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Construction of a global score from multi-item questionnaires in epidemiological studies



Different approaches for the construction of global scores from multi-item questionnaires were discussed. A new approach called criterion based approach was proposed for the Stress-Energy Questionnaire
Construction of a global score from multi-item questionnaires in
epidemiological studies
Emina Hadžibajramović
, Elisabeth Svensson
, Gunnar Ahlborg Jr
The Institute of Stress Medicine, Region Västra Götaland, Gothenburg, Sweden
Department of Statistics, Örebro University School of Business, Sweden
Department of Public Health and Community Medicine, Sahlgrenska Academy, University of
Gothenburg, Sweden
Corresponding author
Address: The Institute of Stress Medicine
Carl Skottsbergs gata 22 B, 413 19 Gothenburg, Sweden
Telephone: +46 31 342 07 14
Fax: +46 31 41 42 73
Email addresses:
Perceived health, mood, job demands and social support are common outcome variables in
epidemiological studies of the psychosocial work environment, as measured by multidimensional multi-
item questionnaires. The Stress-Energy Questionnaire (SEQ) is one such questionnaire and was
developed to measure two critical aspects of mood at work. When a variable is measured by more than
one item, the construction of a global score for that particular variable is often necessary. The most
common way of aggregating items into a total or global score is to sum or average the responses, which
requires equidistance scale categories and all items to be equally important.
Assessments on many questionnaires, including the SEQ, are made on rating scales, meaning that the
data consist of ordered categories irrespective of the type of coding system. These codes do not
represent numerical values, but rather only convenient labelling devices for ordering responses from the
lowest to the highest amount of the characteristic being measured. They do not have the mathematical
properties needed for arithmetic calculations.
In this study, different approaches for the construction of global scores are discussed. We have showed
that there are alternative methods for the construction of global scores that take into account the non-
metric properties of data from questionnaires. The median and the criterion based approaches are
proposed as the appropriate methods to use for ordinal data and these were applied to the empirical
Keywords: global scores, ordinal data, questionnaires, rating scales
The use of questionnaires is an essential tool in epidemiological studies. Epidemiological findings and
information about exposures, outcomes, modifying and confounding variables are often based, partly or
completely, on self-reported data from questionnaires. In clinical trials many variables can be measured
objectively (e.g. height, weight, blood pressure, etc) and these are often continuous quantitative
variables. In epidemiological studies, on the other hand, many qualitative variables, such as stress,
depression, anxiety and psychosocial working conditions, are not directly observable as they are
hypothetical in character and refer to subjective ratings.
Some variables are measured by a single item scale, but multi-item questionnaires are very common.
Each item usually has several numerically coded response categories. These values are rank ordered,
meaning that each category has more of the attribute being measured than the previous category, but
the differences between the categories are unknown and thus these values do not have the mathematical
properties needed for arithmetic calculations. The numbers assigned to the response alternatives are
arbitrary and can be changed as long as the ordering between them is preserved (1, 2). The stress-energy
questionnaire (SEQ) is an example of one such questionnaire. The variables stress and energy are
measured by six items each. The SEQ is used in epidemiological studies for measuring critical aspects of
mood at work (3, 4).
When a variable is measured by more than one item, the construction of a global scale for that
particular variable is often necessary and the way that this is done has been discussed for a long time (5).
In epidemiology, these scales are called the total, overall or global scores. Various nonparametric and
parametric approaches for handling data from multi-item questionnaires have been proposed, such as
the Classical Test Theory, the Rasch model and the Item Response Theory, which is also called the
underlying variable approach. Probably the most common approach for creating global scores from
multi-item questionnaires is based on summation or averaging the responses (6-10), which ignores the
fact that assessments on scales produce ordinal data (1, 2).
The aim of this paper is to present approaches for the construction of global scores that take into
account the non-metric properties of ordinal data obtained from scale assessments. Data regarding
perceived stress and energy measured by the SEQ will be used to demonstrate alternative approaches.
