Moacyr Machado Cardoso Junior
Instituto Tecnológico de Aeronáutica, Brazil
E-mail: moacyr@ita.br
Submission: 26/07/2017
Revision: 06/03/2018
Accept: 15/03/2018
ABSTRACT
Risk management focus
main on technical and rational analysis about operational risks and by those
imposed by occupational environment. In this work one looks to contribute to
perception study of work safety professionals about a series of activities and
environment agents. In this way it was used theory sustained by psychometric
paradigm and multivariate analysis tools, mainly multidimensional scaling,
generalized Procrustes analysis and facet theory, in order to construct the
perceptual map of occupational risks. The results obtained showed that the
essential characteristics of risks, which were initially split in 4 facets were
detected and maintained in perceptual map. The construction of perceptual map
also permitted to verify the formation of a new facet, not considered in the
beginning. The facet theory which by hypothesis was used in this work showed
adequate, providing the regional interpretation of the map. The inferential
analysis realized showed fine results for the final configuration validation,
indicating which risks and/or activities belongs to the same facet.
1. INTRODUCTION
The
perception of occupational risks is gaining prominence in Brazilian preventionist
scenario, as recent work of Cabral et al. (2010), McGrath (2010), Johnsen et
al. (2010) and Bjerkan (2010) in the oil and gas industry. In the same vein
Soares et al. (2008) developed a study on risk perception in the port area.
The
perception of risk is the subjective assessment of the likelihood of a specific
type of accident occurs, and to what degree a person is worried about its
consequences. The perception of risk however goes far beyond the individual and
the result is a construct that reflects social and cultural values, symbols,
history and ideology (WEINSTEIN, 1980).
Johnsen
et al. (2010) advocate the use of an indicator of risk perception among the
stakeholders involved in a remote operation. The authors suggest measuring the
impact of risk perception on safety and resilience when a task is distributed
between onshore and offshore.
Hussin
and Wang (2010) compared safety perception among post-graduate students and
discovered that oil and gas and aviation are considered safe industries and
that nuclear and mining industries are considered unsafe. The students relate
risk perception more linked with severity of accidents rather than probability
of occurring.
Leiter
et al. (2009) studied occupational risk perception in relation to safety training
and injuries in a printing industry. Using structural equation analysis the
authors confirmed a model of risk perception based on employee’s evaluation of
prevalence and lethalness of hazards as well as control over hazards the
employees gain through training.
The
study of risk perception has been developed since the initial work of Starr
(1969) cited by Sjoberg et al. (2004). Two theories currently prevail, one
represented by the psychometric paradigm, based on psychology and decision
sciences and cultural theory developed by sociologists and anthropologists.
This
paper aims to: i) obtain the perceptual map of the occupational risk, from the
standpoint of psychometric paradigm in a group of safety engineering graduate
students. The group was submitted to a list of hazards involving four facets
represented by physical and chemical agents, activities with a predominance of
ergonomic hazards and activities with various risks and admittedly dangerous,
ii) testing the hypothesis of regional interpretation of the solution space of
perceptual mapping, iii) to test statistical differences between the objects
evaluated using multivariate statistical tools.
The
expected contribution of the work is to produce a perceptual map using
visualization techniques of multidimensional data, known as multidimensional
scaling (MDS), aided by tools of shape statistics, the Procrustes. The
methodological approach employed in this study was an exploratory research.
This
paper is organized as follows: in the introduction section, dealt with the
motivation and objectives for development of this work, Section 2 a brief
review of the psychometric paradigm and studies of risk perception. Section 3
presents the method used in this study, the non-metric MDS and Procrustes
analysis, Section 4 presents the analysis and results obtained using
psychometric paradigm associated with visualization tools and multivariate
statistics, and finally Section 5 with final remarks.
2. RISK PERCEPTION AND THE PSYCHOMETRIC PARADIGM
The
ability to sense and avoid hazardous environmental conditions is necessary for
the survival of Human beings. Survival is also assisted by the ability to
encode and learn from past experiences. Humans also have an ability that allows
them to change the environment and adapt it. This ability may both decrease and
increase risks (SLOVIC, 2001).
