Basic Statistics

DIFFERENTTYPES OFTABLES 145

When two-way frequency tables are presented that simply give the frequencies

without the row and column labels, one cannot possibly know how they should be

interpreted. It is essential that tables be clearly labeled in order that readers can

understand them.

11.1.4 Relationship Between Type of Study Design

and Type of Table

In Chapter 1 we introduced the major types of studies used in the biomedical field.
Studies were divided into those in which treatment was assigned (experiments) and
observational studies in which exposure or risk factors were compared to outcomes
such as disease. In performing an experiment, we want to study the effect of a treat-
ment in a laboratory experiment, a clinical trial, or a field trial. In these experiments,
the two-way table obtained from the results typically fits the two-sample type of ta-
ble. We will assume that the sample size in the two treatment groups is fixed and
we will not be interested in estimating it. In studies of surgical treatments performed
on animals, the experimental surgical treatment is sometimes performed on one side
of each animal and the control treatment is performed on the opposite side. Here,
the outcome for the two sides of the animal are compared. In this case, the sample
consists of matched pairs.
In observational studies, the sample is often considered to be a single sample or two
fixed samples. In surveys, we usually take a single sample and compare two variables
measured in the survey. We assume that the row and column proportions estimate the
proportions in the population being sampled. For example, we would assume that
the proportion of current smokers in Table 11.1 is an estimate of the proportion in
the population of respondents we sample from and that the proportion of respondents
with low vital capacity is an estimate of the proportion in the population. In other
observational studies, samples may be taken from two or more groups.
In prospective studies, all three ways of sampling mentioned previously are possi-
ble. Sometimes a single sample is taken and the exposure or risk variable is measured
on all the subjects during the first time period and the disease outcome is measured
as it occurs. In this type of prospective sample, the proportion of subjects who are
exposed or not exposed are considered to be an estimate of the proportion in the
population. The heart studies (e.g., the Framingham heart study) are examples of
this type of prospective study. In other prospective studies, two samples are taken
based on exposure status (an exposed sample and a nonexposed sample). Here, the
proportion of subjects does not represent the proportion in the population since often
the exposed group is oversampled. Finally, if the same measurement is taken at two
time periods in a prospective study, the data can be considered a matched sample.
The result of measurement at time 1 could be displayed in columns 1 and 2, and the
results at time 2 could be displayed in rows 1 and 2 (as with the operation on two
sides of each animal). In essence, a table similar to Table 1 1.4 is obtained.
In casdcontrol or retrospective studies, there are usually far fewer cases available
for study than there are controls. Almost all of the available cases are studied and
only a small fraction of the controls are sampled. Hence, there are two samples