Variables and Scaling Techniques

Basics in Educational Research UnitIV
Annammal College of Education for Women 1
UNIT-IV: VARIABLES AND SCALING TECHNIQUES
Variables- Meaning, Types- Method of selecting variable , Scale Measurement, Scaling,
properties- Types of Scales : Nominal, Ordinal, Interval and Ratio Scales.
A variable is any entity that can take on different values. OK, so what does that mean?
Anything that can vary can be considered a variable. For instance, age can be considered a variable
because age can take different values for different people or for the same person at different times.
Similarly, country can be considered a variable because a person’s country can be assigned a value.
Variables aren’t always ‘quantitative’ or numerical. The variable city consists of text values
like Chennai, Coimbatore, Madurai etc., We can also assign quantitative values instead of the text
values, but we don’t have to assign numbers in order for something to be a variable. It’s also
important to realize that variables aren’t only things that we measure in the traditional sense.
An attribute is a specific value on a variable. For instance, the variable Student grade has
two attributes: pass and fail. Or, the variable agreement might be defined as having five attributes:
1 = strongly disagree
2 = disagree
3 = neutral
4 = agree
5 = strongly agree
Types of Variables
Variables can be classified as quantitative or qualitative or categorical variable.
Quantitative variable
A variable that contains quantitative data is a quantitative variable. Quantitative variables are
numeric and represent some kind of measurement. They represent a measurable quantity.
Examples: height, weight, time, number of items sold, number of programs attended etc.,
Quantitative variables are divided into two types: discrete and continuous.

Quantitative - Discrete
Quantitative discrete variables are variables for which the values it can take are countable and have
a finite number of possibilities. The values are often (but not always) integers. Here are some
examples of discrete variables:
 Number of children in a family
 Number of students in a class
 Number of citizens of a country
Even if it would take a long time to count the citizens of a large country, it is still technically
possible. Moreover, for all examples, the number of possibilities is finite.
Quantitative - Continuous
On the other hand, quantitative continuous variables are variables for which the values are not
countable and have an infinite number of possibilities. For example:
 Age
 Weight
 Height
For simplicity, we usually referred to years, kilograms (or pounds) and centimeters (or feet and
inches) for age, weight and height respectively.
Qualitative Variable or Categorical Variable
Variables that are not measurement variables. Their values do not result from measuring or
counting. Qualitative variables (also referred as categorical variables or factors in R) are variables
that are not numerical and which values fits into categories.
Examples: hair color, religion, political party, profession
Qualitative variables are divided into two types: nominal and ordinal.
Qualitative - Nominal
A qualitative nominal variable is a qualitative variable where no ordering is possible or implied in
the levels. For example, the variable gender is nominal because there is no order in the levels

female/male. Eye color is another example of a nominal variable because there is no order among
blue, brown or green eyes. A nominal variable can have between two levels (e.g., do you smoke?
Yes/No or what is your gender? Female/Male).
Qualitative - Ordinal
On the other hand, a qualitative ordinal variable is a qualitative variable with an order implied in
the levels. For instance, if the severity of road accidents has been measured on a scale such as light,
moderate and fatal accidents, this variable is a qualitative ordinal variable because there is a clear
order in the levels.
Another good example is health, which can take values such as poor, reasonable, good, or
excellent. There is clear order in these levels so health is in this case a qualitative ordinal variable.
Variables involved in an Experimental Research
Another important distinction having to do with the term ‘variable’ is the distinction between an
independent and dependent variable. This distinction is particularly relevant when you are
investigating cause-effect relationships. Experiments are usually designed to find out what effect
one variable has on another.
Independent variable and Dependent Variable
In an experiment, the investigator manipulate the independent variable (the one you think might
be the cause) and then measure the dependent variable (the one you think might be the effect) to
find out what this effect might be.