The
most common strategy for the study of risk perception employs the psychometric
paradigm, which uses psychophysical scaling methods and multivariate analysis
techniques to produce quantitative representations or also known as cognitive
maps of attitudes and perceptions.
Within
the psychometric paradigm people make quantitative judgments about the current
and desired risk of various hazards and desired level of regulation of each of
the risks. These judgments are then related to judgments about other
properties, such as: willingness, fear, knowledge, control, benefits to
society, the number of deaths in one year, number of deaths due to a disastrous
year (SLOVIC, 1987, 2001).
Several
authors have identified behavioral factors that affect risk perception, whether
the risk is natural or anthropogenic, whether it is voluntary or not, whether
it generates fear, whether it is familiar or new, whether it can produce
chronic effects, (i.e.: the damage is small, but steady in contrast to the
catastrophic effects many deaths instantly), whether the person has control
over them or memorable situations, due to personal experiences, family
situations or widely known in the media. (BAUMGARTEN; MCCRARY, 2004).
According
Sojberg et al. (2004), the work of Fischhoff, Slovic, Lichtenstein, Read and
Combs, 1978, reproduced in Slovic (2001) was a landmark of psychometric theory.
The authors have compiled nine dimensions from the literature related to perception
studies. The first refers to the risk exposure is being voluntary or
involuntary, the second referring to the immediacy of the consequences or not,
the third assesses the extent to which risk is known by the person who is
exposed, the fourth refers to the potential chronic or catastrophic risk, (i.e.
chronic risks are those that cause harm (deaths) in large time and catastrophic
cause many damage (deaths) instantly).
The
fifth dimension involves deciding whether the risk is common, (ie. A risk already
assimilated by the people or causes a great fear). The sixth dimension relates
to the severity of the consequences imposed by the risk, the seventh to the
extent to which the risk is known by science, the eighth evaluates the level of
control the person has upon risk and the last one if the risk is new to society
or not.
Several
surveys were conducted on a large number of activities (smoking, use of dyes in
food, nuclear operations, vehicles, skiing, among others) described in nine
dimensions. Data were analyzed with factor analysis and the authors identified
two major factors that explain most of the data variance, which are: Fear and
the Newness of Risk
McDaniels
et al. (1995) cited by Sjoberg et al. (2004) defined the psychometric paradigm
as an approach to identify the characteristics that influence the perception of
risk. The approach assumes that risk is multidimensional, with many
characteristics other than individual judgments of the likelihood of damage to
health or life. The method application in studies of human health risk
perception include: - develop a list of hazards based on events, technologies
and practices that include a broad spectrum of potential hazards - developing a
number of psychometric scales that reflect characteristics of the risks are
important to map the human perception in response to the risks - to ask the
respondents to evaluate each item on the list of hazards in each of the nine
dimensions - using multivariate analysis to identify and interpret a set of
latent factors that capture the variations the responses of individuals and the
group.
Sjoberg,
(2000, 2002) and Marris et al. (1998), mentioning that some analysis takes into
account up to 18 dimensions, but typically 80% of the variance is explained by
three dimensions by factor analysis and the factors that have been reported in
studies of perception are New or Old, Feared or Common and Number of exposed
persons. The author also presents some criticisms of the psychometric paradigm
as regards the small number of dimensions evaluated from 9 to 18, and the fact
of not including an important dimension which is related to the risk is natural
or not, and finally that the analysis is based on average, not all data
collected.
3. METHOD
Aiming
to assess the perception of a population of safety engineers students to
occupational risks a questionnaire was applied. The questionnaire listed 29
objects divided into four facets, 5 physical agents, 8 chemical agents, 11
activities that involve various hazards and 5 typical office activities, with
emphasis on ergonomics. Table 1 shows the objects of research.
Table
1: Objects of Perception Survey of Occupational Risk divided into four Facets.
