Critical Reasoning Test

Critical Reasoning Test
INTERNATIONAL
CRTB2
CRITICAL REASONING
TEST BATTERY
technical manual
c
ONTENTS
1
THEORETICAL OVERVIEW
2
THE CRITICAL REASONING TESTS
3
THE PSYCHOMETRIC PROPERTIES OF THE CRITICAL REASONING TESTS
4
REFERENCES
5
APPENDICES
ADMINISTRATION INSTRUCTIONS
SCORING INSTRUCTIONS
CORRECTION FOR GUESSING
NORM TABLES
2
LIST OF TABLES
1
MEAN AND SD OF AGE, AND GENDER BREAKDOWN, OF THE NORMATIVE SAMPLE
FOR THE VCR2
2
3
MEAN SCORES FOR MEN AND WOMEN (MBAS) ON THE VCR2 AND NCR2
ALPHA COEFFICIENTS FOR THE VERBAL AND NUMERICAL CRITICAL REASONING
TESTS
4
5
CORRELATIONS BETWEEN THE VCR2 AND NCR2
CORRELATIONS BETWEEN THE VERBAL AND NUMERICAL CRITICAL REASONING
TESTS WITH THE APIL-B
6
CORRELATIONS BETWEEN THE ORIGINAL VERSIONS OF THE VCR2 AND NCR2
WITH THE AH5
7
8
ASSOCIATION BETWEEN THE VCR2, NCR2 AND INSURANCE SALES SUCCESS
CORRELATIONS BETWEEN THE VCR2, NCR2 AND MBA PERFORMANCE
3
4
1
THEORETICAL
OVERVIEW
1
THE ROLE OF PSYCHOMETRIC TESTS
IN PERSONNEL SELECTION AND
ASSESSMENT
2
THE ORIGINS OF REASONING TESTS
6
THE ROLE OF
PSYCHOMETRIC TESTS IN
PERSONNEL SELECTION
AND ASSESSMENT
A major reason for using psychometric tests to aid selection decisions is
that they provide information that
cannot be obtained easily in other
ways. If such tests are not used then
what we know about the applicant is
limited to the information that can
be gleaned from an application form
or CV, an interview and references. If
we wish to gain information about a
person’s specific aptitudes & abilities
and about their personality, attitudes
and values then we have little option
but to use psychometric tests. In fact,
psychometric tests can do more than
simply provide additional information about the applicant. They can
add a degree of reliability and validity to the selection procedure that it
is impossible to achieve in any other
way. How they do this is best
addressed by examining the limitations of the information obtained
through interviews, application
forms and references and exploring
how some of these limitations can be
overcome by using psychometric
tests.
While much useful information
can be gained from the interview,
which clearly has an important role
in any selection procedure, it does
nonetheless suffer from a variety of
weaknesses. Perhaps the most
important of these is that the interview as been shown to be a very
unreliable way to judge a person’s
character. This is because it is an
unstandardised assessment procedure. That is to say, each interview
will be different from the last. This is
true even if the interviewer is
attempting to ask the same questions
and act in the same way with each
applicant. It is precisely this aspect
of the interview that is both its main
strength and its main weakness. The
interview enables us to probe each
applicant in depth and discover individual strengths and weaknesses.
Unfortunately, the interviews
unstandardised, idiosyncratic nature
makes it difficult to compare applicants, as it provides no base line
against which to contrast interviewees’ differing performances. In
addition, it is likely that different
interviewers may come to radically
different conclusions about the same
applicant. Applicants will respond
differently to different interviewers,
quite often saying very different
things to them. In addition, what any
one applicant might say will be
interpreted quite differently by each
interviewer. In such cases we have to
ask which interviewer has formed
the correct impression of the candidate? This is a question to which
there is no simple answer.
A further limitation of the interview is that it only assesses the
candidate’s behaviour in one setting,
and with regard to a small number
of people. How the candidate might
act in different situations and with
different people (e.g. when dealing
with people on the shop floor) is not
assessed, and cannot be predicted
from an applicant’s interview performance. Moreover, the interview
provides no reliable information
about the candidate’s aptitudes and
abilities. The most we can do is ask
the candidate about his strengths
and weaknesses, a procedure that
has obvious limitations. Thus the
range, and reliability of the informa-
7
tion that can be gained through an
interview are limited.
There are similar limitations on
the range and usefulness of the information that can be gained from
application forms or CV’s. While
work experience and qualifications
may be prerequisites for certain
occupations, in and of themselves
they do not determine whether a
person is likely to perform well or
badly. Experience and academic
achievement is not always a good
predictor of ability or future success.
While such information is important
it may not be sufficient on its own to
enable us to confidently choose
between applicants. Thus aptitude
and ability tests are likely to play a
significant role in the selection
process as they provide information
on a person’s potential and not just
their achievements to date.
Moreover, application forms tell us
little about a person’s character. It is
often a candidate’s personality that
will make the difference between an
average and an outstanding performance. This is particularly true
when candidates have relatively
similar records of achievement and
past performance. Therefore,
personality tests can play a major
role in assisting selection decisions.
There is very little to be said
concerning the usefulness of references. While past performance is
undoubtedly a good predictor of
future performance references are
often not good predictors of past
performance. If the name of the
referee is supplied by the applicant,
then it is likely that they have chosen
someone they expect to speak highly
of them. They will probably have
avoided supplying the names of
those who may have a less positive
view of their abilities. Aptitude and
ability tests, on the other hand, give
us an indication of the applicant’s
probable performance under exam
conditions. This is likely to be a true
reflection of the person’s ability.
