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following two procedures, which have been typically used for this type of measure-
ment in medical research (see, for instance, Wewers and Lowe [20], Grant et al. [9],
Laerhoven et al. [19]):
(i) The patient is given a list of five categories: (1) very unhappy, (2) unhappy, (3)
neither unhappy nor happy, (4) happy, and (5) very happy. The patient is asked
to choose one of them.
(ii) The patient is asked to mark a point on the interval [
100 in-
dicates the greatest degree of unhappiness, and 100 indicates the greatest degree
of happiness.
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100, 100]. Here
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The scale of measurement used in (i) is categorical. In this example, the five cate-
gories can be ordered according to the degree of happiness, so it can also be consid-
ered an ordinal scale. To process the five categories numerically, integers 1-5 can be
assigned to the five categories (1 and 5 represent the lowest and the greatest degrees
of happiness); the resulting scale is a Likert-type scale. The scale used in (ii) is an
example of visual analogue scale, which can be considered an interval scale or a
ratio scale for subjective measurements. Figure 19.1 shows a sample response using
the visual analogue scale in (ii).
Fig. 19.1
A perceived degree of happiness on the visual analogue scale described in (ii)
Grant et al. [9] and Laerhoven et al. [19] compared these scales in medical re-
search.
There are several disadvantages to using the scale in (i). The scale provides the
patient with only five possible responses, so it is not suitable for fully capturing the
details of the patient's response. Another disadvantage is that the scale fails to fully
record the variability of responses. For example, suppose that two patients, call them
A and B, choose (4). In this case, it is highly unlikely that their degrees of happiness
are exactly the same—A's “true” degree of happiness may be between (4) and (5),
whereas B's may be between (3) and (4). As illustrated here, the scale disregards the
variability within each category. Also, it is important to note that Likert-type scales
are not interval scales; although integers are often assigned to represent possible
responses, it may be unreasonable to assume that the intervals between two adja-
cent responses have the same length (e.g., Wu [21]). Abrupt transitions between
these measures are often undesirable for encoding imprecise observations. These
characteristics severely limit the type of statistical analysis that we can apply to the
measurements with this scale.
The scale in (ii) provides the patient with infinitely many (in fact, uncountably
many) possible responses. It can be considered an interval scale, so it permits a
variety of statistical analyses (e.g., Stevens [17], Chimka and Wolfe [1]). However,