Physical agents |
Noise Heat Vibration Humidity Non ionizing radiation |
Chemical agents |
Metal fumes Asbestos Silica Lead Gasoline Benzene Mercury Nanotechnology |
Activities that involve various hazards |
Hospital laundry Working under the sun Forest harvesting Electrical Maintenance Caisson Diving Confined space Working at height X-ray Operator Electroplating Electric Welding |
Typical office activities, with emphasis on ergonomics |
Labor office Telemarketing operator Bank Teller Posture Exertion |
Facet
theory is a way of linking the geometric properties of an MDS configuration
with attributes of the objects represented in it. This is a regional
interpretation of the MDS space based on a theoretical framework (BORG;
GROENEN, 2005).
In
this study the facets are grouped according to 3 classes of occupational
hazards: physical, chemical and ergonomic hazards and a different class, which
involves various different hazards.
For
each object the respondents were asked to assign scores on a Likert scale from
1 to 7 in nine dimensions, as Figure 1.
The
forms provided to respondents contained objects arranged in a random way,
aiming to eliminate any possibility of systematic error in data collection.
Dimensions |
Scale |
Willingness to risk. People "take" this
risk voluntarily |
Voluntary
Involuntary 1 2 3
4 5 6
7 |
Time to Effect. To what extent there is risk
of immediate death or the risk of death is delayed. |
Immediate Late 1 2 3
4 5 6
7 |
Knowledge of Risk. –
Exposed. To what degree the risk is
known by people who are exposed to it. |
Known
Not Known 1 2 3
4 5 6
7 |
Knowledge of Risk. - Science To what degree the risk is
known to science. |
Known
Not Known 1 2 3
4 5 6
7 |
Control of Risk. If you are exposed to risk,
to what extent you can, because your skills, avoid death while engaged in
activity. |
Incontrolable
Controlable 1 2 3
4 5 6
7 |
Newness. This threat is new or old,
familiar |
New Old 1 2 3
4 5 6
7 |
Chronic-Catastrophic. This risk kills one person
at a time (chronic) or risk kills a large number of people at once
(catastrophic) |
Chronic
Catastrophic 1 2 3
4 5 6
7 |
Common-Feared. People have learned to live
with this risk and may decide to quietly about the same, or is a risk that
people have a great fear |
Common Feared 1 2 3
4 5 6
7 |
Severity of Consequences. What is the likelihood that
the consequence of that risk is fatal |
Not Fatal Fatal 1 2 3
4 5 6
7 |
Figure 1:
Dimensions of risk perception and their Likert scales.
Respondents
were only given instructions on how to fill, using the Likert scale, with no
explanation of the meaning of each object. The respondent group comprised 13
students from a Safety Engineering course.
3.1.
Multidimensional
Scaling (MDS)
The
method used to draw the perceptual map of risk was a non-metric Multidimensional
Scaling (NMDS). The MDS also called classical metric was introduced by
Torgerson (1952, 1958) and Gower (1966), as quoted by Wickelmaier, (2003), Borg
and Groenen (2005). The classic MDS is also known as Torgerson Scaling or even
Torgerson-Gower Scaling (BORG; GROENEN, 2005).
Classic
MDS starts with a distance matrix D with elements dij, where i, j = 1 ,.... n,
and the goal is to find a configuration of points in p-dimensional space from
the distances between the points so that the coordinates of n points along the
dimension p will produce a matrix whose elements are Euclidean distances as
close as possible to the elements of distance matrix D. In this paper the
distance matrix was obtained from the consensus configuration of generalized Procrustes
analysis (GPA).
The
GPA is a statistical tool shape. The term shape is defined by Brombin and
Salmaso (2009) involving the geometric properties of a configuration of points
that are invariant to changes in translation, rotation and scale. Direct analysis
of a set of points is not appropriate due to the presence of systematic errors
such as position, orientation and size, and usually to conduct a reliable
statistical analysis GPA is used to eliminate factors not related to shape and
to align the settings for a common coordinate system (BROMBIN; SALMASO, 2009).
The
GPA, a multivariate statistical technique in which three empirical dimensions
are involved: the objects of study, people who value the objects and attributes
in which the objects are evaluated. In the case of this study p attributes,
with (p = 1 ,..., 9), represented by the dimensions of risk perception, was
measured on n objects, with (n = 1 ,..., 29), which in this case are
represented by four facets, with (m = 1 ,..., 13), evaluators. The GPA is an
ideal method to analyze data from different individuals (DIJKSTERHUIS; GOWER,
2010).
