Basic Statistics

DIFFERENTTYPES OFTABLES 143

Table 11.1 Illustrating Counts (A) and Symbols (B): Single Sample

A. Association Between Smoking and Low Vital Capacity: Counts

Smoking

Low Vital Capacity Yes No Total

Yes 11 10 21

No 19 80 99

Total 30 90 120

B. Association Between Smoking and Vital Capacity: Symbols

Smoking

Low Vital Capacity Yes No Total

Yes a b a+b

No C d c+d

Total a+c b+d n

Table 11.2 Proportions of Total Sample from Smoking and Vital Capacity Frequencies

Smoking

Low Vital Capacity Yes No Total

Yes .092 ,083 .115

No .158 ,667 22.5

Total .250 .I50 1.000

could be either the number or the percentage of patients with low and normal vital

capacity.

11 .I .2 Tables Based on Two Samples

Alternatively, the data displayed in a two-way table can be from two samples. For
example, the categorical data might be from a clinical trial where one group of patients
had been randomly assigned to a new experimental treatment and the other group of
patients had been assigned to the standard treatment. These two groups of patients will
be considered to be two samples. The outcome of the two treatments can be classified
as a success or a failure. Table 11.3 displays the outcome of such a trial where 105
patients received the experimental treatment and 100 the standard treatment.
If proportions are computed from the results in Table 11.3, they are obtained by
treatment groups. From Table 11.3 we compute the proportion of patients who were
successfully treated in the experimental group as 95/105 = .905 and the proportion
treated successfully in the standard group as 80/100 = 300. The proportions that
were failures are .095 in the experimental group and ,200 in the standard group. If the
proportions are computed by treatment groups, they are reported as in Section 10.6.2.