What advantages do psychometric
tests have over other forms of assessment? The first advantage they have
is that they add a degree of reliability to the selection procedure that
cannot be achieved without their
use. Test results can be represented
numerically making it easy both to
compare applicants with each other,
and with pre-defined groups (e.g.
successful vs. unsuccessful job
incumbents). In the case of personality tests the test addresses the issue
of how the person characteristically
behaves in a wide range of different
situations and with different people.
Thus psychometric tests, both
personality tests and aptitude and
ability tests provide a range of information that are not easily and
reliably assessed in other ways. Such
information can fill important gaps
which have not been assessed by
application forms, interviews and
references. It can also raise questions
that can later be directly addressed
in the interview. It is for this reason
that psychometric tests are being
used increasingly in personnel selection. Their use adds a degree of
breadth to assessment decisions
which cannot be achieved in any
other way.
8
RELIABILITY AND VALIDITY
As previously noted, besides providing information that cannot be easily
obtained in other ways psychometric
tests also add reliability and validity
to the selection procedure. There are
two ways in which psychometric
tests increase the reliability of the
assessment procedure:
i) The use of a standardised
assessment procedure:
Reliability is achieved by using the
same tests on each applicant and
administering, scoring and interpreting the test results in the same way.
Thus, individual biases and distortions are removed from the
assessment procedure. By comparing
each applicant’s scores against an
agreed norm we create a baseline
that enables us not only to compare
applicants with each other, but also
to contrast them against some agreed
criterion (e.g. against the performance of a sample of graduates,
accountants etc.). Thus, subjective
and idiosyncratic interpretations of a
candidate’s performance are
removed from the assessment
process.
ii)The use of well standardised
& reliable psychometric tests:
To ensure the assessment procedure
produces reliable and consistent
results it is necessary to use wellconstructed psychometric tests. It is
not sufficient simply to administer
any questionnaire that purports to be
a psychometric test, or assessment
system. If the test has been
constructed badly, it will neither be
reliable nor valid and will add little
to the assessment process. In the
most extreme case the use of such a
test may invalidate an otherwise
valid selection procedure. For a test
to be reliable each of the questions in
each scale must be a good measure
of the underlying trait that the scale
is attempting to assess. To this end
the test publisher should provide
data to demonstrate that the test is
both reliable and valid. (The statistics that are used to determine this
are described later in the manual).
THE ORIGINS OF
REASONING TESTS
The assessment of intelligence or
reasoning ability is perhaps one of
the oldest areas of research interest
in psychology. Gould (1981) has
traced attempts to scientifically
measure psychological aptitudes and
abilities to the work of Galton at the
end of the last century. Prior to
Galton’s pioneering work, however,
interest in this area was aroused by
phrenologists’ attempts to assess
mental ability by measuring the size
of people’s heads. Reasoning tests, in
their present form, were first developed by Binet, a French
educationalist who published the
first test of mental ability in 1905.
Binet was concerned with assessing the intellectual development of
children and to this end invented the
concept of mental age. Questions,
assessing academic ability, were
graded in order of difficulty according to the average age at which
children could successfully complete
each item. From the child’s performance on such a test it was possible
to derive its mental age. This
involved comparing the performance
of the child with the performance of
the ‘average child’ from different age
groups. If the child performed at the
level of the average 10 year old, then
the child was said to have a mental
age of 10, regardless of its chronological age. From this idea the
concept of the Intelligence Quotient
(IQ) was developed by William Stern
(1912) who defined it as mental age
divided by chronological age multiplied by 100. Previous to Stern’s
paper chronological age had been
subtracted from mental age to
provide a measure of mental alertness. Stern showed that it was more
appropriate to take the ratio of these
two constructs, which would provide
a measure of the child’s intellectual
development relative to other children. He further proposed that this
ratio should be multiplied by 100 for
ease of interpretation; thus avoiding
cumbersome decimals.
Binet’s early tests were subsequently revised by Terman et al.
(1917) to produce the now famous
Stanford-Binet IQ test. These early
IQ tests were first used for selection
by the American’s during the first
world war, when Yerkes (1921)
tested 1.75 million soldiers with the
army alpha and beta tests. Thus by
the end of the war, the assessment of
reasoning ability had firmly established its place within psychology.
9
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2
THE CRITICAL
REASONING TESTS
1
THE DEVELOPMENT OF THE
CRITICAL REASONING TESTS
2
REVISIONS FOR THE SECOND EDITION
bm
THE DEVELOPMENT
OF THE CRITICAL
REASONING TESTS
Research has clearly demonstrated
that in order to accurately assess
reasoning ability it is necessary to
develop tests which have been
specifically designed to measure that
ability in the population under
consideration. That is to say, we
need to be sure that the test has been
developed for use on the particular
group being tested, and thus is
appropriate for that particular
group. There are two ways in which
this is important. Firstly, it is important that the test has been developed
in the country in which it is intended
to be used. This ensures that the
items in the test are drawn from a
common, shared cultural experience,
giving each candidate an equal
opportunity to understand the logic
which underlies each item. Secondly,
it is important that the test is
designed for the particular ability
range on which it is to be used. A
test designed for those of average
ability will not accurately distinguish
between people of high ability as all
the scores will cluster towards the
top end of the scale. Similarly, a test
designed for people of high ability
will be of little use if given to people
of average ability. Not only will it not
discriminate between applicants, as
all the scores will cluster towards the
bottom of the scale, but also as the
questions will be too difficult for
most of the applicants they are likely
to be de-motivated, producing artificially low scores. Consequently, the
VCR2 and NCR2 have been developed on data from undergraduates.
That is to say, people of above
average intelligence, who are likely
to find themselves in senior management positions as their career
develops.