Suppose
there are m (nxp) configurations X1, ... Xm and each ith row of Xj (j = 1, ...
m) contain the coordinates Pi (j) in p-dimensional Euclidean space, eg scores
of the attributes of a product i (i = 1, ... n) by evaluator j. Naturally it is
considered that the m configurations contain information about the same n
objects in the same attributes. The objective of the GPA is to determine to
what extent the m configurations are consistent.
This
problem can be described as the measure of similarity between the m
configurations, or interrater reliability judge (RODRIGUE, 1999). The
mathematical formulation of the GPA can be described as follows, Tj is an nxp
matrix with all n rows equal to tj (1xp row vector), an orthogonal matrix Hj
(pxp), and ρj a scalar (j = 1, ... m). The translation to the origin is given
by adding the same row vector (1xp) tj to all line of Xj. The scaling, rotation
and translation can therefore be expressed by the transformation given by
Equation (1).
|
(1) |
The
GPA also allows to analyze the data set, to verify the similarity between
judges, the influence of causal factors, using the Procrustes ANOVA, termed as
PANOVA by Nestrud and Lawless (2008), and Dijksterhuis and Gower (2010); Gower
(2004).
The
NMDS ordinal is a special case of MDS, and possibly the most important in
practice (COX; COX, 2000). It is normally used when, for example, we want to
get the trial, placing the objects in ascending or descending order of
importance from the perspective of an evaluator. The most common approach used
to determine the elements dij and to get the coordinates of objects x1, x2,
..., xn is an iterative process, implemented in the Shepard-Kruskal algorithm,
with the minimization of a function known as Stress as in Equation (2)
(Kruskal, 1964). The NMDS is an iterative and its point of departure is the
metric MDS.
|
(2) |
The
Stress function represents and evaluates the inadequacy (admissible
transformation) of proximities and the corresponding distances. Stress is very
similar to the correlation coefficient, except that it measures the misfit and
not the adjust of a model. A comparison with the correlation coefficient is
because the researchers know that a correlation may be artificially high by the
presence of outliers, and also very low due to, for example, the linear model
is not the most appropriate. What is done in these circumstances is to examine
the scatter plot. The same practice is advocated in the NMDS, by means of a
graph with the proximities in the abscissa axis against the corresponding
distances in the y-axis. Typically a regression shows how the proximity and
distance estimates are related. This chart is known as the Shepard diagram (BORG;
GROENEN, 2005).
Another
way is to determine the space dimensionality from which do not occur a
significant reduction in the value of stress, ie solve the NMDS for several
dimensions and plot the values of stress as the ordinate and dimension in the
abscissa axis. This chart is known as "Scree Plot". The curve shape
is generally monotonic downward, but at a very low rate as it increases the
size (convex curve). What is sought is the "elbow", the point where a
decrease in stress is less pronounced (BORG; GROENEN, 2005).
Finally,
the trial dimension for use in the final configuration of points uses the
criterion of interpretability, as cited by Kruskal (1964), i.e.: m dimensions provides a satisfactory
interpretation, and m +1 in no way improves the interpretation, it makes
perfect direction set in m-dimensions. That is the Stress obtained is only a
technical measure and the NMDS. Evaluation of NMDS should be made knowing the
theory that explains the behavior of the data.
In
the specific case of this study it was defined a priori that two dimensions is
a good representation, and relying on the Facets theory described by Borg and
Groenen (2005) analyzed the differences between objects obtained in the final
configuration of consensus.
The
statistical differences between the objects of a facet were determined by
Hotteling - T2 multinormal test, with 0.05 of significance, according to the
hypothesis:
where j and k are object of the same facet, e
i=1,...,4.
To
check the interrater reliability respondent used the RV coefficient, which is a
multivariate statistical ranging between 0 and 1 (0 representing total
disagreement, orthogonality and 1 a perfect agreement). According to Cartier et
al. (2006); Nestrud and Lawless (2008) Rv values above 0.7 are accepted as a
good level of agreement between the configurations. However, Josse, et al.
