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Introduction to Categorical Data Analysis Procedures |

Consider a *randomized experiment* in which patients are assigned
to one of two treatment groups according to a randomization process that
allocates fifty patients to each group. After a specified period of
time, each patient's status (cured or uncured) is recorded. Suppose the
data shown in Table 5.5 give the results of the experiment.
The null hypothesis is that the two treatments are equally effective.
Under this hypothesis, treatment is a randomly assigned label that has
no effect on the cure rate of the patients. But this implies that each
row of the table represents a simple random sample from the finite
population whose cure rate is described by the column marginal totals.
Therefore, the column marginals (58, 42) are fixed under the hypothesis.
Since the row marginals (50, 50) are fixed by the allocation process,
the hypergeometric distribution is induced on the cell frequencies.
Randomized experiments can also be specified in a stratified framework,
and Cochran-Mantel-Haenszel statistics can be computed relative to the
corresponding multiple hypergeometric distribution.

Status | |||||

Treatment | Cured | Uncured | Total | ||

1 | 36 | 14 | 50 | ||

2 | 22 | 28 | 50 | ||

Total | 58 | 42 | 100 |

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