For example: The effect of Computer Assisted Instruction in enhancing the academic performance
of students.
In the above experiment the treatment ie. Computer Assisted Instruction is the independent
variable and the academic performance of students is the dependent variable.
Confounding Variables
Confounding variable is an unmeasured third variable that influences both the supposed cause and
the supposed effect. Factors that might influence the dependent variable (outcome measure) and
whose effect may be confused with the effects of the independent variable are called as
confounding variable.
Intervening variables
Certain variables that cannot be controlled or measured directly may have an important
effect on the outcome. These variables intervene between the cause and effect and are called as
intervening variables. (Eg. anxiety, fatigue, motivation) These variables can be controlled by using
proper experimental designs.
Extraneous variables
Those uncontrolled variables that may have significant influence on the results of the study.
(Eg. teacher enthusiasm, age, socio economic status)
Method of Selecting the Variables
Variable selection means choosing among many variables which to include in a particular model,
that is, to select appropriate variables from a complete list of variables by removing those that are
irrelevant or redundant. The purpose of such selection is to determine a set of variables that will
provide the best fit for the model so that accurate predictions can be made. Variable selection is
one of the most difficult aspects of research. It is often advised that variable selection should be
more focused on conceptual knowledge and previous literature than statistical selection methods
alone.
However, remember that especially for complex variables, measurement may always be
incomplete or inaccurate because you may not be able to find a variable that captures all aspects

of a concept completely. Therefore, your goal should be to select the best possible variables to
describe the concept. As suggested earlier, a good way to make sure you select the most appropriate
variables is to review studies similar to yours, and check if the variables used would be appropriate
or applicable to your study. If it is not possible to find appropriate variables in the literature, you
may want to conduct some pretests to make sure the measures you have selected are appropriate.
You could also use different measures of a concept to check how the results differ. For example,
instead of using only “income levels’ to operationalize the concept of socioeconomic status, you
could also use “educational levels” or “ownership of different assets” in a single study to see how
these multiple measures influence your findings.
Measurement
Measurement is the process of observing and recording the observations that are collected as part
of research. The recording of the observations may be in terms of numbers or other symbols to
characteristics of objects according to certain prescribed rules. The respondent’s characteristics
are feelings, attitudes, opinions etc. The most important aspect of measurement is the specification
of rules for assigning numbers to characteristics. The rules for assigning numbers should be
standardized and applied uniformly. This must not change over time or objects.
Scaling
Scaling is the assignment of objects to numbers according to a rule. In scaling, the objects are text
statements, usually statements of attitude, opinion, or feeling.
Measurement Scales
Measurement scales are used to categorize and/or quantify variables. A common feature of
research is the attempt to have respondents communicate their feelings, attitudes, opinions, and
evaluations in some measurable form. Hence researchers have developed a range of scales. Each
of these scales have unique properties. The researcher should realize that they have widely
differing measurement properties. Some scales are at very best, limited in their mathematical
properties to the extent that they can only establish an association between variables. Other scales

have more extensive mathematical properties and some have the possibility of establishing cause
and effect relationships between variables.
Properties of Measurement Scales or Scaling Properties
The properties of the abstract number system that are relevant to scales of measurement are
identity, magnitude, equal interval, and absolute/true zero.
Identity: Identification refers to assignment of a number to respondents’ response, and these
number are just for the sake of identification and the numbers itself cannot be used in mathematical
operations thus numbers assigned are just to convery a particular meaning. E.g. Assigning 1 to
Male, 2 to Female.
Magnitude: Numbers can have an inherent order from smaller to larger. For instance Position in
Class or Rank in Organization. Here the values of the variable have numbers for identification but
also the values have some order. E.g. difference of Marks between 1st and 2nd could be 30 whereas
difference between 2nd and 3rd could be of 50 marks, meaning on the continuum the difference is
not the same.
Equal Intervals: It means that difference between numbers anywhere on the scale are the same.
E.g. take the variable Position, it is measured on Ordinal Scale but not on Interval Scale because
the distance between 1st and 2nd position may well not be the same as 2nd and 3rd, or 3rd and 4th.
Here the distance refers to the Marks obtained by the position holders. Likert Scale is an example
for equal interval scale.
Absolute/true zero: It means that the zero as a response represents the absence of the property
being measured (e.g., no money, no behavior, none correct) but temperature on 0 is not absolute
zero as it still has some effect and we cannot say no temperature.
Types of Scales
There are 4 scales of measurement, namely Nominal, Ordinal, Interval and Ratio, all variables fall
in one of these scales. Understanding the mathematical properties and assigning proper scale to
the variables is important because they determine which mathematical operations are allowed and
determines the statistical operations that can be used.