(2008) argue that the RV coefficient between the two extremes (0 and 1) is not
informative because their value depends on the number of individuals, the number
of variables, and dimensionality (i.e. Structure covariance) of each data set,
and hence a high value of Rv is not necessarily a significant relationship
between the data sets.
One
way to solve this problem is to perform a statistical test on the coefficient
Rv. Josse, et al. (2008) proposed a permutation test to calculate the p-value.
The hypothesis is:
H0: Rv=0 (no significant association between the data
sets)
Thus
it is calculated the Rv coefficient according to Equation (3) and using
Permutation test calculates the
significance of it according to H0 hypothesis.
|
(3) |
where
and variance de Y, is X variance and is the covariance XY.
The
NMDS solution was achieved using MASS package (VENABLES; RIPLEY, 2002). The GPA
and the Rv coeficient were determined by FactoMineR package, (HUSSON, et al.
2009). Both implemented in R - CRAN Version 2.9.2 (R Development Team, 2009).
4. RESULTS AND DISCUSSION
The
13 sets of data for each of the respondents were submitted to GPA procedure, to
obtain the aligned configurations. After the initial alignment each
configuration was submitted to nonmetric multidimensional scaling to obtain
representation in two dimensions. In this step the respondents A4, A6, A8 and
A12, were eliminated from the process because one or more of the Euclidean
distances between objects resulted in zero value, suggesting that the
respondent gave the same scores for different objects.
With
9 other settings, we proceeded back to the alignment settings and obtaining
consensus configuration.
The
final consensus configuration is shown in Figure 2. The objects were grouped
under the same initial Facets, where it was shown that the initial hypothesis
was proved in the low dimension space, i.e. the original facets are mirrored in
the configuration obtained. The only exception occurred with the humidity,
because it remains located outside the facet of physical agents, as expected.
The
first dimension divides the perceptual map in the inferior quadrant chemical
risks, linking them with the greatest risk of death and physical risks, linking
them with a lower risk of death.
The
separation, however, is not perfect, since the facet of chemical risks tends to
invade the field of physical risks facet, but this fact can be explained by the
low level of knowledge about the risks posed by nanotechnology among the
respondents. Although many already know the topic, unaware of the risks.
In
relation to dimension 2, the map is divided between activities/operations and
environmental agents.
In
the first quadrant (left) activities related to office, bank teller,
telemarketing operator, posture and physical effort to compose facet of
activities with a predominance of ergonomic hazards and in the second quadrant
(right) facet of activities with various risks are allocated. Again one cannot
obtain a perfect facet, since working under the sun, forest harvesting and
hospital laundry tend to be more distant from the group. The object humidity,
as reported above, stands out in terms of dimension 2, being isolated at the
top of the map.
The
next step was to test the hypothesis that objects belonging to a particular
facet cannot be separated statistically, which reinforces the initial
hypothesis that the representations in four facets were demonstrated in the
perceptual map. For that we use the test Hotteling T2, which is equivalent to
"t" test of one-dimensional case.
To
perform this test data initially arranged in an array (O, D, K) (O = 1,...,
29), (D = 1.2) and (K = 1,..., 9 ) were rearranged into an array (K, D, O).
A
necessary condition for using the T2 test is that data is distributed as a
multivariate normal, and in this case, the data were tested for multivariate
normality with the Shapiro-Wilk (SHAPIRO; WILK, 1965).
The
hypothesis H0 is that the data follow a multivariate normal distribution with a
significance level of 0.05.
Figure 2:
Configuration of consensus obtained for the NMDS.
The
results of multivariate normality test for the data, showed that only the
objects 5, 15, 22, 23 and 26 do not follow the multivariate normal
distribution, and therefore the results obtained with the test T2 are
unreliable for these objects.
In
this paper it is assumed, although there are exceptions in some data, that
Hotteling T2 can be used to test the hypothesis H0 of statistical equality of
the objects within a single facet.
Table
2 shows the overall outcome of the activities of the facet comparisons with
other risks.
Table 2: P-values for the Hotteling T2 test of Facet
Activities with several risks.
