Variables

1. 2.
Variables
[Q:
1. Write short note on: Variable. (BSMMU, January 2010),
2. Define variable. (BSMMU, January 2011, January 2009,
July 2009 )]
A variable is any measured characteristic or attribute that differs for
different subjects. For example, if the weight of 30 subjects were
measured, then weight would be a variable. Thus sex, height, weight etc
are variables since they take on different values when different
individuals are observed.
Variable is contrasted with a constant, the value of which never changes
(e.g. П)
Type of variables
[Q:
1. Classify variable. Give example in each case. (BSMMU,
January, 2011)

2. Biostatistics-5
2. Classify variable with examples. (BSMMU, July 2009,
January 2009) ]
Two types:
1. Quantitative and
2. Qualitative (Qualitative variables are sometimes called
"categorical variables.")
1. A Quantitative variable is a variable that takes on numerical
values determined by the outcome of a random experiment.
2. A Qualitative variable is one for which numerical measurement is
not possible. Qualitative variables are also named as attributes:
these variables are not capable of being described numerically e.g.
sex (male or female), Nation (USA/UK/Bangladesh), Religion
(Muslim/Hindu/Christian), Color of the eye or skin
(Red/White/Black) etc. These characteristics are called attributes
/attributive variates / descriptive characteristics.
If five-year old subjects were asked to name their favorite color, then the
variable would be qualitative. If the time it took them to respond were
measured, then the variable would be quantitative.
Discrete or continuous variables
Continuous: A quantitative variable is continuous if it can take any
value in an interval. A continuous variable is one for which all values in

3. Biostatistics-6
some range are possible. For continuous random variables, one can not
attach probabilities to specific values e.g. the probability that today's
temperature will be precisely 77.23°F is 0. However, probabilities can be
determined for ranges e.g. "today's high temperature will be between
75 and 80°".
Discrete: Variables in any calculation can be characterized by the value
assigned to them. A discrete variable consists of separate, indivisible
categories. No values can exist between a variable and its neighbors.
For example, if you were to observe a class attendance registered from
day-to-day, you may discover that the class has 29 students on one day
and 30 students on another. However, it is impossible for student
attendance to be between 29 and 30. (There is simply no room to
observe any values between these two values, as there is no way of
having 29 and a half student.)
[Q:
1. Differentiate with example dependent, independent and
confounding variables. (BSMMU, January, 2009)
2. Write short notes on: Dependant variable (BSMMU, July,
2009)
3. Define dependent, independent and confounding variable
with an example in each case. (BSMMU, January, 2009)]
Dependent and independent Variable
The variable that is used to describe or measure the problem under
study is called dependent variable.
The variable that is used to describe or measure the factors that are
assumed to cause or to influence the problem is called independent
variable.
Example
Cigarette smoking may cause lung cancer.
Here cigarette smoking is independent variable, lung cancer is
dependent variable.
Confounding Variable (Lurking Variable)

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Any variable that correlates with the main variables under study, but is
hidden or unknown and therefore may cause distortions in one's data is
called Confounding variable (also called a third variable).
Example
Consider a study in which a new drug for the control of hypertension
(high blood pressure) was being investigated. We set up a trial in which
two groups are compared, one group with the drug, another with a
placebo. When we look at the data we find the group receiving the
drug does indeed have lower blood pressure than the control group.
However then we notice, that for some reason the average age of the
experimental group, i.e. those receiving the drug, is significantly lower
than that of the control group. Now we know hypertension is age
related, and therefore the difference in blood pressure between the two
groups might be due to age differences rather than the effect of the
drug. We say the age differences have confounded the findings.
MEASUREMENT OF VARIABLES:
[Q: Write short notes on: i) Measurement scale used in
research (BSMMU, January, 2011)]
MEASUREMENT may be defined as the assignment of numbers to
objects or events according to a set of rules. There are various
measurement scale results from the fact that it may be carried out
under different sets of rules.
Qualitative variables are measured on a nominal or ordinal scale;
Quantitative variables are measured on an interval, or ratio scale.
a. Nominal scales
 Allow for only qualitative classification. That is, they can be
measured only in terms of whether the individual items
belong to some distinctively different categories, but we
cannot quantify or even rank order those categories.

5. Biostatistics-8
 For example, all we can say is that 2 individuals are different
in terms of variable A (e.g., they are of different race), but
we cannot say which one "has more" of the quality
represented by the variable. Typical examples of nominal
variables are gender, race, color, city, etc.
b. Ordinal scales
 allow us to rank order the items we measure in terms of
which has less and which has more of the quality
represented by the variable, but still they do not allow us to
say "how much more."
 A typical example of an ordinal variable is the
socioeconomic status of families. For example, we know
that upper-middle is higher than middle but we cannot say
that it is, for example, 18% higher.
c. Interval scales
 Allow 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. We can
say that a temperature of 40 degrees is higher than a
temperature of 30 degrees, and that an increase from 20 to
40 degrees is twice as much as an increase from 30 to 40
degrees.
d. Ratio scales
 are very similar to interval variables; in addition to all the
properties of interval variables, they feature an identifiable
absolute zero point, thus they allow for statements such as x
is two times more than y.
 Typical examples of ratio scales are measures of time or
space. For example, as the Kelvin temperature scale is a ratio
scale, not only can we say that a temperature of 200

6. Biostatistics-9
degrees is higher than one of 100 degrees; we can correctly
state that it is twice as high. Interval scales do not have the
ratio property. Most statistical data analysis procedures do
not distinguish between the interval and ratio properties of
the measurement scales.
Table: Examples of the Measurement Scales
Nominal Ordinal Interval Ratio
Gender.
Ethnicity.
Marital Status.
Movie ratings (0, 1 or
2 thumbs up).
U.S.D.A. quality of
beef ratings (good,
choice, prime).
The rank order of
anything.
Degrees F.
Most
personality
measures.
WAIS
intelligence
score.
Degrees K.
Annual
income in
dollars.
Length or
distance in
centimeters,
inches, miles,
etc.
References
American Psychological Association. (1994). Publication manual of the
American Psychological Association (4th ed.). Washington, DC: Author