The shortcomings of the mean scores will be explained. The median and criterion based approaches,
which are appropriate for the ordinal data (8, 11), will be introduced for the SEQ and compared
regarding the purpose of the SEQ, which is the identification of individuals with low and high levels of
stress and energy respectively.
An example from an epidemiological study
The empirical data used for the applications come from an ongoing cohort study of psychosocial
working conditions, stress, health and well-being among human service organization (HSO) workers
(12-16). The goal is to recognize groups at risk of adverse health effects, by indentifying individuals with
low and high levels of stress and energy. This is essential since previous research has shown that a low
level of stress both at work and during leisure time is prospectively associated with good subjective
health, and similarly a high level of stress and low energy can be related to adverse health effects (15, 17-
The variables stress and energy are measured by the stress-energy questionnaire (SEQ). The SEQ is an
adjective checklist, which was developed for measuring two aspects of mood at work (3, 19). The overall
question to be answered by means of the checklist is: “During the past week, how did you usually feel
when you were at work?” Each dimension consists of three positively loaded items (stress: rested, relaxed,
calm; energy: active, energetic, focused) and three negatively loaded items (stress: tense, stressed,
pressured; energy: dull, ineffective, passive). The response alternatives are: not at all, hardly, somewhat,
fairly, much, and very much and are coded from 0 to 5. The interpretation of the responses goes in
opposite directions for positive and negative items. For positively loaded items, very much implies the
lowest stress level and the highest energy level (the most favourable response), while not at all is the
least favourable. The opposite is true for negatively loaded items.
Data was collected through a mailed questionnaire sent to a random sample of employees in the human
service sector in Sweden in 2004 and 2817 individuals with complete data sets on all SEQ items were
Mean scores
Under the mean score approach, all items are considered equally important and the equidistance
between scale categories is implied. Taking an the item stressed in the SEQ as an example, this assumes
that the distance between not at all stressed and hardly stressed is the same as the distance between
somewhat stressed and fairly stressed, or the distance between any other two adjacent scale categories.
Before the calculation of the mean score, the numerical coding of the stress items rested, stressed and
pressured and the energy items dull, ineffective and passive are reversed, so that the interpretation of the
response categories goes in the same direction. Again, equal spacing between the scale categories is
assumed, which makes the reversing of the numerical coding possible.
Responses in the SEQ can be assessed in many different ways, resulting in different response profiles.
Since each item is assessed on a scale consisting of six ordered categories, there are in total 6
possible permutations for each dimension of the SEQ. Given that it is the mean values that are of
interest, the ordering of the items is not important and the total number of distinct response
combinations can be calculated by counting according to unordered sampling with replacement (21),
and reduces to:
We can let Y represent the mean score. Then
is a discrete variable with 31 possible
outcomes. It should be noted that, in many published studies, these types of discrete variables are used
in parametric analysis that assumes continuous normally distributed variables, which is obviously
erroneous (22, 23).
Sufficiency of the mean scores
In order to be regarded as a sufficient statistic, the mean scores for stress or energy assessments should
contain all information captured by the raw data and the inference about the stress/energy levels should
be the same regardless of whether the mean score or the individual items, X
for i=1,…6, are recorded in
the data material (21). Respondents sharing the same mean score should be experiencing the same
magnitude of the measured construct. However, this may not always hold for the mean scores. In order
to exemplify this, consider the response profiles in table 1, which represents the possible combinations
in the SEQ, all of which result in a mean of 3. As seen in the table, the mean value of 3 can be obtained
in 29 different ways, representing rather heterogeneous response profiles. The combination [29], for
example, is obtained by exclusively choosing the category coded as 3. Applied to the stress items in the
SEQ, this would imply medium stress levels on all items (categories fairly and somewhat
. The
combinations [2] and [9], on the other hand, are obtained by assessing the highest stress levels (4 and 5)
on most of the items. A similar response combination is [0,1,4,4,4,4], which results in a lower mean value
(2.67), but share the same median as [2] and [9], namely the response category 4. The range of the
median for these 29 combinations is from 2 to 5.