In constructing the items in the
VCR2 and NCR2 a number of guide
lines were borne in mind. Firstly,
and perhaps most importantly,
special care was taken when writing
the items to ensure that in order to
correctly solve each item it was
necessary to draw logical conclusions
and inferences from the stem
passage/table. This was done to
ensure that the test was assessing
critical (logical/deductive) reasoning
rather than simple verbal/numerical
checking ability. That is to say, the
items assess a person’s ability to
think in a rational, critical way and
make logical inferences from verbal
and numerical information, rather
than simply check for factual errors
and inconsistencies.
In order to achieve this goal for
the Verbal Critical Reasoning
(VCR2) test two further points were
born in mind when constructing the
stem passages for the VCR2. Firstly,
the passages were kept fairly short
and cumbersome grammatical
constructions were avoided, so that a
person’s scores on the test would not
be too affected by reading speed;
thus providing a purer measure of
critical reasoning ability. Secondly,
care was taken to make sure that the
passages did not contain any information which was counter-intuitive,
and was thus likely to create confusion.
To increase the acceptability of
the test to applicants the themes of
the stem passages were chosen to be
relevant to a wide range of business
situations. As a consequence of these
constraints the final stem passages
were similar in many ways to the
short articles found in the financial
pages of a daily newspaper, or trade
magazines.
REVISIONS FOR THE
SECOND EDITION
The second edition of the Verbal and
Numerical Critical Reasoning tests
has been revised To meet the following aims:
● To impove the face validity of the
test items, thus increasing the
test’s acceptability to respondents.
● To modernise the items to reflect
contemporary business and financial issues.
● To improve the tests’ reliability
and validity while maintaining
the tests’ brevity – with the CRBT
being administrable in under one
hour.
● To simplify test scoring.
● To make available a hand scored
as well as a computer scored
version of the tests.
● To remove the impact of guessing
on raw VCR2scores, thus increasing the power of the VCR2 to
discriminate between respondents.
As noted above the most significant
change in the second edition of the
VCR2 has been the incorporation of
a correction for guessing. This obviates the problem that, due to the
three-point response scale that is
used in most verbal critical reasoning
test, it is possible for respondents to
get 33% of the items correct simply
by guessing.
While a variety of methods have
been proposed for solving this
problem (including the use of negative or harsh scoring criteria) we
believe that a correction for guessing
is the most elegant and practical
solution to this problem.
This correction is based on the
number of items the respondent gets
wrong on the test. We know that to
get these items wrong the respondent
must have incorrectly guessed the
answer to that item. We can further
assume that, by chance, the respondent incorrectly guessed
the answer 66% of the time and
correctly guessed the answer 33%
of the time. Thus it is possible to
estimate the number of correct
guesses the respondent made from
the number of incorrect responses.
This correction can then be
subtracted from the total score to
adjust for the number of items the
respondent is likely to have correctly
guessed.
The use of this correction
improves the test’s score distribution,
increasing its power to discriminate
between the respondents’ ‘true’
ability level. Thus it is recommended
that test users correct sores for
guessing before standardising scores.
However, as the norm tables for
corrected and uncorrected scores are
significantly different from each
other it is important, if hand scoring
the Critical Reasoning tests, to
ensure that the correct norm table is
used to standardise the scores on the
VCR2. That is to say, either the
norm table for the uncorrected
(Appendix IV - Table 2) or corrected
scores (Appendix IV - Table 3)
depending upon whether or not the
correction for guessing has been
applied).
bn
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3
THE PSYCHOMETRIC
PROPERTIES OF THE
CRITICAL REASONING
TESTS
This chapter presents information
describing the psychometric properties of the Verbal and Numerical
Critical Reasoning tests. The aim will
be to show that these measures meet
the necessary technical requirements
with regard to standardisation, reliability and validity, to ensure the psychometric soundness of these test
materials.
1
2
3
4
INTRODUCTION
STANDARDISATION
BIAS
RELIABILITY OF THE CRITICAL
REASONING TESTS
5
6
VALIDITY
STRUCTURE OF THE CRITICAL
REASONING TESTS
7
CONSTRUCT VALIDITY OF THE
CRITICAL REASONING TESTS
8
CRITERION VALIDITY OF THE CRITICAL
REASONING TESTS
bq
INTRODUCTION
STANDARDISATION –
NORMATIVE
RELIABILITY – ASSESSING
STABILITY
Formative data allows us to compare
an individuals score on a standardised scale against the typical score
obtained from a clearly identifiable,
homogeneous group of people.
Also known as test-retest reliability,
an assessment is made of the similarity of scores on a particular scale
over two or more test occasions. The
occasions may be from a few hours,
days, months or years apart.
Normally Pearson correlation coefficients are used to quantify the
simi-larity between the scale scores
over the two or more occasions.
Stability coefficients provide an
important indicator of a test’s likely
usefulness of measurement. If these
coefficients are low (< approx. 0.6)
then it is suggestive of either that the
abilities/behaviours/attitudes being
measured are volatile or situationally
specific, or that over the duration of
the retest interval, situational events
have made the content of the scale
irrelevant or obsolete. Of course, the
duration of the retest interval
provides some clue as to which effect
may be causing the unreliability of
measurement. However, the second
measure of a scales reliability also
provides valuable information as to
why a scale may have a low stability
coefficient. The most common
measure of internal consistency is
Cronbach’s Alpha. If the items on a
scale have high inter-correlations
with each other, and with the total
scale score, then coefficient alpha
will be high. Thus a high coefficient
alpha indicates that the items on the
scale are measuring very much the
same thing, while a low alpha would
be suggestive of either scale items
measuring different attributes or the
presence of error.
RELIABILITY RELIABILITY
The property of a measurement
which assesses the extent to which
variation in measurement is due to
true differences between people on
the trait being measure or to
measurement error. In order to
provide meaningful interpretations,
the reasoning tests were standardised
against a number of relevant groups.
The constituent samples are fully
described in the next section.
Standardisation ensures that the
measurements obtained from a test
can be meaningfully interpreted in
the context of a relevant distribution
of scores. Another important technical requirement for a
psychometrically sound test is that
the measurements obtained from
that test should be reliable.
Reliability is generally assessed using
two specific measures, one related to
the stability of scale scores over time,
the other concerned with the internal
consistency, or homogeneity of the
constituent items that form a scale
score.
br
RELIABILITY – ASSESSING
INTERNAL CONSISTENCY
Also known as scale homogeneity, an
assessment is made of the ability of
the items in a scale to measure the
same construct or trait. That is a
parameter can be computed that
indexes how well the items in a scale
contribute to the overall measurement denoted by the scale score. A
scale is said to be internally consistent if all the constituent item
responses are shown to be positively
associated with their scale score. The
fact that a test has high internal
consistency & stability coefficients
only guarantees that it is measuring
something consistently. It provides
no guarantee that the test is actually
measuring what it purports to
measure, nor that the test will prove
useful in a particular situation.
Questions concerning what a test
actually measures and its relevance
in a particular situation are dealt
with by looking at the tests validity.
Reliability is generally investigated
before validity as the reliability of
test places an upper limit on tests
validity. It can be mathematically
demonstrated that a validity coefficient for a particular test can not
exceed that tests reliability coefficient.
VALIDITY
The ability of a scale score to reflect
what that scale is intended to
measure. Kline’s (1993) definition is
‘A test is said to be valid if it
measures what it claims to measure’.
Validation studies of a test investigate the soundness and relevance of
a proposed interpretation of that test.
Two key areas of validation are
known as criterion validity and
construct validity.
VALIDITY – ASSESSING
CRITERION VALIDITY
Criterion validity involves translating
a score on a particular test into a
prediction concerning what could be
expected if another variable was
observed. The criterion validity of a
test is provided by demonstrating
that scores on the test relate in some
meaningful way with an external
criterion. Criterion validity comes in
two forms – predictive & concurrent.
Predictive validity assesses whether a
test is capable of predicting an
agreed criterion which will be available at some future time – e.g. can a
test predict the likelihood of someone
successfully completing a training
course. Concurrent validity assesses
whether the scores on a test can be
used to predict a criterion measure
which is available at the time of the
test – e.g. can a test predict current
job performance.
VALIDITY – ASSESSING
CONSTRUCT VALIDITY
Construct validity assesses whether
the characteristic which a test is
actually measuring is psychologically
meaningful and consistent with the
tests definition. The construct validity of a test is assessed by
demonstrating that the scores from
the test are consistent with those
from other major tests which
measure similar constructs and are
dissimilar to scores on tests which
measure different constructs.
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STANDARDISATION
The critical reasoning tests were
standardised on a mixed sample of
365 people drawn from graduate,
managerial and professional groups.
The age and sex breakdowns of the
normative sample for the VCR2 and
NCR2 are presented in Tables 1 and
2 respectively. As would be expected
from an undergraduate sample the
age distribution is skewed to the
younger end of the age range of the
general population. The sex distribution is however broadly consistent
with that found in the general population.
Norm tables for the VCR2 and
NCR2 are presented in Appendix IV.
For the Verbal Critical Reasoning
test different norm tables are
presented for test scores that have, or
have not, been corrected for guessing. (A correction for guessing has
not been made available for the
Numerical Critical Reasoning test as
the six-point scale this test uses mitigates against the problem of
guessing.) As noted above it is
recommended that scores on the
VCR2 are corrected for guessing.
The correction for guessing should
be applied to the raw score (i.e. to
the score before it has been standardised.) The corrected (or
uncorrected) raw score is then standarised with reference to the
appropriate norm table (Appendix
IV Table 2 for uncorrected scores
and Table 3 for corrected scores.)
Thus it is important that particular care is taken to refer to the
correct norm table when standradising VCR2 raw scores.
In addition, for users of the
GeneSys system normative data is
available also from within the software, which computes for any given
raw score, the appropriate standardised scores for the selected reference
group. In addition the GeneSys™
software allows users to establish
their own in-house norms to allow
more focused comparison with
profiles of specific groups.
BIAS
GENDER AND AGE
DIFFERENCES
Gender differences on CRTB were
examined by comparing samples of
males and female respondents
matched, for educational and socioeconomic status. Table 2 opposite
provides mean scores for men and
women on the verbal and numerical
critical reasoning tests, along with
the F-ratio for the difference
between theses means. While the
men in this sample obtained marginally higher scores on both the verbal
and numerical reasoning tests, this
was not statistically significant.
bt
Age
Mean
Age
SD
Male
Female
31.7
7.9
n=245
n=119
Table 1 – Mean and SD of age, and gender breakdown, of the normative
sample
mean
men
women
(n=218)
(n=166)
F-ratio
Significance
of difference
VCR2
21.1
22.1
.64
n.s.
NCR2
9.0
10.1
.15
n.s.
Table 2 – Mean scores for men and women (MBAs) on the VCR2 and NCR2
ck
RELIABILITY OF THE
CRITICAL REASONING
TESTS
If a reasoning test is to be used for
selection and assessment purposes
the test needs to measure each of the
aptitude or ability dimensions it is
attempting to measure reliably, for
the given population (e.g. graduate
entrants, senior managers etc.). That
is to say, the test needs to be consistently measuring each ability so that
if the test were to be used repeatedly
on the same candidate it would
produce similar results. It is generally recognised that reasoning tests
are more reliable than personality
tests and for this reason high standards of reliability are usually
expected from such tests. While
many personality tests are considered to have acceptable levels of
reliability if they have reliability
coefficients in excess of .7, reasoning
tests should have reliability coefficients in excess of .8.
GRT2 INTERNAL CONSISTENCY
Table 3 presents alpha coefficients
for the Verbal and Numerical
Critical Reasoning tests. Each of
these reliability coefficients is
substantially greater than .8, clearly
demonstrating that the VCR2 and
NCR2 are highly reliable across a
range of samples.
alpha
Insurance Sales Agents
(n=132)
MBA’s
(n=205)
Undergraduates
(n=70)
VCR2
.88
.84
.88
NCR2
.83
.81
.86
Table 3 – Alpha coefficients for the Verbal and Numerical Critical
Reasoning Tests
VALIDITY
Whereas reliability assess the degree of measurement error of a reasoning
test, that is to say the extent to which the test is consistently measuring one
underling ability or aptitude, validity addresses the question of whether or
not the scale is measuring the characteristic it was developed to measure.
This is clearly of key importance when using a reasoning test for assessment
and selection purposes. In order for the test to be a useful aid to selection we
need to know that the results are reliable and that the test is measuring the
aptitude it is supposed to be measuring. Thus after we have examined a test’s
reliability we need to address the issue of validity. We traditionally examine
the reliability of a test before we explore its validity as reliability sets the
lower bound of a scale’s validity. That is to say a test cannot be more valid
than it is reliable.
STRUCTURE OF THE
CRITICAL REASONING
TESTS
Specifically we are concerned that
the tests are correlated with each
other in a meaningful way. For
example, we would expect the Verbal
and Numerical Critical Reasoning
tests be moderately correlated with
each other as they are measuring
different facets of critical reasoning
ability – namely verbal and numerical ability. Thus if the VCR2 and
NCR2 were not correlated with each
other we might wonder whether each
is a good measure of critical reason-
ing ability. Moreover, we would
expect the Verbal and Numerical
Critical Reasoning tests Not to be so
highly correlated with each other as
to suggest that they are measuring
the same construct (i.e. we would
expect the VCR2 and NCR2 to show
discriminant validity). Consequently,
the first way in which we might
assess the validity of a reasoning test
is by exploring the relationship
between the tests.
THE GRADUATE REASONING TESTS (GRT1) THE GENERAL
REASONINGTHE CRITICAL REASONING
Table 4, which presents the Pearson
Product moment correlation between
the VCR2 and NCR2, demonstrates
that while the Verbal and Numerical
tests are significantly correlated, they
are nevertheless measuring distinct
abilities.
Insurance
Sales Agents
(n=132)
MBA’s
(n=170)
Undergraduates
(n=70)
.40
.57
.49
Table 4 – Correlations between the VCR2 and NCR2
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CONSTRUCT VALIDITY OF
THE CRITICAL REASONING
TESTS
As an evaluation of construct validity, the Verbal and Numerical
Critical Reasoning tests were correlated with other widely used
measures of related constructs.
The VCR2 and NCR2 were correlated with the APIL-B (Ability,
Processing of Information and
Learning Battery) that has been
developed by Taylor (1995). The
APIL-B has been specifically developed to be a culture fair assessment
tool for use in a multi-racial context
(South Africa). As such, it has been
designed to assess an individual’s
core cognitive capabilities, rather
than specific skills that may depend
upon educational experience and life
advantagement/disadvantagement.
Table 5 presents the correlations
between the Verbal and Numerical
Critical Reasoning tests with the
APIL-B, on a sample of MBA
students. These correlations are
highly statistically significant, and
substantial in size, providing strong
support for the construct validity of
the VCR2 and NCR2.
The VCR2 and NCR2 were also
found to correlate substantially
(r=.42 and r=.36 respectively) with
Factor B (Intellectual Self-confidence) on the 16PFi on a sample
(n=132) of insurance sales agents.
This suggests that those respondents
who were more confident of their
own intellectual ability had higher
levels of critical reasoning ability;
providing some tangential support
for the construct validity of the
VCR2 and NCR2.
Table 6 presents the correlations
between the original edition of the
Verbal and Numerical Critical
Reasoning tests and the AH5 – a
widely respected measure of general
reasoning ability. These data thus
provide evidence demonstrating that
the first edition of these two tests
measure reasoning ability rather than
some other (related) construct (i.e.
verbal or numerical checking ability).
As was noted above, because of the
nature of critical reasoning tests
items, it is particularly important
when developing such tests to
demonstrate that they are measuring
reasoning ability, and not checking
ability. This is demonstrated by
inspection of table 6.
The relationship between the first
edition of the CRTB and the WatsonGlaser Critical Thinking Appraisal
was examined by Correlating the
VCR2 and NCR2 with the W-GCTA.
The correlations with the W-GCTA
were .38, for both the Verbal and
Numerical tests. While modest, these
correlations nonetheless demonstrate
a degree of congruence between
these two tests, as would be expected
from different measures of critical
reasoning.
cn
APIL-B
sample size
significance
VCR2
.569
n=250
p<.001
NCR2
.512
n=169
p< .001
Table 5 – Correlations between the Verbal and Numerical
Critical Reasoning tests with the APIL-B
Verbal/Numerical
subscale of the AH5
VCR2
NCR2
.60
.51
Table 6 – Correlations between the original
versions of the VCR2 and NCR2 with the AH5
co
CRITERION VALIDITY OF
THE CRITICAL REASONING
TESTS
In this section, we provide details of
a number of studies in which the
critical reasoning tests have been
used to predict job related performance criteria.
