-acekg||Who gets theA and theK? This is basically the same kind of test as above.||
|h-akq||Who gets the K when theAQJ are on the same hand?||
|split||When NS have exactly 8 s between them, how do the remaining 5 s split?||
The results are fine so far. Empty chi2 values are
given where the spreadsheet for the calculation is not made yet.
More statistics will appear later as they get processed.