Core course Session 2

1
Core course Session 2

• Sampling, Surveys
• Measurement

KW 5
2
Total Quality Management Powell (1995) The past
decade has seen the rapid diffusion of Total
Quality Management (TQM). TQM is viewed as a key
driver to the successful revival of the Japanese
postwar economy. Also, it is quoted as an
important cause of the restoration of the US
competitiveness in the eighties. Parallel to the
rapid diffusion of TQM, is the shift in strategic
management thinking away from industry structure
and towards a firms own characteristics as a
source of competitive advantage. It is therefore
natural to ask whether TQM indeed has a positive
impact on the performance of business. TQM is
described as an integrated management philosophy
and set of business practices that emphasize
continuous improvement, meeting customers
requirements, rework reduction, among other
things. The origins of TQM can be traced to Japan
1949, where Deming built a name with his advise
about quality in business processes. Adherents
of TQM of course claim that TQM generates better
products, more satisfied clients and suppliers,
and higher profits. Opponents of TQM state that
TQM leads to excessive overhead activities and
costs, and that it is not particularly suited for
small firms. Powells position (p. 18) is that
most of the studies were conducted by consulting
firms or quality associations with vested
interests in their outcomes, and most did not
conform with generally accepted standards of
methodological rigor. Following this
observation, the question for this session is
what methodological issues should be taken into
account when aiming to validate this sort of
claims? Powell, T.C., 1995, Total Quality
Management as Competitive Advantage A Review and
Empirical Study, Strategic management Journal
16(1), 15-37
3
Intro Agenda Session 2

• Research questions like Powells are often
  addressed by developing a theoretical framework
  which is (hopefully) put to test
• The latter involves the development of indicators
  to operationalize the theoretical concepts, a
  sampling design and a measurement tool (survey,
  for instance) to collect the relevant
  information, and to prepare for further analysis
• This session aims to discuss basic parts of
  empirical research. Agenda
• sampling and sampling designs
• measurement problem
• measurement scales
• internal consistency of scales

4
Sampling
KW 5
5
In the first phase, the researchers reviewed the
TQM literature, underwent TQM training, developed
measurement scales for the TQM dimensions, and
pretested these scales, including review and
feedback from TQM consultants, trainers and
executives. In the second phase, the researchers
mailed the pretested survey to the CEOs of all
firms with 50 employees or more within selected
zip codes in northeastern U.S. (...) In the third
phase, the researchers conducted on-site personal
interviews with CEOs and quality executives in 30
firms, also in selected zip codes in the
northeastern U.S., but not in zip codes included
in the mail survey. (...) 23 were also asked to
complete the structured survey. (...) Of the 143
surveys mailed in the second phase, 40 were
returned, 36 of which were complete, for a usable
response rate of 25.2. (...) In the third phase
of the research, 19 of 23 surveys were returned,
18 of which were complete (...), for a usable
response rate of 78.3, and an overall usable
response rate of 32.5. (Powell, p. 23, 24)
6
Sampling intro

• Sample and population
• Population (relevant aspects of) all entities of
  interest for the research question. Sample
  subset of elements from the population
• The characteristics of a population are called
  parameters the characteristics of a sample are
  called statistics ( functions of sample
  information).
• Please note that the definitions of population
  and sample refer to relevant subsets of
  characteristics. For instance, a persons height,
  but not her ability to complete MBA exams. In
  studies of TQM, a firms TQM quality, but not its
  location while in studies of accessibility, a
  firms location and not its TQM quality
• The ambition to make general statements about
  populations is at angle with the availability of
  only a limited set of data to do so

The latter problem (i.e. the availability of a
limited set of information for statements about
the general state of affairs) requires criteria
for the quality of the data in relation to the
research aim
7
Sampling intro

• A sample is desired to be representative for the
  population (as far as the observed aspects are
  concerned)
• Representativity the characteristics of the
  sample conform with those of the population.
  Example, if the mean height of RSM students in
  the population is equal to 175cm then also the
  average height in a sample should be more or less
  equal to 175 cm.
• Problems
• the population is not known (in general), which
  was the very reason to start the research, so
  representativity can not be checked
• population information is available, but refers
  to a limited set of sampled characteristics. For
  instance, Powell might be able to check whether
  the average firm size in the sample corresponds
  with the mean firm size in the population, but he
  is not able to check the representativity of the
  other characteristics sampled, such as rivalry,
  performance, TQM quality
• In order to deal with this problem, attention is
  shifted away from the quality of the sample
  (representativity) towards the procedural quality
  of the way in which the sample has been drawn
  (sampling design).
• Simple Random Sample all elements of the
  population have the same probability to be
  selected for the sample

