DATA

categorical data?
Categorical data is a collection of information that is divided into
groups.

Categorical data can take on numerical values (such as “1” indicating

Yes and “2” indicating No), but those numbers don’t have mathematical
meaning. One can neither add them together nor subtract them from
each other.

Types of categorical data

1. Nominal data
2. Ordinal data

Continuous data
Continuous data cannot take on exact values but can only be given
within a certain range /degree of accuracy.
Types of continuous data
1. Scale data
2. Interval data

Scales
Scales of measurement refer to ways in which variables or numbers are
defined and categorized. Each scale of measurement has certain
properties which in turn determines the appropriateness for use of
certain statistical analyses. The four scales of measurement are nominal,
ordinal, interval, and ratio.

Nominal Scale
A nominal scale is a scale of measurement used to assign events or
objects into discrete categories. This form of scale does not require the
use of numeric values or categories ranked by class, but simply unique
identifiers to label each distinct category.
Basically, Nominal scale is a naming scale, where variables are simply
“named” or labelled, with no specific order
Example:
• Hair Colour (brown, blonde)
• Gender (men, women)
• Ethnicity (Asian, Hispanic)
• Political preference (PPP/C, APNU)

There are cases where this scale is used for the purpose of classification
– the numbers associated with variables of this scale are only tags for
categorization or division. Calculations done on these numbers will be
futile as they have no quantitative significance.

Nominal scale is often used in research surveys and questionnaires

where only variable labels hold significance. There are two primary
ways in which nominal scale data can be collected:

1. By asking an open-ended question, the answers of which can be

coded to a respective number label decided by the researcher.

For a question such as:

“Which brand of smartphones do you prefer?”

Options:

1- Apple
2- Samsung
3- OnePlus

• In this survey question, only the names of the brands are

significant for the researcher conducting consumer research. There
 is no need for any specific order for these brands. However, while
capturing nominal data, researchers conduct analysis based on the
associated labels.

• In the above example, when a survey respondent selects Apple as

their preferred brand, the data entered and associated will be “1”.
This helped in quantifying and answering the final question – How
many respondents selected Apple? how many selected Samsung?
and how many went for OnePlus? – and which one is the highest.

2. Include a multiple-choice question in which the answers will be

labelled (a,b,c,d)

Ordinal Scale

An ordinal scale is a measurement scale that allocates values to

variables based on their relative ranking with respect to one another in
each data set.
These scales are generally used to depict non-mathematical ideas such
as frequency, satisfaction, happiness, a degree of pain, etc. It is quite
straightforward to remember the implementation of this scale as
‘Ordinal’ sounds like ‘Order’, which is exactly the purpose of this scale.
For example, a semantic differential scale question such as:

How satisfied are you with our services?

• Very Unsatisfied – 1
• Unsatisfied – 2
• Neutral – 3
• Satisfied – 4
• Very Satisfied – 5
 1. Here, the order of variables is of prime importance and so is the
labelling. Very unsatisfied will always be worse than unsatisfied and
satisfied will be worse than very satisfied
2. This is where ordinal scale is a step above nominal scale – the order
is relevant to the results and so is their naming
3. Analysing results based on the order along with the name becomes a
convenient process for the researcher
4. If they intend to obtain more information than what they would
collect using a nominal scale, they can use the ordinal scale

This scale not only assigns values to the variables but also measures
the rank or order of the variables, such as:

• Grades (grade I, grade II, grade III)

• Satisfaction (1,2,3,4)

• Happiness (1,2,3,4,5)

How satisfied are you with our services?

• 1- Very Unsatisfied
• 2- Unsatisfied
• 3- Neural
• 4- Satisfied
• 5- Very Satisfied

Interval scale
Interval scale is defined as a numerical scale where the order of the
variables is known as well as the difference between these variables.
Variables that have familiar, constant, and computable differences are
classified using the Interval scale. It is easy to remember the primary
role of this scale too, ‘Interval’ indicates ‘distance between two
entities’, which is what Interval scale helps in achieving.
Mean, median, or mode can be used to calculate the central tendency in
this scale. The only drawback of this scale is that there no pre-decided
starting point or a true zero value.
Apart from the temperature scale, time is also a very common example
of an interval scale as the values are already established, constant, and
measurable

Question: Which of the following questions fall under the Interval Scale
category
• What is your family income?
• What is the temperature in your city?

Examples of Interval data are temperature (Farenheit), temperature

(Celcius), pH.

Ratio Scale
Ratio scale is defined as a variable measurement scale that not only
produces the order of variables but also makes the difference between
variables known along with information on the value of true zero. It is
calculated by assuming that the variables have an option for zero, the
difference between the two variables is the same and there is a specific
order between the options.
Mean, mode and median can be calculated using the ratio scale.
Ratio scale provides the most detailed information as researchers can
calculate the central tendency using statistical techniques such as mean,
median, mode.
Ratio scale accommodates the characteristic of three other variable
measurement scales, i.e. labelling the variables, the significance of the
order of variables, and a calculable difference between variables (which
are usually equidistant).
 Because of the existence of true zero value, the ratio scale doesn’t have
negative values.
To decide when to use a ratio scale, the researcher must observe
whether the variables have all the characteristics of an interval scale
along with the presence of the absolute zero value.

The following questions fall under the Ratio Scale category:

1. What is your daughter’s current height?

• Less than 5 feet.
• 5 feet 1 inch – 5 feet 5 inches
• 5 feet 6 inches to – feet
• More than 6 feet

2. What is your weight in kilograms?

• Less than 50 kilograms
• 51- 70 kilograms
• 71- 90 kilograms
• 91-110 kilograms
• More than 110 kilograms

Examples of ratio scale are: weight, length

What is the difference between interval scale and ratio scale?

Interval: the data can be categorized and ranked, and evenly spaced.

Ratio: the data can be categorized, ranked, evenly spaced and has a natural
zero.