Rank-invariant approaches
Median score
The median is defined as the category, θ, such that P(X< θ) and P(X> θ) are both less than or equal to
one-half (24). The median score for the variables stress and energy as measured by the SEQ was
calculated for each individual by ordering the responses of the six items from the lowest to the highest
stress levels. As the interpretation of the positively and negatively loaded items goes in opposite
directions, the items stressed, pressured and tense were ordered from not at all to very much and the
items relaxed, rested and calm from very much to not at all. The energy items active, energetic, focused
were ordered from not at all to very much and the items passive, ineffective, dull were ordered the other
way around. For simplicity, it was decided for all items that the lowest levels would be called not at all
and the highest very much.
Since the variables stress and energy are each measured by six items, both the third and the fourth
ordered response could serve as the median level. When these two responses differ, the decision of
which category is to be regarded as the median should then be made on theoretical grounds, based on
previous research (8). The median global scores of much or very much were regarded as high stress or
high energy. The median score corresponding to not at all or hardly was regarded as low stress or low
Criterion based approach
Another approach that is appropriate considering the rank invariant properties of the data, the criterion
based approach. It is defined on the basis of theoretical knowledge by experts in the particular field of
interest, and based on the frequency distribution of the item responses into predefined response
combinations. In this study, the criterion based global scores for stress and energy measured by the
SEQ, were suggested after considering the experts in the stress research field. For simplicity, only the
global stress scores are presented here. The same rationale is applied for the energy scores.
First, the six scale categories of the SEQ were grouped into low, medium and high stress responses. For
the items stressed, pressured and tense, the low stress responses were the categories not at all or hardly
and the high stress responses were the categories much or very much. The reverse was the case for the
items relaxed, rested and calm. The categories somewhat/fairly were considered as medium stress
responses for all six items.
Then, the criteria for scoring an individual’s level of stress were defined by the frequency distribution of
the responses in the three predefined groups and classified as highly, medium and low stressed. In table
2, the possible response combinations are shown and classified into the three stress levels. Taking the
response combination [26] as an example, none of the six responses are found in the lowest response
categories (A), two items are assessed by either somewhat or fairly (B) and four were found on the
response categories defined as high (C). The global stress score for this response combination was
defined as high stress.
Comparison of the median and criterion based approach for the SEQ
The measure of order consistency between the median and criterion based ordinal scores was calculated
according to Svensson was calculated (25, 26). Each pair of data is classified as ordered, disordered or
tied. The measure of disorder (D) is the proportion of disordered pairs among all possible combinations
of pairs. Possible values of D range from 0 (complete ordering) to 1 (complete disorder). Differences in
proportions of individuals classified as being highly stressed by the median and criterion based approach
were estimated by the 95% confidence interval (CI) (27, 28). Given that both the third and the fourth
ordered responses could serve as the median level, the comparisons of the median and criterion based
global scores were made for both scenarios.
First, the median score was defined as the third of the six ordered responses. The frequency distribution
of the pairs of global scores for stress was presented in a contingency table, and the marginal
distributions showed the row and column totals (table 3a). The measure of disorder was negligible
(D=0.0006), meaning that most of the pairs were ordered. However, there was some inconsistency
regarding the classification of individuals into the high stress group. More specifically, 181 individuals
that were classified as the highly stressed by the criterion based score had a median equal to somewhat
and fairly, which implies medium stress levels.
According to the criterion approach, 21% (596) of the
individuals were classified as highly stressed, compared with 15% by the median score (much=351, very
. The 95% CI for difference in proportions ranged from 5.55 to 7.35. The corresponding
proportions for low stress were 26% and 27% (95% CI -1.12; -0.45).
In the case of defining the median score as the fourth of the six ordered responses, the discrepancy was
seen for the low stress groups (table 3b). The measure of disorder was 0.0029. Similar results were seen
for the energy assessments (table 4). The measure of disorder for comparisons of energy scores was
0.0006 and 0.0014, respectively for the two scenarios.
To measure the studied construct in each subject, it is often necessary to combine the responses to
several items into a single global score. The way this is done, in particular, and how the analysis of the
ordinal data is to be performed, in general, has been a subject of an ongoing debate for a long time (5).
Methodological and statistical problems regarding the construction of global scores are discussed
elsewhere (8, 29-31). A review of methods for ordinal data is given by Agresti and Liu (32, 33). In this
study, we have shown that there are various approaches for the construction of the global scores. The
use of mean scores is regarded as a standard procedure, but this ignores the non metric properties of the
ordinal data. In this study, the median and criterion based approaches are introduced for the global
scores on the SEQ. The criterion based approach for the SEQ is recommended as it better fits the
purpose of the study.
Global scores in the context of different measurement theories
Measurement consists of rules for assigning numbers to objects in a meaningful way to represent
quantities of attributes. The rules for the measuring of quantitative attributes such as height and weight
are well defined. The definition of meaningful rules for the measurement of the hypothetical constructs,
i.e. qualitative variables such as stress and energy, varies considerably, depending on the application
field, the paradigm and the measurement theory, but also on statistical knowledge (1, 34-39).
The three major measurement theories, representational, operational and classical (35), can influence
the choice of the global scores. In the representational theory, the numbers are assigned to the objects
so that the empirical relationship between them is modelled by the numerical relationship (1, 2, 35).
There are four measurement scales (nominal, ordinal, interval and ration) and for each scale, there is a
set of appropriate or permissible transformations (1) and these are either meaningful or meaningless (40-
42). According to this theory, the responses generated by rating scales are ordinal variables. The values
are rank ordered, meaning that each response category has more of the attribute being measured than
the previous category, but the differences between the categories are unknown. In the case of ordinal
variables, only strictly monotonic increasing transformations are permissible. Thus, the median and
criterion based global scores are recommended. Summated or mean global scores are rejected by the
representational theory since a suitable ordinal transformation will change its values. In other words,
the mean scores do not have empirical support since the numbers or coding assigned to the response
alternatives are arbitrary and can be changed as long as ordering between them is preserved.
On the other hand, according to the operational theory mean scores would be perfectly legitimate since
the measurement is defined to be identical to the attribute of interest (34, 35). There is no underlying
empirical relationship to be modelled. The concept of interest is simply defined by its measuring
procedure and measurement is any precisely specified operation that yields numbers (34, 35).
Consequently, as described in a paper by Hand (35) p.481: “the notion of empirical meaningfulness is
meaningless in operational context”. The mean scores are also legitimate according to the classical
theory where measurements are always real numbers (if we have been able to measure them in the first
place) and satisfy all the properties required for any numerical operations (35).
However, regardless of which measurement theory is adopted, the global scores need to be sufficient
statistics and should be meaningful and interpretable. Moreover, a change of one unit on a global scale
should be well defined and constant across the entire scale, meaning that a one-unit change should
reflect the same magnitude of change on the parameter of interest, regardless of the position on the
global scale. In this article, it is shown that this may not always be the case with the mean score, as the
same mean value can result in heterogeneous response profiles and as a higher mean score compared to
lower mean score, may not always indicate the higher stress and energy levels. On the other hand, the
proposed criterion based approach is sufficient, meaning that it is in accord with the meaning of the
responses on the individual items. The same information about the stress and energy assessments is
obtained regardless of whether the individual items or the global score are recorded in the data material.
The rank invariant approaches
Both the median and the criterion approaches provide scores that are interpretable and easily described
in words. The definition of high and low stress and energy are independent of empirical data and thus
consistent over time and groups. The criterion based approach is flexible in the way that the items do
not need to be considered as being equally important. The median and the criterion based approaches
where combined in a study by Starke (11) in order to create global score for a questionnaire measuring
family function. In this paper, the criterion approach was proposed for the SEQ.
The comparison of these two approaches using empirical data showed that the measure of disorder was
negligible, meaning that the ordering of the pairs was preserved for both the stress and the energy
assessments and regardless of whether the median was defined as the third or the fourth of the six
ordered responses. Nevertheless, there was a large difference in the identification of individuals scored
as being highly stressed or having high energy, when the median was defined as the third response. The
differences in identifying the individuals with low stress and low energy were small. The reserve was
observed when the median was defined as the fourth ordered response. Consequently, either approach
can be used if the goal is to identify only one group of individuals (either high or low). However, when
both groups are of interest, the criterion based approach is recommended as it is operationally defined
by the theoretical knowledge of the experts.
The validity of an epidemiological study is closely related to the quality of the data used for the study’s
findings. The data properties should be taken into a consideration before the construction of the global
scores, in order to provide a useful basis for inference drawing procedure. The use of mean values is not
recommended for ordinal data as it provides meaningless results from meaningful data. Both the
median and the criterion based approach are appropriate for ordinal. In this study, the criterion based
approach was proposed for the construction of the global score for the SEQ, but it can easily be applied
to other multi-item questionnaires.
Table 1
Response profiles resulting in a mean score of 3, based on six item responses with the six response categories
coded 0 to 5, and with the higher numbers representing the greater severity of an attribute being measured. The
median level is shown in the last column.
Response Item responses Median
profiles X
[1] 0 0 3 5 5 5 5
[2] 0 0 4 4 5 5 4
[3] 0 1 2 5 5 5 5
[4] 0 1 3 4 5 5 4
[5] 0 1 4 4 4 5 4
[6] 0 2 2 4 5 5 4
[7] 0 2 3 3 5 5 4
[8] 0 2 3 4 4 5 3
[9] 0 2 4 4 4 4 4
[10] 0 3 3 3 4 5 3
[11] 0 3 3 4 4 4 4
[12] 1 1 1 5 5 5 5
[13] 1 1 2 4 5 5 4
[14] 1 1 3 3 5 5 3
[15] 1 1 3 4 4 5 4
[16] 1 1 4 4 4 4 4
[17] 1 2 2 3 5 5 3
[18] 1 2 2 4 4 5 4
[19] 1 2 3 3 4 5 3
[20] 1 2 3 4 4 4 4
[21] 1 3 3 3 3 5 3
[22] 1 3 3 3 4 4 3
[23] 2 2 2 2 5 5 2
[24] 2 2 2 3 4 5 3
[25] 2 2 2 4 4 4 4
[26] 2 2 3 3 3 5 3
[27] 2 2 3 3 4 4 3
[28] 2 3 3 3 3 4 3
[29] 3 3 3 3 3 3 3
Table 2
The low, medium and high levels of stress based on the number of responses found in response categories A,
B and C out of six stress items in the Stress-Energy questionnaire. For the items stress, pressured and tense: A= not
at all/hardly, B=somewhat/fairly C=much/very much. For the items rested, relaxed and calm: A=much/very much,
B=somewhat/fairly, C=not at all/hardly.
Number of responses Stress level Response
combination A B C
Low stress [1] 6 0 0
5 1 0
5 0 1
4 2 0
4 1 1
3 3 0
Medium stress [7]
4 0 2
3 2 1
3 1 2
3 0 3
2 4 0
2 3 1
2 2 2
2 1 3
1 5 0
1 4 1
1 3 2
1 2 3
0 6 0
0 5 1
0 4 2
High stress [22]
2 0 4
1 1 4
1 0 5
0 3 3
0 2 4
0 1 5
0 0 6
Table 3
Paired frequency distribution of the variable stress measured by the Stress-Energy questionnaire computed
as the median scores (not at all to very much) and criterion based scores (low, medium, high). The median defined as
a) the third of the six ordered responses and b) the fourth of the six ordered responses.
a) Criterion based scores
Median Low
Medium High Total
Not at all 109 4 113
Hardly 616 18 634
Somewhat 1014 14 1028
Fairly 460 167 627
Much 351 351
Very much 64 64
Total 725 1496 596 2817
b) Criterion based scores
Median Low
Medium High Total
Not at all 27 27
Hardly 442 3 445
Somewhat 255 778 1033
Fairly 1 692 693
Much 22 484 506
Very much 1 112 113
Total 725 1496 596 2817
Table 4
Proportions (%) and frequencies (n) of individuals classified as high and low stress and energy by the
criterion based approach (CBA) and by the median, as measured by the Stress-Energy questionnaire, and the 95%
confidence interval (CI) for the difference in proportions between the criterion and the median scores. Median 3
and Median 4 are the median scores defined as the third and fourth of the six ordered responses, respectively.