which occasionally goes wrong ...
8
Sampling Roosevelt versus Landon, 1936

• Roosevelt versus Landon
• In 1936, monitoring the presidency election
  campaign between the democrat Roosevelt and the
  republican Landon, the Literary Digest conducted
  a poll among 10 million voters. These voters were
  carefully selected on the basis of car
  registration, telephone numbers and subscription
  to the magazine. About 2.3 million people
  responded, leading the Literary Digest to predict
  an overwhelming victory for the republican
  governor Landon. The predicted numbers were
• (also KW, p.143)

Landon Roosevelt States (48) 32
16 Election votes (531) 370 161

• What was the outcome of the election about only
  four days later?

9
Sampling Roosevelt versus Landon, 1936

• Outcome of the election

Landon Roosevelt States (48) 2
46 Election votes (531) 8
523

• Possible explanations
• reactivity social measurement (polls, surveys)
  typically affects the way how people think about
  issues this may have wanted (sample exams) or
  unwanted (polls) side-effects
• selection bias the sample design may be biased
  towards particular groups of respondents (in
  casu, car and telephone owners, subscribers to
  the Literary Digest, who might be expected to be
  inclined towards republican voting behavior)
• self selectivity / non-response bias particular
  groups of respondents systematically do or do not
  respond to the survey which may affect the
  overall validity of the sample results

Could this have been foreseen?
10
Sampling systematic and non-systematic sampling
errors

• Non-systematic sampling errors sampling
  variation
• Systematic sampling errors
• selection bias (see Literary digest)
• response bias (tendency towards undesired answers
  to ill-stated questions, evasive answers to
  delicate questions)
• non-response bias (see Literary Digest)
• errors in data collection process
• Such sampling errors may occur in all stages of
  the data collection process planning/design
  stage, collection/execution stage, data
  processing stage

11
Sampling sampling methods

• Back to the issue of sampling methods
• Various sampling procedures have been designed to
  increase the efficiency of the data collection
  process
• simple random sampling
• stratified sampling
• cluster sampling
• systematic sampling
• All alternatives make use of additional
  information about the population

Examples
12
Sampling stratified sampling

• Stratified sampling
• populations may be divided into sub-populations,
  from (all of) which samples are taken
• deliberate under or over-representation of known
  subpopulations
• example production statistics of SN large
  companies (gt20 employees) are all observed small
  companies (lt20 employees) are partly observed by
  means of sampling

• Advantages
• less survey pressure for firms
• better estimates by utilizing additional business
  information (firm size)

There are consequences for data handling...
Number of employees
13
Sampling stratified sampling
Determining average turnover Suppose that a
particular industry consists of 90 firms (N), of
which 10 are large (Nlarge) and 80 are small
(Nsmall). A stratified sample of n 26 firms
from this population is taken, which consists of
10 large firms ( nlarge) and 16 small firms (
nsmall). The average turnover of the top 10 is
40 m and that of the sweet 16 is 4 m what is
the average turnover of firms in this industry?
(a) 22.0 m
In general
(b) 17.8 m
where i 1, ..., m, are the subpopulations
(c) 8.0 m
14
Sampling other procedures
Passenger satisfaction Management of the local
public transport firm expresses a sudden interest
in the satisfaction of its passengers about their
transport services. It starts a survey by
randomly selecting bus lines, bus stops, and
departure times. Subsequently, it interviews a
sample of passengers in a particular bus.

• Cluster sampling
• population is organized in clusters (boxes,
  trains, classes)
• clusters are randomly selected and all elements
  in the cluster are observed (1 stage cluster)
• clusters are randomly selected, and a sample is
  drawn from the cluster (multi-stage cluster)
• Difference with stratified sampling is that the
  subgroups themselves are being sampled. Not all
  clusters are represented in the sample which
  leads to a lower precision of the cluster
  sampling estimators

15
Sampling other procedures
An auditing accountant An accountant auditing the
20,000 files of a particular state department
searches for ways to alleviate her task. Knowing
that she gets paid for checking only 200 files,
she imagines the archive as if consisting of 200
subgroups of 100 ( 20,000/200) files. Next, she
randomly selects one file from the first 100
files, say file 74, and subsequently selects the
(74100)th, (74200)th, ... (74 100i)th file
until she has the required 200 files.

