For example, suppose we knew probabilities formula_16 with formula_17 such that (male studier, male non-studier, female studier, female non-studier) had respective probabilities formula_18 for each individual encountered under our sampling procedure. Then still, were we to calculate the distribution of cell entries conditional given marginals, we would obtain the above formula in which neither formula_14 nor formula_20 occurs. Thus, we can calculate the exact probability of any arrangement of the 24 teenagers into the four cells of the table, but Fisher showed that to generate a significance level, we need consider only the cases where the marginal totals are the same as in the observed table, and among those, only the cases where the arrangement is as extreme as the observed arrangement, or more so. (Barnard's test relaxes this constraint on one set of the marginal totals.) In the example, there are 11 such cases. Of these only one is more extreme in the same direction as our data; it looks like this: