1. Variable &
Levels of Measurement
1. Variable
Suppose that we have a research problem namely: The
Relationship between Attitude toward Instruction and English
Writing Ability, so we have one independent variable (X), and
one Dependent variable (Y). Alternatively, we can write them
as follow:
X : Attitude toward English Instruction
Y : English Writing Ability
What is Variable?
(Hatch and Farhady, 1982: 12-15)
Variable can be defined as an attribute of a person or of an object
which ‘varies’ from person to person or from object to object.
The syntactic, semantic, and phonological elements of
language, for example, are variables. They are attributes of
language and they are also something which people may
possess (to some varying degree of proficiency)… The more
specific variable is, the easier it will be to locate and measure.
Independent Variable
: is the major variable which you hope to investigate. It is the
variable which is selected, manipulated, and measured by the
researcher.
Dependent Variable
: on the other hand, is the variable which you observe and
measure to determine the effect of the independent variable.
Before using any statistical technique (chi-square, product
moment, t-test, regression, etc.), we have to determine the
Variable Scales or sometimes termed as Scale of Measurement/
Levels of Measurement.
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2. 2. Levels of Measurement
The concept of level of measurement or scales of measurement
is central to statistical analysis and helps to determine the types
of procedure that may be carried out on particular variables.
(Miller, et.al., 2002:59)
There three broad levels of measurement. They are:
1. Nominal/Categorical
 Classification into categories
 Numerical labels are sometimes used to identify the
categories (e.g., 1 = male and 2 = female)
 The numbers are merely labels and have no intrinsic
meaning.
 Examples of variables measured on the nominal scale are:
sex, race, religion, marital status.
2. Ordinal
 Classification into categories
 The categories have meaningful order (for example, from
highest to lowest)
 We cannot determine the degree of difference between
the categories.
 Example of variables measured on the ordinal scale are:
social class, attitude, opinion, etc.
4= strongly agree; 3 agree; 2 disagree; 1 strongly disagree
Learning English is to get a good job 4 3 2 1
We can also use such order as:
Very happy – happy – unhappy
Poor – fair – good – excellent
3. Interval
 Shares all the qualities of nominal and ordinal variable
 Precise distance between each categories
 Examples of variables commonly measured on the
interval scale are: age, test score, income, etc.
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3. According to Hatch and Farhady, 1982: 12-15
“Whether a variable is placed on a nominal, ordinal, or
interval scale is sometimes determined by the type of variable, but
more frequently the researcher must decide on the most
appropriate scale for the variable. For example, if bilingualism is
the variable you wish to research, you could place it on a nominal
scale – your Ss (students,_pen.) either are or not bilingual—and
assign a 1 or 2 value to variable. You could also assign it to an
ordinal scale and either rank order your Ss in relation to each
other on how bilingual you think they are or assign them to a
scale of extremely to not very bilingual. Or you could give them a
test to measure proficiency in each language and thus obtain data
on an interval scale for the variable.”
“Whatever the variables are that you want to investigate
and whatever scale you select for the variables, you will need to
define them further in terms of your research design. You must be
clear about the function of each variable in your investigation.”
3. Implication of Level of Measurement
a. Chi-Square X2; Statistical Test of Nominal Data
When we measure nominal variables, we are concerned not
with how much but with how many or how often. Our data is in
terms of frequency counts rather than scores (Hatch and Farhadi,
1982: 165)
Case example:
In Academic Year of 2003/2004, 1032 students enrolled at
the English Department of STAIN Jurai Siwo Metro. After
grouping them according to their type of schools, we know that
543 students are from MAN, 437 from SMUN, and 52 from SMK.
We want to know the relationship between the type of
school and the enrolled students at the English Department of
STAIN Jurai Siwo Metro . For this, we use Chi-square by doing
the following steps:
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4. Hypotheses
Ha = There is a significant relationship between the
type of school and the enrolled students at the
English Department of STAIN Jurai Siwo Metro.
Ho = There is not a significant relationship between the
type of school and the enrolled students at the
English Department of STAIN Jurai Siwo Metro.
b. T-test
The t-test is one of the most frequently used statistical
procedures in our field. (Hatch and Farhadi, 1982: 114). It is most
often used to compare two groups. It is most commonly used to
examine whether the means of two groups of data are
significantly different from one another. (Miller, at.al., 2002: 119)
With a t-test the independent variable is nominal or categorical
and the dependent variable is measured at interval or ratio scale
of measurement. (Miller, at.al., 2002: 119)
X = nominal/categorical scale and Y = Interval or ratio scale.
Case example:
We want to know whether there is a difference between male
students and female students in learning English. We, then,
observe the students’ grades of English and try analyze them
using t-test.
X1 : male students (nominal)
X2 : female students (nominal)
Y : English grades (interval)
Hypothesis:
Ha = There is a significant different between female and
male students in learning English.
Ho = There is not a significant different between female and
male students in learning English.
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