• Systematic sampling
• an ordered population of N elements is available
  (ordered, for instance, on the basis of social
  security numbers, or grades), from which a sample
  of size n is to be selected
• a step length is determined as k N/n (or its
  nearest integer)
• the first element is randomly selected from the
  first k files, afterwards each kth element is
  selected until the sample of size n is obtained

16
Sampling Powells case

• Powell sampled firms from the northeastern part
  of the US using ZIP codes (slide 5)
• how would you label his sampling design?
• what is the population?
• do you think the sample is representative for the
  population?

If you would be invited to redo Powells
research, how would you set up the sampling
design?
17
Measurement problem
KW --
18
Measurement problem

• Main problem of much business research is that
  real world phenomena are not immediately
  observable (for instance, the extent of rivalry
  is not just something which can be observed when
  looking outside the window nor is the extent of
  TQM quality something that is immediately
  noticed by entering a firms building)
• Theories or suggestions about the existence
  and/or (causal) interrelatedness of phenomena
  therefore are speculative, which means that they
  are void of empirical content ...
• ... unless one is willing to put these theories
  to test (as Powell does)
• But how can we ever hope to find appropriate
  empirical measures or perform satisfactory
  hypothesis tests if we do not have these
  immediate observations

measurement problem

• ... this is sometimes called the measurement
  problem and it boils down to finding an auxiliary
  (or measurement) theory to complement our
  substantive theory (the hypotheses we want to
  test)

19
Measurement problem
Industry Rivalry (Z)
The conceptual model is in terms of theoretical
variables (concepts) and relations between these
variables (hypotheses). Concepts and relations
exist by assumption
TQM performance (Y)
TQM measurement (X)
Epistemic correlations or Correspondence rules
Conceptual model
Empirical model
The empirical model is in terms of the empirical
counterparts (indicators) of the concepts. Based
on the observed outcomes of the indicators, the
assumed relationships are tested.
TQM measurement (x1)
TQM performance (y1)
TQM performance (y2)
Industry Rivalry (z1)
20
Measurement problem

• The subsequent question is, of course, how and
  how well are the indicators related to the
  concepts they aim to measure. An important
  framework to answer this question is the
  so-called classical test theory, which in its
  simplest form is given as follows

Classical measurement model (in its simplest form)
see also slide 38
E(?) 0 Cov(T, ?) 0
X T ?
Nice, but how good are our indicators X
Observational score the observable outcome of an
indicator (it is assumed to be composed of a
(hypothetical) true score and a measurement error)
True score the hypothetical score, the value
that an entity has in theory
Measurement error random error occurring in the
measurement process it is assumed to be
distributed independently with mean value zero
21
Measurement problem

• Measurement theory provides two different answers
  to the question about the quality of indicators
  validity and reliability

extent to which the indicator (X) measures what
it should measure (T)
Validity
extent to which the indicator (X) gives the same
results in repeated measurements (under the same
conditions)
Reliability
22
Measurement problem
Validity
As a test of the convergent validity of the
total performance measure, objective financial
measures were obtained for 15 publicly-held
survey participants. In this subsample, return on
sales, a commonly-used measure of financial
performance (...) correlated significantly with
the subjectively derived total performance
measure ... (Powell, p. 25)

• Validity extent to which the indicator (X)
  measures what it should measure (T) validity is
  inversely related with the amount of systematic
  measurement error
• content validity extent to which the indicator
  reflects the domain debated issue degree of
  belief
• criterion-related validity extent to which the
  indicator correlates with an alternative
  indicator (the criterion)
• predictive validity/concurrent validity
• convergent/discriminant validity
• known group validity
• construct validity extent to which the indicator
  is able to uncover empirical regularities

23
Measurement problem
Reliability
In the third phase, six firms were asked to
complete two surveys per firm to establish
interrater reliability ... (Powell, p.
24) Cronbach alpha coefficients were computed
to test the reliabilities of the TQM scales ...
(powell, p.24)

• Reliability extent to which the indicator
  yields the same results when repeatedly applied
  (under the same conditions) reliability is
  inversely related with the amount of unsystematic
  measurement error
• reliability ratio of the true score variance,
  V(T), and the variance of observational score,
  V(X)
• reliability correlation between parallel
  measures (X1, X2) of the same concept (T)