INSURANCE SALES
A sample of 132 Insurance Sales
Agents completed the CRTB as part
of a validation study. The association
between their scores on the VCR2
and NCR2 and their job performance was examined using t-tests.
Job incumbents were classified as
either successful or unsuccessful
depending upon their performance
after one year in post. Table 7
presents the mean scores for these
two groups on the VCR2 and NCR2.
Inspection of this table indicates
that, on average, the successful
incumbents had significantly higher
scores on these tests than did the
non-successful incumbents. The
difference in scores between these
two groups reached statistical significance for the NCR2. This provides
strong support for the criterionrelated validity of this test.
A group of MBA students
completed the VCR2 and NCR2
prior to enrolling. Their scores on
these tests were then correlated with
their performance across different
courses on the MBA syllabus. The
results of this analysis are presented
in Table 8. Inspection of table 8 indicates that the critical reasoning tests
were predictive of performance
across a number of areas of study.
This provides strong support for the
predictive validity of the CRTB.
Mean
(n=29)
Mean
(n=23)
unsuccessful
successful
VCR2
18.13793
NCR2
9.72414
t-value
p
21.21739
1.47715
n.s.
12.60870
2.18352
< .05
Table 7 – Association between the VCR2, NCR2 and insurance sales success
cp
VCR2
NCR2
Innovation & design
.374 (n=89, p< 01)
.260 (n=89 p< .01)
Business decision making
.467 (n=35, p<.01)
.433 (n=35 p<.01)
Macro economics
.478 (n=89, p<.001)
.386 (n=89, p<.001)
IT
.468 (n=35, p<.01)
.511 (n=35 p<.01)
Post Graduate Diploma
in Business Administration
Average to date
.364 (n=34, p<.05)
.510 (n=34, p<.01)
Economics
.236 (n=56, n.s.)
.013 (n=56, n.s.)
Analytical Tools and
Techniques
.312 (n=51, p<.05)
.134 (n=51, n.s.)
Marketing
.204 (n=53, n.s.)
-.124 (n=53, n.s.)
Finance & Accounting
.209 (n=56, n.s.)
-.007 (n=56, n.s.)
Organisational Behaviour
.296 (n=56, p<.05)
-.032 (n=56, n.s.)
MBA Category
.389 (n=48, p<.01)
.109 (n=48, n.s.)
Table 8 – Correlations between the VCR2, NCR2 and MBA performance
cq
4
REFERENCES
Binet. A (1910) Les idées modernes
sur les enfants Paris: E. Flammarion.
Cronbach L.J. (1960) Essentials of
Psychological Testing (2nd Edition)
New York: Harper.
Budd R.J. (1991) Manual for the
Clerical Test Battery: Letchworth,
Herts UK: Psytech International
Limited
Galton F. (1869) Heriditary Genuis
London: MacMillan.
Budd R.J. (1993) Manual for the
Technical Test Battery: Letchworth,
Herts UK: Psytech International
Limited
Gould, S.J. (1981). The Mismeasure
of Man. Harmondsworth, Middlesex:
Pelican.
Stern W (1912) Psychologische
Methoden der Intelligenz-Prüfung.
Leipzig, Germany
Heim, A.H. (1970). Intelligence and
Personality. Harmondsworth,
Middlesex: Penguin.
Barth Terman, L.M. et. al., (1917).
The Stanford Revision of the BinetSimon scale for measuring
intelligence. Baltimore: Warwick and
York
Heim, A.H., Watt, K.P. and
Simmonds, V. (1974). AH2/AH3
Group Tests of General Reasoning;
Manual. Windsor: NFER Nelson.
Jackson D.N. (1987) User’s Manual
for the Multidimensional Aptitude
Battery London, Ontario: Research
Psychologists Press.
Johnson, C., Blinkhorn, S., Wood, R.
and Hall, J. (1989). Modern
Occupational Skills Tests: User’s
Guide. Windsor: NFER-Nelson.
Watson & Glaser (1980) Manual for
the Watson-Glaser Critical Thinking
Appraisal Harcourt Brace
Jovanovich: New York
Yerkes, R.M. (1921). Psychological
examining in the United States
army. Memoirs of the National
Academy of Sciences, 15.
cs
5
APPENDIX I
ADMINISTRATION
INSTRUCTIONS
Good practice in test administration requires the assessor to set the scene
before the formal administration of the tests. This scene-setting generally
includes: welcome and introductions; the nature, purpose and use of the
assessment and feedback arrangements.
If only one (either the Verbal or Numerical) of the Critical Reasoning tests is
being administered then Say:
‘From now on, please do not talk among yourselves, but ask
me if anything is not clear. If you have a mobile phone
please ensure that it is switched off. We shall be doing only
one of the two tests contained in the booklet that I will
shortly be distributing.
Say either:
The Verbal Critical Reasoning Test which takes 15 minutes
or
The Numerical Critical Reasoning Test which takes 25
minutes
Continue
During the test I shall be checking to make sure you are not
making any accidental mistakes when filling in the answer
sheet. I will not be checking your responses to see if you are
answering correctly or not.’
If you are administering both the Verbal and Numerical Critical Reasoning
tests (as is more common), and if this is the first or only questionnaire being
administered give an introduction as per or similar to the example script
provided.
dk
Continue by using the instructions exactly as given. Say:
‘From now on, please do not talk among yourselves, but
ask me if anything is not clear. If you have a mobile phone
please ensure that it is switched off. We shall be doing two
tests, the Verbal Critical Reasoning Test which takes 15
minutes and the Numerical Critical Reasoning Test which
takes 25 minutes. During the test I shall be checking to
make sure you are not making any accidental mistakes
when filling in the answer sheet. I will not be checking your
responses to see if you are answering correctly or not.’
