The second column ‘mark relative to 40% pass mark’ = mark out of 100 - 40
Measurment and scale
MEASUREMENT AND SCALE
Dep. Of Food Science & Nutrition
ASPEE College of Home Science
Sardar Krushinagar Dantiwada Agricultural University
• Measurement is a process of mapping aspect of a
domain on to other aspect of a range according to some
rules of correspondence.
Acc. To Stevens(1946),
Measurement is assigning numbers to the objects or
The purpose of measurement is to have information in a
form in which a variables can be related to each other.
The "levels of measurement" are expressions that typically
refer to the theory of scale developed by the psychologist
Stanley Smith Stevens .
Stevens claimed that all measurement in science was
conducted using four different types of scales that he called
"nominal", "ordinal", "interval" and "ratio".
• Nominal measurement is a system of assigning number
symbols to event in order to label them.
• No quantitative information is conveyed in nominal data.
• No ordering of the items is implied.
• Nominal scales are used to measure QUALITATIVE
• Nominal scale simply describe differences between
things by assigning them to categories.
• Nominal scale are very useful and are widely used in
survey and other ex-post facto research when data are
being classified by major sub- group of the population .
• For example… Assignment of numbers of basketball
player in order to identify them.
• Other example… Religious preference, race, and
Ordinal Scale: The lowest level of the ordered scale that is
commonly used is the ordinal scale.
The ordinal scale place event in order.
The intervals between the numbers are not necessarily
Allow us to rank order the items in terms of “which has
less?” and “which has more?”
Cannot say “how much more?”
Rank order represent ordinal scales and are frequently used
in research related to qualitative phenomena.
A student’s rank in his graduation class involves the use of
an ordinal scale
Examples:- If Ram’s positions in his class is 10th and
Mohan’s positions is 40th it cannot be said that Ram’s position
is four time as good as that of Mohan. All that can be said
that one person is higher or lower on the scale than another,
but not precise comparisons cannot be made.
Other examples.. Socio economic status of families, Level of
education, Gold Silver and Bronze at the Olympics.
In Interval scale, the intervals are adjusted in term of
some rule that has been established as a basis for
making the unit equal.
The are equal only in so far as one accepts the
assumptions on which the rules is based.
Interval scale can have an arbitrary zero, but it is not
possible to determine them what may be called an
absolute zero or the unique origin.
The primary limitation of the interval scale is the lack
of a true zero; it does not have the capacity to
measure the complete absence of a trait or
Allows us not only to rank order the items that
are measured, but also to quantify and compare
the sizes of differences between them.
For example… temperature, as measured in
degrees Fahrenheit or Celsius, constitutes an
interval scale. Equal differences on this scale
represent equal differences in temperature, but
a temperature of 30 degrees is not twice as
warm as one of 15 degrees.
Ratio is very similar to interval variables; in
addition to all the properties of interval variables,
it features an identifiable absolute zero "0" point.
For Example :the zero point on a centimeter
scale indicate the complete absence of length or
With ratio scales involved one can make
statement like “Jyoti’s” typing performance was
twice as good as that of Reetu.
The ratio involved does have significance and
facilitates a kind of comparision which is not
possible in case of an interval scale.
Ratio scale represents the actual amount of variable.
Measure of physical dimension such as weight,
height, physical distance etc. are examples.
Mark out of
to 40% pass
Ahmed 56 16 6 Pass
Ali 48 8 7 Pass
Comara 65 25 3 Pass
Dawod 73 33 2 Pass
Elias 62 22 4 Pass
Fatima 35 -5 10 Fail
Sayyed 20 -20 9 Fail
Hana 38 -2 8 Fail
Nurul 58 18 5 Pass
Zaleha 82 42 1 Pass
Ratio Interval Ordinal Nominal
Possible sources of error
Source of Error in Measurement
At time the respondent may be
reluctant to express strong negative
Transient factor like fatigue, boredom,
anxiety, etc may limit the ability of the
respondent to respond accurately and
Any condition which palaces a strain on interview can have
serious effects on the interviewer-respondent rapport.
For instance ,if someone else is present, he/she can distort
responses by joining in or merely by being present.
The interviewer can distort responses by rewording
and reordering questions.
Careless mechanical processing can distort the
Incorrect coding ,faulty tabulation or statistical
calculation particularly in the data analysis stage.
Error may arise because of defective measuring
instrument. Those may be:
Use of complex word
Beyond the comprehension of the respondent
Inadequate space for replies
Response choice omission etc .
Another type of instrument deficiency is the poor sampling
of the universe of items of concern.
Sound measurement must meet the tests of
validity, reliability, practicality .
These are three major consideration one should
use in evaluating a measurement tool.
Tests of sound measurement
Validity means truthfulness .
Validity refers to the extent to which a tests
measures what we actually wish to measure.
Lindquist (1951) defined validity of test as “the
accuracy with which it measures that which is
intended to measure”.
For example, a test to measure farmers’
knowledge about plant protection is valid for
measuring that dimensions & nothing else.
test of validity
It is the degree to which a test measures an
intended content area.
It involves essentially the systematic examination
of the test content to determine whether it covers
a representative sample of behaviour domain to
It is established in two ways by experts
judgement & statistical analysis.
For example the items to be measured were sent to
judges who were experts, with two categories ‘agree’ &
‘disagree’ against each item . In final selection, the items
for which there were at least 80% judges’ agreement
were retained. This indicated validity of scale content.
Similarly statistical methods are also applied, for
example if one wants to know the content of validity of a
Hindi spelling test, then the teacher can correlate the
scores on the said test with another similar Hindi spelling
test. A high correlation coefficient would provide an index
for the content validity (Singh,1997).