24
Measurement problem
Reliability

• Various methods exist to measure reliability. In
  social research these are commonly based on the
  interpretation of reliability as a correlation
  between parallel measurements
• test-retest reliability the same indicator is
  applied twice (in time) reliability is measured
  as the correlation between the two series of
  outcomes disadvantage reactivity, learning,
  subjects may no longer be available
• alternative form reliability a similar indicator
  (different items, same concept) is applied twice
  (in time) reliability is measured as the
  correlation between the two series of outcomes
  disadvantage similar to test-retest
• split halve items are arbitrarily divided into
  two groups from which two indicators are
  calculated, which are correlated to obtain the
  reliability
• internal consistency (Cronbachs alpha)
  generalization of the split halve method,
  explained later on

25
Measurement scales
KW --
26
Measurement scales
In the first phase, the researchers (...)
developed measurement scales for the TQM
dimensions, and pretested these scales, including
review and feedback froim TQM consultants...
(Powell, p. 23) Although TQM assessment
instruments existed prior to this research (...)
none was found suitable for this research, which
required scales that integrated various
approaches to TQM, in a form acceptable for
scholarly survey research and data analysis
... In the pretest phase, the researchers
developed a TQM measurement scale based on an
exhaustive review of the TQM literature, and
revised this scale through repeated discussions
and site visits with consultants and quality
executives... (Powell, p. 24)
27
Measurement scales

• The outcomes of indicators are represented on
  so-called scales measurement scales thus are
  the representation formats for the outcomes of
  indicators

• Apart from the measurement units, scales differ
  with respect to the information content that they
  assign to the outcomes. In Refresher Session 1,
  we distinguished qualitative (nominal, ordinal)
  scales and quantitative (interval, ratio) scales.

• As a general rule (also in business research), we
  want to have our indicators to be measured on the
  highest possible measurement scale, which
  provides the richest information and allows one
  to use the more powerful analytical tools

• In view of this ambition, a problem occurs with
  many broad concepts (rivalry, TQM quality) we
  would like to have them measured on quantitative
  scales, but we have no immediate (physical)
  observations, so how do we proceed?

Note on the measurement of concepts by means of
surveys
28
Measurement scales
As an example, consider Powells concept TQM
measurement quality mentioned in the appendix
(p.37), which is an example of a Likert- or
summated rating scale often used in surveys
Instruction necessary for the interpretation of
the questions
Rating scales or response categories
Items or predicates
The different parts of this indicator are
separately discussed
Where is the scale?
29
Measurement scales response categories
Response categories

• The response categories are ordinal by
  construction ranging from strongly negative to
  strongly positive (or the other way around) the
  digits that are eventually used to characterize
  the categories are merely suggestive (explained
  later on)
• By cross marking a particular category, the
  respondent roughly indicates her relative
  position with respect to the item on the
  continuum
• Respondents are assumed to understand the proper
  meaning of the rating scale (which is not always
  obvious, but it stresses the importance of a
  proper instruction and of pilots)
• The number of response categories usually ranges
  from 3 to 7, though sometimes 2 or 10 categories
  are used. (The optimal number depends on what
  your respondents can bear)
• The number of categories may be even or uneven
  (this depends on taste, although the choice
  between even and uneven may be connected with the
  type of rating scale explained next)

Types of rating scales
30
Measurement scales response categories
Response categories

• Rating scales may refer to different types of
  scales agreement (agree/disagree), evaluative
  (good/bad) or frequency (never/often)
• The choice of rating scale and the formulation of
  the items should always be in concordance

Agreement scale agree/disagree dimension
symmetrical and bipolar
Evaluative scale good/bad dimension
symmetrical bipolar even-numbered
Frequency scale time dimension (usually)
unipolar
31
Measurement scales items
Scale items

• The purpose of the items is to reflect aspects of
  the phenomenon being measured
• The number of items of Likert- or summated rating
  scales varies from 10-20 at the start, which
  number is reduced to 5-10 items after item
  analysis (explained in a next session)
• The use of several items (rather than one item)
  is because of complexity of the concept desired
  precision of the scale the need to assess the
  reliability of the indicator and desirable
  statistical properties
• The formulation of items must be understandable
  to the subjects of your population
• The formulation of the items must reveal a clear
  (positive or negative) tendency otherwise the
  responses will be ambiguous
• Positively and negatively formulated items are
  used alternately to guard against response set.
  During the analysis of the survey results the
  answers to the negatively stated items must be
  recoded

Details
32
Measurement scales items
Scale items

• The latter point (clear positive or negative
  tendency) refers to the so-called scale model
  which underlies all scales and which is reflected
  by the item characteristic function