WARNING: It is most important that answer sheets do not go astray. They
should be counted out at the beginning of the test and counted in again at
the end
DISTRIBUTE THE ANSWER SHEETS
Then ask:√
‘Has everyone got two sharp pencils, an eraser, some rough
paper and an answer sheet. Please note the answer boxes
are in columns (indicate) and remember do not write on
the booklets.’
Rectify any omissions, then say:
‘Print your last name and first name on the line provided,
and indicate your title and sex followed by your age and
today’s date.’
Explain to the respondents what to enter in the boxes marked ‘Test Centre’
and ‘Comments’. Walk round the room to check that the instructions are
being followed.
WARNING: It is vitally important that test booklets do not go astray. They
should be counted out at the beginning of the session and counted in again at
the end.
DISTRIBUTE THE BOOKLETS WITH THE INSTRUCTION:
‘Please do not open the booklet until instructed.’
Remembering to read slowly and clearly, go to the front of the group. If you
are only administering the Numerical Critical Reasoning test then go the
section below head Numerical Critical Reasoning test. If you are administering both Critical Reasoning tests, or if you are just administering the Verbal
Critical Reasoning test say:
‘Please open the booklet at Page 2 and follow the instructions for this test as I read them aloud.’ (Pause to allow
booklets to be opened).
dl
‘In this test you have to draw inferences from short
passages of text. You will be presented with a passage of
text followed by a number of statements. Your task is to
decide, on the basis of the information contained in the
passage, whether each statement is true, false or cannot be
inferred from the passage. Your decision should be based
only on the information contained in the passage and not
on your own knowledge or opinions.’
‘Mark your answer by filling in the appropriate box, on
your answer sheet, that corresponds to your choice.’
‘You now have a chance to complete the example questions
on page 3 in order to make sure that you understand the
test. Enter your responses to the example questions in the
section marked Example Questions at the top of the answer
sheet.’
Point to the section on the answer sheet marked Example Questions (as you
read the above).
Then pause while candidates read the instructions, then say:√
‘Please attempt the example questions now.’
While the candidates are doing the examples, walk around the room to check
that everyone is clear about how to fill in the answer sheet. Make sure that
no-one is looking at the actual test items during the example session. When
all have finished (allow a maximum of two and a half minutes) give the
answers as follows:
‘The correct response to Example 1 is False. It is explicitly
stated within the text that further growth in the number of
radio stations is limited due to there being no new radio
frequencies available.’
‘The correct response to Example 2 is True. It is explicitly
stated that audience figures affect advertising revenue, thus
affecting profitability.’
‘The correct response to Example 3 is Cannot Determine.
It is impossible to infer, from the information provided in
the text, whether radio stations in general will become more
profitable. The text indicates that audience figures arecurrently poor for many radio stations and that it is expected
that some may go bankrupt. However, it is not possible to
infer from this that audience figures (and as a result advertising revenue) will increase for the remaining radio
stations.’
dm
Check for understanding, then say:
‘Time is short so when you begin the timed test work as
quickly and as accurately as you can.
If you are unsure of answer, mark your best choice and
move on to the next question.
If you want to change an answer cross it out, as indicated
in the instructions in the top left-hand corner of the answer
sheet, and fill in your new choice of answer.’
Point to the top left-hand corner of the answer sheet.
Then continue:
‘There are 8 passages of text and a total of 40 questions.
You have 15 minutes in which to answer the questions.
If you reach the ‘End of Test’ before time is called you may
review your answers if you wish.
If you have any questions please ask now, as you will not be
able to ask questions once the test has started.’
Then say very clearly:
‘Is everyone clear about how to do this test?’
Deal with any questions, appropriately, then, starting stop watch or setting
acount-down timer on the word begin say:
‘Please turn over the page and begin’
Answer only questions relating to procedure at this stage, but enter in the
Administrator’s Test Record any other problems which occur. Walk around
the room at appropriate intervals to check for potential problems.
At the end of the 15 minutes, say:
‘Stop’
You should intervene if candidates continue after this point.
If you are only administering the Verbal Critical Reasoning test say:
‘Close the test booklets’
dn
COLLECT ANSWER SHEETS AND BOOKLETS, ENSURING THAT ALL
MATERIALS ARE RETURNED (COUNT BOOKLETS AND ANSWER
SHEETS)
Then say:
‘Thank you for completing the Critical Reasoning Test
Battery’
If you are administering both of the Critical Reasoning tests continue by
saying:
‘ Now please turn to Page 12 which is a blank page’
Then say:
‘We are now ready to start the n ext test. Has everyone stillgot two sharpened pencils, an eraser, some unused rough
paper?’
If not, rectify, then say:
‘The next test follows on the same answer sheet, please
locate the section now.’
Check for understanding.
Then say:
‘Now please turn to page 14…’
If you are only administering the Numerical Critical Reasoning test say:
‘Please open the booklet at Page 14…’
and continue by saying:
‘and follow the instructions for this test as I read them
aloud.’ (Pause to allow booklets to be opened).
In this test you will have to draw inferences from numerical
information which is presented in tabular form.
You will be presented with a numerical table and asked a
number of questions about this information. You will then
have to select the correct answer to each question from one
of six possible choices. One and only one answer is correct
in each case.
do
Mark your answer, by filling in the appropriate box, on
your answer sheet that corresponds to your choice.
