the data as it comes". The second study design is given by the product of two independent binomial distributions; the totals in one of the margins (either the row totals or the column totals) are constrained by the experimental design, but the totals in other margin are free. This is by far the most common form of experimental design, where the experimenter constrains part of the experiment, say by assigning half of the subjects to be provided with a new medicine and the other half to receive an older, conventional medicine, but has no control over the numbers of individuals in each controlled category who either recover or succumb to the illness. The third design is given by the hypergeometric distribution; where both the total numbers in each column and row are constrained. For example an individual is allowed to taste 8 cups of soda, but must assign four to each category "brand X" and "brand Y", so that both the row totals and the column totals are constrained to four. This kind of experiment is complicated to manage, and is almost unknown in practical experiments. The operational difference between Barnard’s exact test and Fisher’s ‘exact’ test is how they handle the nuisance parameter(s) of the common success probability, when calculating the value. Fisher's exact test avoids estimating the nuisance parameter(s) by conditioning on both margins, an approximately ancillary statistic that constrains the possible outcomes. Barnard’s test considers all legitimate possible values of the nuisance parameter(s) and chooses the value(s) that maximizes the value. The theoretical difference between the tests is that Barnard’s test uses the double-binomially distributed, whereas Fisher’s test, because of the conditioning uses is the hypergeometric distribution. However, even when the data come from double-binomial distribution, the conditioning (that leads to using the hypergeometric distribution for calculating the Fisher's exact p-value) produces a valid test. Both tests are valid, that is, bound the type I error rate at the alpha level. However, Barnard’s test can be more powerful than Fisher’s test because it considers more ‘as or more extreme’ tables, by not conditioning on the second margin, which the procedure for Fisher’s test ignores. In fact, one variant of Barnard’s test, called Boschloo's test, is uniformly more powerful than Fisher’s test. A more detailed description of Barnard’s test is given by Mehta and Senchaudhuri (2003). Barnard’s test has been used alongside Fisher's exact test in project management