Example Rotterdam is the worst that can happen
to you (disagree/agree)
Example Rotterdam is a great city
(disagree/agree)
Item trace line
A
B
Items are formulated either positively (A) or
negatively (B). The likeliness that respondents
react positively to A (B) increases (decreases)
when the respondents are situated more towards
the positive side of the continuum
... if not ...
33
Measurement scales items
Scale items

• If items would not have a clear position on the
  continuum the answers would be ambiguous

Example Rotterdam is an acceptable place to
live (disagree/agree)
Respondents on the left side (-) of the continuum
as well as respondents on the right side () of
the continuum would express a negative attitude
towards item C (strongly disagree) Respondents
with a neutral position on the continuum
(somewhere in the neighborhood of item C) would
express a positive attitude (strongly agree)
Examples
34
Measurement scales items
Scale items
In specific, items should be clear and concise
Examples of mal practice
Statistical methods as well as charts and graphs
to measure and monitor Quality
Items should reflect one thought
Items should avoid negation, and particularly
double negations
Statistical methods in TQM are not a bad way to
measure and monitor TQM
Unlike training of personnel, statistical methods
add to the quality of TQM systems
Items should avoid interpretable events
Statistical methods work just as well as
management development to measure and monitor
Quality
Items should avoid comparisons with other events
Items on a Likert-scale should always have a
clear tendency
Statistical methods to measure and monitor
Quality are sometimes to be used
35
Measurement scales assigning values
Calculating respondents scores

• Two different methods to calculate respondent
  scores
• Assume linearity of the answering categories and
  assigning a sequence of numbers (0, 1, 2, et
  cetera) interval scale is imposed
• Assume respondents to be normally distributed on
  the continuum, and that their responses roughly
  indicate their position with respect to the item
  (this method is explained in the add-on (slide
  44-49)

• Both methods yield different respondent scores.
  However, it appears that the overall correlation
  between the scale values based on normality of
  respondent scores and those based on linearity of
  category positions is usually very high.
• Therefore, in practice most researches will
  calculate scale values by imposing a linear set
  of numbers (1, 2, 3, 4, etc or 0, 1, 2 etc or
  2, -1, 0, 1, 2 etc) and adding the respondents
  ratings accordingly

36
Internal consistency of multi-item scales
KW --
37
Cronbach alpha coefficients were computed to
test the reliabilities of the TQM scales
(Cronbach, 1951). Typically, these coefficients
should fall within a range of 0.70 to 0.90 for
narrow constructs (...), and 0.55 to 0.70 for
moderately broad constructs (...). In the
empirical study, the coefficients for the twelve
variables ranged between 0.78 and 0.90, and
varied only trivially between the second and
third phases of the research Powell (p.24)
Cronbachs ? is often encountered in the
literature. It is said to be a measure of scale
reliability or internal consistency of the scale,
but what is meant by this?
38
Internal consistency

• Recall that the observational scores of an
  indicator have been assumed to consist of a true
  score and a random measurement error. This
  assumption applied to each of the items of the
  scale

see also slide 20
X1 T ?1
X2 T ?2
X3 T ?3
X4 T ?4

39
Internal consistency

• Reliability (?), the extent to which an indicator
  yields the same results when repeatedly applied,
  has various definitions. A particularly useful
  one is the ratio of the true score variance and
  the variance of the observational score
• In the case of the indicator Y, the observational
  score is Y ?Xk and the true score is K?T. The
  reliability may therefore be obtained as

• which means that this reliability is inversely
  related with the ratio of the sum of the item
  variances and the variance of the sum of items
  (scale variance).

40
Internal consistency

• The Cronbachs ? is (usually) between 0 and 1. If
  the observed item scores Xk are highly
  (positively) correlated, then V(?Xk ) is (much)
  larger than ?V(Xk), and Cronbachs ? is close to
  1. A high Cronbachs ?, say larger than
  0.70-0.80, is interpreted as a good sign, while a
  small Cronbachs ? , say below 0.50, indicates a
  poor performance of the scale
• If the item scores are completely unrelated, then
  the variance of the scale V(?Xk ) is equal to the
  sum of item variances ?V(Xk), and Cronbachs ?
  is close to 0.
• If item scores are negatively correlated, which
  sometimes occurs when one forgets to recode the
  negatively rated items, the scale variance V(?Xk
  ) may be (slightly) smaller than the sum of item
  variances ?V(Xk), and Cronbachs ? is lower than
  0.
• If the number of items K increases, then also
  Cronbachs ? increases.
• Please note that Cronbachs indicator of
  reliability measures the internal consistency of
  a scale ( the degree to which separate items
  similarly order the respondents), and not the
  behavior of the scale in repeated measurements in
  time.