Object (N°) |
10 |
12 |
13 |
15 |
17 |
22 |
23 |
24 |
25 |
27 |
Forest harvesting – 7 |
0,1741 |
0,8023 |
0,0853 |
0,0017 |
0,1782 |
0,288 |
0,002 |
0,012 |
0,008 |
0,3348 |
Electroplating – 10 |
- |
0,3747 |
0,665 |
0,019 |
0,4908 |
0,468 |
0,029 |
0,132 |
0,097 |
0,0021 |
Hospital laundry – 12 |
|
- |
0,1648 |
0,004 |
0,1881 |
0,163 |
0,006 |
0,026 |
0,018 |
0,125 |
Electrical mantenance – 13 |
|
|
- |
0,2369 |
0,3512 |
0,421 |
0,305 |
0,560 |
0,4380 |
0,0026 |
Diving – 15 |
|
|
|
- |
0,0018 |
0,017 |
0,822 |
0,685 |
0,886 |
0,0000 |
X-Ray Operator – 17 |
|
|
|
|
- |
0,983 |
0,006 |
0,022 |
0,008 |
0,0019 |
Electric Welding – 22 |
|
|
|
|
|
- |
0,052 |
0,066 |
0,014 |
0,0289 |
Working at height – 23 |
|
|
|
|
|
|
- |
0,946 |
0,629 |
0,0000 |
Confined space – 24 |
|
|
|
|
|
|
|
- |
0,467 |
0,0002 |
Caisson – 25 |
|
|
|
|
|
|
|
|
- |
0,0002 |
Work under the Sun – 27 |
|
|
|
|
|
|
|
|
|
- |
Bold
values mean that the hypothesis H0 was rejected, ie there is significant
difference between objects. It is for example the case of Forest Harvesting,
which does not differ statistically from electroplating, hospital laundry,
electrical maintenance, X-ray Operator, welding and work under the Sun, but
differs statistically from Diving, Working at height, Confined Space and
Caisson.
Likewise
occur for other objects. These results lead us to conclusion that cannot be
regarded as a single facet, that is, it can be subdivided, and the initial
hypothesis is partially rejected. It should be noted also that the four objects
mentioned above form a group where the risk of death is pronounced due to the
characteristics of activities which may indicate the existence of a fifth
facet, called activities with high potential for serious accidents.
In the
case of Facet of Activities with a predominance of ergonomic hazards it appears
that only the Bank Teller activity does not differ statistically from the other
objects of the facet and that telemarketing operator differs statistically from
Exertion, which is fairly consistent because we did not identify the presence
of Exertion on office activities. Exertion does not seem to belong to this
facet, as shown in Table 3.
Table 3: P-values obtained in Hotteling T2 in Facet
Activities with a predominance of ergonomic hazards.
Object N° |
4 |
8 |
18 |
26 |
Telemarketing operator – 2 |
0,9161 |
0,0466 |
0,2799 |
0,648 |
Bank teller – 4 |
|
0,1927 |
0,5461 |
0,489 |
Exertion – 8 |
|
|
0,2113 |
0,007 |
Posture – 18 |
|
|
|
0,043 |
Office – 26 |
|
|
|
- |
The
most consistency Facet was for physical agents, except for humidity, as shown
in Table 4.
Table 4: P-values for the T2 Test Hotteling Facet
Physical Agents.
Object N° |
19 |
20 |
29 |
28 |
Heat – 5 |
0,1825 |
0,443 |
0,7357 |
0,0697 |
RNI – 19 |
|
0,4758 |
0,4487 |
0,1465 |
Noise – 20 |
|
|
0,9225 |
0,0967 |
Vibration – 29 |
|
|
- |
0,022 |
Humidity – 28 |
|
|
|
- |
In
this case an inconsistency is identified in Table 4, because the p-values
revealed no statistical differences among the other objects, except for
vibration, which does not arise in the positioning on the map. This
inconsistency may be linked to the fact that the theoretical inadequacy of the
humidity agent to other agents, or problems due to the strong assumption of
multivariate normality test imposed by Hotteling.
And
finally on the facet chemical agents, the objects metal fumes and Nanotechnology
were those who differ from the others, except for lead and metal fume and metal
fumes and nanotechnology that were not statistically different, as shown in
Table 5.
Table 5: P-values for the Test Hotteling T2 in the
Facet Chemical Agents.