1. Nominal Scale: It is the crudest among all measurement scales but it is also the simplest
scale. In this scale the different scores on a measurement simply indicate different
categories. It does not have magnitude, equal intervals and absolute zero. The nominal
scale does not express any values or relationships between variables. The nominal scale is
often referred to as a categorical scale. The assigned numbers have no arithmetic properties
and act only as labels. Nominal variables are the most basic level of measurement. These
are variables that have two or more mutually exclusive and exhaustive categories.
However, these categories cannot be ordered or ranked. An example of this type of variable
would be the states of India. Thus, Himachal Pradesh, Uttaranchal, Maharashtra are all
states of India, but they do not have an intrinsic ranking order. You would have to apply
some rule in order to rank them. Similarly, “gender” is also a nominal variable –
male/female/ third gender are the three categories within this variable, but they cannot be
ranked – they can only be compared. The only statistical operation that can be performed
on nominal scales is a frequency count. We cannot determine an average except mode. For
example: labeling men as ‘1’ and women as ‘2’ which is the most common way of labeling
gender for data recording purpose does not mean women are ‘twice something or other’
than men. Nor it suggests that men are somehow ‘better’ than women.
2. Ordinal Scale: It involves the ranking of items along the continuum of the characteristic
being scaled. In this scale, the items are classified according to whether they have more or
less of a characteristic. It has magnitude but does not have equal intervals and absolute
zero. The main characteristic of the ordinal scale is that the categories have a logical or
ordered relationship. This type of scale permits the measurement of degrees of difference,
(i.e. ‘more’ or ‘less’) but not the specific amount of differences (i.e. how much ‘more’ or
‘less’). Ordinal variables are also variables that have two or more categories, but they are
different from nominal variables because they can be ranked, and ranks are used to
determine the differences between the categories. However, while we can rank them, they
do not carry a numerical value. They can only measure how one value is greater or lesser
than another value. An example may be asking someone how often he or she watch movies
on television – their response options are Very often, Frequently, Sometimes or Never.
From his or her responses, we will know that someone who responds “frequently” watches
movie more often than someone who responds “sometimes.” However, none of these

responses has a numerical value, so we cannot assess what is the numerical distance
between “frequently” and “sometimes.” Using ordinal scale data, we can perform statistical
analysis like Median and Mode, but not the Mean. For example, a fast food home delivery
shop may wish to ask its customers:
How would you rate the service of our staff? (1) Excellent • (2) Very Good • (3) Good •
(4) Poor • (5) Worst •
3. Interval Scale: It is a scale in which the numbers are used to rank attributes such that
numerically equal distances on the scale represent equal distance in the characteristic being
measured. An interval scale contains all the information of an ordinal scale, but it also one
allows to compare the difference/distance between attributes. Interval scales may be either
in numeric or semantic formats. It has magnitude and equal intervals but no absolute zero.
Interval variables are variables that have a numerical value, and are measured on a
continuum. The most common example of this type of variable is the temperature when
measured in Celsius or Fahrenheit. We know that temperature is measured on a continuum
on thermometer. Therefore, we know that the difference between 10 to 20 degrees Celsius
is the same interval value (10 degrees) as 30 to 40 degrees Celsius. Test scores on an IQ
test is another example of an interval variable. The interval scales allow the calculation of
averages like Mean, Median and Mode and dispersion like Range and Standard Deviation.
For example, the difference between ‘1’ and ‘2’ is equal to the difference between ‘3’ and
‘4’. Further, the difference between ‘2’ and ‘4’ is twice the difference between ‘1’ and ‘2’.
4. Ratio Scale: It is the highest level of measurement scales. This has the properties of an
interval scale together with a fixed (absolute) zero point. The absolute zero point allows us
to construct a meaningful ratio. It has all the three properties such as magnitude, equal
intervals and absolute zero. Ratio scales permit the researcher to compare both differences
in scores and relative magnitude of scores. Examples of ratio scales include weights,
lengths and times. For example, the difference between 10 and 15 minutes is the same as
the difference between 25 and 30 minutes and 30 minutes is twice as long as 15 minutes.

Variables and Scaling Techniques

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