41
to conclude
Next Week
42
End of Session 2

• Suggestions for further reading (for those
  interested, no obligations)
• Nunnaly, J.C., 1972, Psychometric Theory, New
  York McGraw-Hill.
• Lewis-Beck, M.S., 1994, Basic Measurement,
  International Handbook of Quantitative
  Applications in the Social Sciences, Vol. 4, Sage
  Publications
• Cochran, W.G., 1977, Sampling Techniques, New
  York Wiley.
• Next time
• estimation of the population mean, variance and
  proportion
• introduction SPSS for Windows
• The topic of item/scale analysis is scheduled
  for the fourth session

43
Assigning values to ordinal responses
KW --
Extra explanation about the assumptions of the
Likert scale. Not needed for the exam.
44
Measurement scales assigning values
Assigning category values

• The response categories are ordinal by
  assumption how then can we meaningfully assign
  numbers to these categories in order to determine
  scale values for all respondents?

• This is where some further assumptions need to be
  made.
• the respondents are scattered over the continuum
  that the indicator is aiming to measure in fact,
  they are normally distributed over the continuum
• the items are also somewhere on the continuum to
  the left, if they are negatively formulated, to
  the right if they are positively stated
• the distance between the position of the
  respondent and the position of the item
  determines which response category for an item is
  marked
• the specific responses roughly indicate the
  respondents position with respect to the item
  position on the continuum
• varying response patterns are partly due to the
  item position (extremity) and partly to
  measurement error

Illustrations
45
Measurement scales assigning values
Assigning category values
The process of assigning values to the response
categories (so not yet to the respondents!) is
illustrated by scale item 3, which is supposed to
have the following relative frequency scores
associated with the 6 outcomes 0.10 (0), 0.15
(1), 0.20 (2), 0.30 (3), 0.20 (4), and 0.05 (5),
which gives an average of 2.5. Let us see what
happens when this is compared with a more
extremely formulated item
Example of a respondent who marks a 3 on the
regular item but a 2 (so, less intention) on the
more extreme item
Respondents are scattered over the continuum
TQM Measurement
?
?
?
?
?
?
Responses depend on the relative position of
respondents to the item
0
1
2
3
4
5

• (current item) Statistical methods to measure and
  monitor Quality

0.10
0.15
0.20
0.30
0.20
0.05

• (extreme alternative) Multivariate statistical
  methods to measure and monitor Quality

46
Measurement scales assigning values
Assigning category values
The respondents are assumed to be normally
distributed over the continuum

• (current item) Statistical methods to measure and
  monitor Quality

Scale ratings are determined as the class mid
points that equally distribute the probability
mass
Relative frequencies
0.10
0.15
0.20
0.30
0.20
0.05
z such that P(Z lt z) 0.05
Cumulative frequencies
0.10
0.25
0.45
0.75
0.95
1.00
Cum. frequency at midpoint
0.05
0.175
0.35
0.60
0.85
0.975
Category rating
-1.64
-0.93
-0.39
0.25
1.04
1.96
... and for the extreme alternative...
Category rating
-1.44
-0.67
-0.06
0.57
1.31
2.33
47
Measurement scales assigning values
Assigning category values

• Based on the frequency distributions, category
  rating values can be similarly calculated for all
  other items (of the entire survey)
• The category ratings may differ as a consequence
  of the extremity of an item

Scale values of respondents
48
Measurement scales assigning values
Calculating respondents scores

• The overall scale value (or score) of a
  respondent is defined as the sum of rating values
  of the marked options of all the items.
• Imagine a respondent who marked the second
  category (1) for item 1 (Measurement of Quality
  performance in all areas), the third category
  for item 2, the third for for item 3 and the
  fourth for item 4. The overall score for the
  respondent may now be obtained as

Respondents score
-0.45 -0.06 -0.39 0.00 -0.90
49
Measurement scales assigning values
Calculating respondents scores

• Alternatively, a more easy route is followed by
  assuming linearity between the answering
  categories and and assigning a sequence of
  numbers (0, 1, 2, et cetera)

• Of course, this will lead to different respondent
  scores than the ones calculated before. However,
  it appears that the overall correlation between
  the scale values based on normality of respondent
  scores and those based on linearity of category
  positions is usually very high.
• Therefore, in practice most researches will
  calculate scale values by imposing a linear set
  of numbers (1, 2, 3, 4, etc or 0, 1, 2 etc or
  2, -1, 0, 1, 2 etc) and adding the respondents
  ratings accordingly