Page 268 - Handbook of Properties of Textile and Technical Fibres

242 Handbook of Properties of Textile and Technical Fibres

relationships, yet they are associated with many assumptions, none of which is tested
for validity in most textile research papers. These include existence, linearity, indepen-
dence, collinearity, homoscedasticity, and normality. Unfortunately, none of these
assumptions is tested in any of the research studies on the relationships between bundle
strength and single-fiber strength. When data taken from these studies were analyzed
independently, it was found that there is a great deal of violation of these assumptions.
The problem becomes even greater when the so-called stepwise regression analysis
is used to develop empirical relationships. This approach is widely used among
nonstatisticians, but you will hardly see it used by statisticians or even discussed in
statistics books, except to illustrate the enormous risk of using it. The approach is
based on using an automatic computational routine to determine the best empirical
relationship, without much involvement of the analyst; it is what we call an
“automatic-pilot regression analysis.” This approach is highly sensitive to any
violation of the regression assumptions mentioned above. In addition, it has other
serious problems including (Hansen et al., November 2015; Elmogahzy, 2002) the
following: (1) at any given step, the model is fit using unconstrained least squares,
making it far inferior to other methods such as factor analysis and (2) the method is
typically associated with a significant bias in parameter estimation. For these reasons,
stepwise regression analysis is not standard in most software programs, and different
software programs may use different computations of both “forward elimination” and
“backward elimination” stepwise regression. Obviously, this subject is outside the
scope of this chapter. However, it is critical to warn textile and cotton researchers
from jumping into computational methods to develop empirical relationships without
prior validation analysis.
In the sections below, some of the empirical relationships between bundle strength
and single-fiber strength are presented. It is important that each empirical relationship
is viewed within its own context; meaning, no generalization to other situations, and
certainly, no prediction outside the given data range or the cotton varieties used in
each article.

7.11.3 Empirical relationships between HVI and Stelometer
bundle strength and Mantis single-fiber strength

The introduction of the Mantis single-fiber strength tester led researchers in the USDA,
ARS, Southern Regional Research Center to conduct a study by Thibodeaux et al.
(1998) in which the Mantis parameters were related to HVI and Stelometer strength
parameters. The samples tested included eight Egyptian cottons, seven American
cottons, and five genetically related Texas cottons. The idea was to utilize cotton fibers
of high genetic diversity and wide variation in fiber properties (length, strength, and
fineness). In this study, many structural parameters were considered in addition to
the Mantis breaking load. These included Mantis ribbon width, cell wall area by
AFIS, cell wall area by image analysis, fiber perimeter by AFIS, fiber perimeter by
image analysis, fiber micronaire, X-ray crystallinity index (CRYST), and X-ray
orientation angle. Using stepwise regression analysis, it was revealed that the relation-
ship between bundle strength and single-fiber strength was improved significantly