Object N° |
3 |
6 |
9 |
11 |
14 |
16 |
21 |
Asbestos – 1 |
0,2639 |
0,5581 |
0,0154 |
0,1843 |
0,9556 |
0,0027 |
0,188 |
Benzene – 3 |
|
0,1226 |
0,0014 |
0,4789 |
0,5413 |
0,0003 |
0,077 |
Lead – 6 |
|
|
0,1825 |
0,2010 |
0,6605 |
0,0105 |
0,877 |
Metal fumes – 9 |
|
|
|
0,0148 |
0,0728 |
0,1549 |
0,230 |
Gasoline – 11 |
|
|
|
|
0,2077 |
0,0011 |
0,348 |
Mercury - 14 |
|
|
|
|
|
0,0068 |
0,372 |
Nanotechnology - 16 |
|
|
|
|
|
|
0,014 |
Silica - 21 |
|
|
|
|
|
|
- |
Intergroup
comparison showed that only the evaluator A2 with A5, A7, A9, A10 and A11 the
Rv coefficient did not differ from zero, ie only in those cases the evaluators
disagree strongly. In other cases there is coincidence between the evaluations.
This assessment points towards the evaluator A2 be an outlier within the group
studied. The results of the RV coefficient and significance test obtained by Permutation
are shown in Table 6. In the upper diagonal are the Rv values and the bottom
diagonal are the p-values obtained by Permutation.
TABLE 6: Coefficients Rv and significance test
(p-value) inter evaluators.
A1 |
A2 |
A3 |
A5 |
A7 |
A9 |
A10 |
A11 |
A13 |
|
A1 |
1.0000 |
0.1763 |
0.2460 |
0.3570 |
0.4823 |
0.4968 |
0.5253 |
0.4386 |
0.5254 |
A2 |
0.0289 |
1.0000 |
0.1612 |
0.1211 |
0.1007 |
0.0810 |
0.1329 |
0.0334 |
0.1596 |
A3 |
0.0049 |
0.0389 |
1.0000 |
0.1898 |
0.1924 |
0.3981 |
0.2241 |
0.2524 |
0.2725 |
A5 |
0.0002 |
0.1176 |
0.0211 |
1.0000 |
0.1710 |
0.2756 |
0.2765 |
0.1926 |
0.2797 |
A7 |
0.0000 |
0.1436 |
0.0181 |
0.0307 |
1.0000 |
0.2920 |
0.5056 |
0.3194 |
0.4264 |
A9 |
0.0000 |
0.1983 |
0.0001 |
0.0021 |
0.0028 |
1.0000 |
0.4389 |
0.4563 |
0.4067 |
A10 |
0.0000 |
0.0692 |
0.0085 |
0.0021 |
0.0000 |
0.0002 |
1.0000 |
0.3385 |
0.5664 |
A11 |
0.0000 |
0.7138 |
0.0033 |
0.0187 |
0.0009 |
0.0000 |
0.0006 |
1.0000 |
0.4453 |
A13 |
0.0000 |
0.0425 |
0.0025 |
0.0018 |
0.0001 |
0.0003 |
0.0000 |
0.0000 |
1.0000 |
5. CONCLUDING REMARKS
This
study investigated the occupational hazards perception of a safety engineers
group of students when subjected to a questionnaire administered according to
the psychometric paradigm, considering the initial assumption of 29 objects
divided into four facets. The result of the NMDS obtained through analysis of
nine dimensions of the risk perception, created a perceptual map in two
dimensions where the four facets were represented in low-dimensional space.
Statistical
analysis between the objects of the facets showed that there are some objects
that are not well represented, because they differ from the others, but
generally speaking the facets generated are appropriate. The regional
interpretation of the NMDS was positive due to the generation of the
representation of the facets considered in the initial hypothesis.
A
fifth facet can be determined from objects with high potential for serious
accidents.
The
introduction of the analysis of statistical inference can be regarded as an
increment to the NMDS analysis, although the hypothesis of multivariate
normality has been shown to be limiting. Future studies should be conducted
using bootstrap or permutation test that are indifferent to the multivariate
normality assumption and also to confirm the settings obtained in this work.
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