Median 3 95% CI Median 4 95% CI
% (n) % (n) % (n) % (n) % (n)
High stress 21 (596) 15 (415) 5.53;7.35 22 (619) -1.17;-0.47
Low stress 26 (725) 27 (747) -1,12;-0.45 17 (472) 7.92;10.07
High energy 79 (2221) 62 (1752) 15.27;18.03 81 (2271) -2.28;-1.28
Low energy 1 (25) 1 (36) -0.69;-0.15 0.4 (11) 0.14;0.77
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Thinking about the millions of people who are affected worldwide by depressive disorders (322 million, more than 11 million in Brazil and almost 450.000 in Sweden), we tried to create an instrument to assess depression more effectively. In general, depressive disorders are characterized by sadness, loss of interest/pleasure, feelings of guilt or low self-esteem, changes in sleep and appetite, tiredness, and low concentration. In addition to the diagnostic criteria, several instruments evaluate depressive disorders. We used the Beck Depression Inventory to validate the Borg CR100 Scale® for scaling depressive symptoms. The Borg Scales® were developed in the 60's for the evaluation of perceived exertion. The CR100 is a scale from 0 to 100, with verbal categories placed in agreement with the numerical scale so as to obtain ratio data. This type of scale has several advantages, such as allowing comparison between and within subjects and groups, creating symptoms profile, analyzing individual symptoms and the intensity ratio between them. This thesis consists of three papers using the CR100. Study #1 investigated the properties of CR100 compared to BDI. Fifty Swedish students of Psychology answered an online questionnaire and the results pointed a high correlation between the two scales (r = 0.754, p <0.001), demonstrating that the Borg Scale evaluates depression as well as the BDI, providing more results though. The symptom profile generated was much more detailed than the BDI, in addition, the data was more accurate and not that sensitive to mathematical transformations. Study #2 looked after the validation of CR100 for Brazilian Portuguese and, like #1, the application in 50 Brazilian students. The results also pointed to the high correlation between the scales (r = 0.824, p <0.001) with all characteristics preserved in both nationalities. The first reliability analysis revealed a high alpha value (between 0.952 and 0.947) and R2 (between 0.778 and 0.976), higher than the BDI. The aim of Study #3 was to investigate the psychometric properties of CR100 in depressive (N = 25) and healthy participants (N = 25), and to find cutoff points for light, medium and severe depression. The reliability analysis of the Scale revealed an alpha of 0.954 and by running a factorial reduction, the 32 items were grouped into seven components. It was also possible to construct a profile of symptoms between the two populations verifying the sensitivity of CR100 to differentiate healthy from depressive population, in a 95% confidence interval. An index of the ratio between patients and healthy subjects could be created, generating a mini scale with eight items with an alpha value of 0.80 and correlation with the full scale of r = 0.915 (p <0.001) and with the BDI of r = 0.820 (p <0.001). The three studies have shown satisfactory results that match with what has already been demonstrated by researches with the Borg Scales®. It has also been presented the possibility of using the CR100 to assess depressive symptoms with more information and which data are more accurate than the instruments analyzed.
The predominant current opinion appears to be that it is scarcely possible to set up criteria of empirical meaningfulness for individual statements. What is required, it is said, is an analysis of theories taken as a whole. There is even some skepticism regarding this, and it has been romantically suggested that the entire fabric of experience and language must be considered and taken into account in any construction of general categories of meaning or analyticity. What I have to say makes no contribution to the attempt to find a general criterion of meaning applicable to arbitrary statements. Rather I am concerned to exemplify a general method that will yield specific positive criteria for specific branches of science.
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