Information Technology Reference
In-Depth Information
19
Statistical Procedures for Fuzzy Data
in Medical Research
Takehiko Nakama
19.1
Introduction and Summary
Observations or measurements in many real-world problems tend to be inherently
imprecise, uncertain, or linguistic. In medical research, there has been an increas-
ing interest in statistical analysis of such observations—perceived breathlessness,
general fatigue, and self images, for example (e.g., Grant et al. [9], Laerhoven et
al. [19]). Fuzzy sets can effectively encode those observations. Nominal or ordinal
measurements can also be used to represent them, but statistical analyses are quite
limited for those measures (see Section 19.2).
In this paper, we examine advantages of using fuzzy sets to represent observations
in medical research and review some of the statistical procedures that have been de-
veloped for quantitatively analyzing fuzzy data. Various statistical tests are available
for analyzing fuzzy data. For instance, Körner [10], Montenegro et al. [13], and
González-Rodríguez et al. [8] developed one-sample methods for hypothesis testing
about the fuzzy population mean. Montenegro et al. [12] and González-Rodríguez
et al. [7] established a two-independent-sample test of equality of fuzzy means, and
González-Rodríguez et al. [7] developed a paired-sample test of the same type. These
are considered extensions of classical
t
tests to fuzzy data. Gil et al. [5] and González-
Rodríguez et al. [6] developed a multiple-sample test of equality of fuzzy means; this
is one-way analysis of variance (ANOVA) for fuzzy data. Recently, Nakama et al.
[14, 15] have established factorial analysis of variance for fuzzy data. Using exam-
ples, we will explain how they can be applied to medical research.
Instead of describing mathematical details of the statistical procedures for fuzzy
data, we provide a tutorial exposition of the methods in this paper. We will direct
the reader interested in the technical details to relevant papers.
19.2
Scales of Measurement
Suppose that we are concerned with a patient's mental health and that we wish
to measure the degree of happiness that the patient feels.
First we consider the
