BIOSTATISTICAL APPROACHES TO ASSESSMENT 123Figure 7.1. The H, N and L regions of possible study results. Exposed cases are on the
vertical axis and non-exposed cases on the horizontal axis.sensitivity unless the spontaneous rate exceeds 20%. Likewise, studies with
more than 20 cases in the unexposed group have no chance at all of demon
strating an H effect. Even when there are 50 subjects in each group, though,
there must still be at least 5 diseased subjects in the unexposed group before
a significantly beneficial effect can occur. But now the 5 cases represent
only 10% of the sample of 50, whereas before the 5 cases represented 20%
of the sample.
Probabilities of Study Outcomes
For any given sample sizes nj and n0, not necessarily equal, an ac rectan
gle can be constructed as above. The calculations involved are entirely
independent of the actual values of the rates Pj and p0, and depend only on
the assumed null hypothesis that they are equal. The H, N, and L regions
define the result for any possible outcome of the study because, for fixed
sample sizes and n0, the study outcome is completely specified by the
values for a and c.
As stressed above, the 10% significance figure is only nominal. But,
while the H, N, and L regions were constructed using this 10% for defining
the value of chi-square, the actual probabilities of a study result, (a,c),
falling in any particular region, including the null N region, depend strongly