You now have a chance to complete the example questions
on Pages 15 in order to make sure that you understand the
test. Enter your responses to the example questions in the
section marked Example Questions at the top of the answer
sheet.’
Point to the section on the answer sheet marked Example Questions (as
youread the above).
Then pause while candidates read the instructions, then say:
‘Please attempt the example questions now.’
While the candidates are doing the examples, walk around the room to check
that everyone is clear about how to fill in the answer sheet. Make sure that
no-one is looking at the actual test items during the example session. When
all have finished (allow a maximum of three minutes) give the answers as
follows:
‘The correct answer to Example 1 is Design (answer no. 5).
It can be seen, in the table, that amongst women, design
was consistently chosen by the lowest percentage as the
most important feature of a car.
The correct answer to Example 2 is performance (answer
no. 1). It can be seen that of all the features of a car, performance is rated by men as being the most important
featureof a car.
The correct answer to Example 3 is 10.4 (answer no.5). Of
men below the age of 30, 5% identified safety and 52%
identified performance as the most important feature of a
car. 52 over 5 is 10.4, therefore the answer is number 5.
Please do not turn over the page yet’
Then say:
‘Time is short so when you begin the timed test work as
quickly and as accurately as you can.
If you want to change an answer cross it out, as indicated
in the instructions in the top left-hand corner of the answer
sheet, and fill in your new choice of answer.’
Point to the top left-hand corner of the answer sheet.
dƒ p
Then continue:
‘There are 6 tables of numerical information and a total of
25 questions. You have 25 minutes in which to answer the
questions.
If you reach the √‘End of Test’ before time is called you
may review your answers if you wish.
If you have any questions please ask now, as you will not be
able to ask questions once the test has started.’
Then say very clearly:
‘Is everyone clear about how to do this test?’
Deal with any questions, appropriately, then, starting stop watch or setting
acount-down timer on the word begin say:
‘Please turn over the page and begin’
Answer only questions relating to procedure at this stage, but enter in the
Administrator’s Test Record any other problems which occur. Walk around
the room at appropriate intervals to check for potential problems.
At the end of the 25 minutes, say:
‘Stop. Close the test booklets’
You should intervene if candidates continue after this point.
If you are only administering the Verbal Critical Reasoning test say:
COLLECT ANSWER SHEETS AND BOOKLETS, ENSURING THAT ALL
MATERIALS ARE RETURNED (COUNT BOOKLETS AND ANSWER
SHEETS)
Then say either:
‘Thank you for completing the Critical Reasoning Test
Battery’
or
‘Thank you for completing the Numerical Critical
Reasoning Test’
dq
APPENDIX II
SCORING INSTRUCTIONS
The completed answer sheets are scored and profiled by following the steps
listed below:
1
Remove the top cover sheet of the combined answer/scoring sheet to
reveal the scoring key.
To score and standardise the VCR2 follow steps 2-8. To score and standardise the NCR2 follow steps 9-10.
2
Count up the number of correct responses for the VCR2 and enter the
total in the box marked ‘Total’ (Raw Score).
If you do not wish to correct the VCR2 score for guessing go straight to step 7.
To correct the VCR2 score for guessing add up the total number of
incorrect responses (i.e. the total number of items attempted minus the
raw score) and enter this in the box marked ‘Number Wrong’.
4 The correction for guessing can be found in Appendix III. The number
of incorrect responses is listed in the first column of this table and the
corresponding correction for guessing is listed in the second column.
Make note of the correction for guessing (that corresponds to the
number of incorrectly completed items).
5 To obtain the corrected raw score, subtract the correction for guessing
from the raw score. If this number is negative (i.e. the number corrected
for guessing is larger than the raw score) then the corrected raw score is
zero. Enter the corrected raw score in the box marked
‘Corrected/Uncorrected Raw Score’. To indicate that you have made the
correction, delete ‘Uncorrected’.
6 To standardise the corrected raw score, look this up in the norm table
presented in Appendix IV – Table 3 and enter this in the box marked
‘Standard Score’.
have
scored and standardised the VCR2. If you wish to score and stanYou
dardise the NCR2 follow steps 9-10.
3
Enter the total score obtained from step 2 in the box marked
‘Corrected/Uncorrected Raw Score’. To indicate that you have not made
the correction, delete ‘Corrected’.
8 To standardise the uncorrected raw score, look this value up in the norm
table presented in Appendix IV – Table 2 and enter this in the box
marked ‘Standard Score’.
9 Count up the number of correct responses to the NCR2 and enter the
total in the box marked ’Total’.
10 To standardise the raw score, look this value up in the norm table
presented in Appendix IV – Table 1 and enter this in the box marked
‘Standard Score’.
7
APPENDIX III
CORRECTION FOR
GUESSING
Number of
incorrect
answers
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Correction
(to be deducted
from raw score)
.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
11.5
12
12.5
13
Corrected
Raw Score = 0
dr
ds
APPENDIX IV
NORM TABLES
Sten
Values
1
2
3
4
5
6
7
8
9
10
NCR2
Raw
0-2
3
4-5
6-7
8-10
11-13
14-16
17-18
19-20
21-25
Table 1 – Norm:
NCR2 Graduates/
Managers
Sten
Values
1
2
3
4
5
6
7
8
9
10
VCR2
Raw
0-7
8-10
11-12
13-16
17-20
21-23
24-27
28-29
30-32
33-40
Table 2 – Norm: VCR2
(Uncorrected)
Graduates/Managers
Sten
Values
VCR2
Correct
Data not yet
available
Table 3 – Norm: VCR2
Corrected Graduates/
Managers
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