This document discusses the four levels of measurement scales: nominal, ordinal, interval, and ratio. It provides examples and key statistical analyses for each scale type. Nominal scales involve simple categorization, ordinal scales add rank/order, interval scales allow for meaningful distances between values, and ratio scales have a true zero point. Common variables like gender, education level, and temperature are used to illustrate the different scales.

1. Dr. Shanti Tejwani
Asst. Prof. M.B. Khalsa Institute of Education, Indore
shanti_tejwani@yahoo.com

2. An attributes/ characteristics of thing ,objects or
events which varies (which can different Values) is
known as Variable.
Attandence of Students
Sex
Religion
Books in library
Mode of journey
Time duration
Aggression
Anger
Age

3. Continuous
Variables Dichotomy
Discontinuous
Polytomy

4. Ratio
Interval
Ordinal
Nominal

5. Nominal Scale
2
4
1
3

6.  Categorization of data
Classified into category
Numbers forming a nominal scale are no more
than labels used solely to identify different
categories of responses
Example:
RELIGION
 Hindu –1
 Christian--2
 Muslim---3
 Buddhism----4

7. The mode is the most frequent category –
only statistics applicable to nominal variable
Non Parametric Statistics ---- Chi- Square

8. Third First
Second
place place
place

9. An ordinal scale is more powerful than a nominal
scale in that the numbers possess the property of rank
order
Classification + Order
Examples : To categories people according to level of
Education
Punctuality
Home work
Cleanliness

10.  Mode
 Median
 Percentile
 Rank Difference Correlation (ρ)

11. 5, 8, 10, 11
3, 6, 8, 9

12. An interval scale has all the properties of an ordinal scale
and the differences between the scale values can be
meaningfully interpreted
EXAMPLE
Achievement of the students
Creativity of Students
All Psychological Variable

13. 9 | 13

14.  Mode
 Median
 Arithmetic Mean
 Rank Difference correlation
 Product Moment Correlation
 Variance

15. Kilogram
Gram

16.  Ratio scales possess all the properties of an
interval scale and the ratios of numbers on
these scales have meaningful interpretations
Examples
Length of the Rod
Weight of School Bag
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9 | 16

17.  Mode
 Median
 Arithmetic Mean
 Rank Difference correlation
 Product Moment Correlation
 Variance

19. Type of Data Numerical Descriptive
Examples
Scale Characteristics Operation Statistics
Nominal Classification but no Counting Frequency in each Gender (1=Male,
order, distance, or category 2=Female)
origin Percent in each
category
Mode
Ordinal Classification and Rank ordering Median Academic status
order but no Range (1=Professor
distance or unique Percentile ranking 2= Associate
origin Professor
3= Assistant
Professor)

20. Type of Data Numerical Descriptive
Examples
Scale Characteristics Operation Statistics
Interval Classification, order, Arithmetic Mean Temperature in
and distance but no operations that Standard deviation degrees
unique origin preserve order and Variance
magnitude
Ratio Classification, order, Arithmetic Geometric mean Age in years
distance and unique operations on Coefficient of Income
origin actual quantities variation

21. Four levels of Measurements
 Nominal
◦ Measures categories
 Ordinal
◦ Categories + rank and order
 Interval
◦ Equal distance between any two consecutive
measures
 Ratio
◦ Intervals + meaningful zeros