It is defined as the extent to which the test may be said to
measure a theoretical construct or trait. (Anastasi,1968)
It is a more complex & difficult process. Hence, a decision to
compute construct validity is taken only when the researcher is
fully satisfied that neither any valid & reliable criterion to define
the quality of test is available.
For example, the attitude of farmer towards the use of
nitrogenous fertilisers. The construct for this purpose was ‘the
more favourable the attitude of a respondent to an improved
farming innovation, the greater is the adoption of that innovation
by the respondent’. This theory or construct was tested by
calculating correlation coefficient between adoption scores of
nitrogenous fertilisers for 50 respondents & the attitude scores
for them obtained on the basis of attitude scale of the study. The
correlation coefficient was found to be positive & highly22
It is defined as the degree to which a measure predicts a
second future measure(Sproull,1988).
In this, test scores are obtained and then a time of gap of
months or years is allowed to elapse, after which the criterion
scores are obtained. Subsequently, the test scores & the
criterion scores are correlated & the obtained correlation
becomes the index of predictive validity.
For example, an investigator may administer a test of
intelligence to the students at the time of their admission to a
college & thus obtains a set of scores. After two years, marks
obtained in the final examination are noted which constitutes
the criterion scores. A product moment correlation may be
computed between the sets of intelligence scores at the time
of admission & the marks obtained after two years.
If the correlation is positive & significant it can be
said that scores on intelligence at the time of
admission are directly predicting the future
performance of the students in the college. The
correlation becomes the index of validity coefficient.
Predictive validity is needed for tests which include
long range forecast of academic achievement,
industrial management etc.
In this method a test is correlated with a criterion
which is available at the present time. Scores on
newly constructed intelligence test may be
correlated with scores obtained on an already
standardised test of intelligence. The resulting
coefficient of correlation is the indicator of
concurrent validity(Singh, 1997).
RELIABILITY & validity OF MEASUREMENT
The key indicators of the quality of a measuring
instrument are the reliability and validity of the measures.
The process of developing and validating an instrument is
in large part focused on reducing error in the
RELIABILITY & validity OF MEASUREMENT
Reliability refers to the consistency of scores
obtained by the same individuals when re-examined
with test on different occasions, or with different sets
of equivalent items or under variable examining
For example, if an individual receives a score of 60
on an achievement test & is assigned a rank, the
person should receive approximately the same rank
when the test is administered on the second
TYPES OF RELIABILITY
Inter method reliability.
Internal consistency reliability.
TYPES OF RELIABILITY
Inter-rater reliability: assesses the degree to
which test scores are consistent when
measurements are taken by different people
using the same methods.
Test-retest reliability: assesses the degree to
which test scores are consistent from one test
administration to the next. Measurements are
gathered from a single rater who uses the
same methods or instruments and the same
testing conditions. This includes intra-rater
Inter method reliability: assesses the degree to
which test scores are consistent when there is a
variation in the methods or instruments used. This
allows inter-rater reliability to be ruled out.
Internal consistency reliability: assesses the
consistency of results across items within a test.
Practicality : Practicality is concerned with a wide range of
factors of economy, convenience and interpretability.
From the operation point of view, the measuring
instrument ought to be practical i.e.it should be
economical, convenient, and interpretable.
Economy consideration suggest that some trade off is
needed between the ideal research project that which the
budget can afford.
Convenience test suggest that the should be easy to
measuring instrument should be easy to administer.
For this purpose one should give due attention to the
proper layout of the measuring instrument.
For Instance, A questionnaire with clear instruction is
certainly more effective and easier to complete to complete
than one which lacks these features.
Test of practicality
Interpretability consideration is specially important
when person other then the designers of the test are
to interpret the result.
The measuring instrument , in the order to be
interpretable, must be supplemented by
a) Detailed instructions for administering the test;
b) Scoring keys;
c) Evidence about the reliability and
d) Guides for using the and for interpreting results.
The technique of developing measurement tools
involves a four stage process ,consisting of the
Specification of concept dimensions;
selection of indicator; and
Formation of index.
Technique of developing measurement tool
First and foremost step which means that the
researcher should arrive at an understanding of the
major concepts pertaining to his/her study.
This step is more apparent in theoretical studies than
in the more pragmatic research , where the
fundamental concepts are already established.
Step first-concept development
This step require the researcher to specify the
dimensions of the concepts that he/she developed in
the first stage.
This task may either be accomplished by deduction
i.e. by adopting a more or less intuitive approach or
by empirical correlation of the individual dimensions
with the total concept and/or other concepts.
For instance: one may think of several dimension
such as product reputation, customer treatment,
corporate leadership, concern for individuals, sense
of social responsibility and so forth when one is
thinking about the image of a certain company.
Step second -concept development
After specification the dimension of concept ,the
researcher must develop indicators for measuring
each concept element.
Indicator are specific question, scales or other
devices by which respondent’s knowledge, opinion
expectation, etc are measured.
As there is seldom a perfect measure of a concept,
the researcher should consider several alternatives
for the purpose.
The use of more than one indicator gives stability to
the scores and it is also improves their validity.
Step third -selecton of indicator
When we have several dimensions of a concept or
different measurements of a dimensions, we may
need to combine them into a single index .
One simple way for getting an overall index is to
provide scale value to the responses and then sum
up the corresponding scores.
Such an overall index would provide a better
measurement tool than a single indicator because of
that an individual indicator has only a probability
relation to what we really want to know.
This way we must obtain an overall index for the
Step fourth - formation of index