This document discusses the four levels of measurement: nominal, ordinal, interval, and ratio. Each level provides more information than the previous. Nominal measurement simply categorizes objects into groups with no ordering. Ordinal adds rank ordering but distances between ranks are meaningless. Interval maintains equal distances between ranks and allows for subtraction and addition, but not ratios. Ratio is the highest level with all interval properties plus a true zero point, meaning ratios are meaningful. Appropriate statistics depend on the level of measurement.

1. Levels of Measurement
Shivani Jha

2. Measurement is assigning numbers to objects or events according to rules.
The level of measurement refers to the relationship among the values that are assigned
to the attributes for a variable.
There are typically four levels of measurement.
1
Nominal 2 Ordinal
3
Interval
4
Ratio
Levels of Measurement

3.  In nominal measurement the numerical values just “name” the attribute uniquely.
 No ordering of the cases is implied.
 In nominal level of measurement, numbers are assigned to objects or events which can be placed into
mutually exclusive and exhaustive categories.
 The term nominal means ‘to name’.
 Names are given to the categories, with no assumption about relationships between them.
 Nominal scales, also called categorical scales, measure categorical data.
For example- people may be classified as male-female, farmer- non-farmer etc. and numbers may be
assigned to them, say 1 for male and 2 for female. Number 1 simply indicates category.
Nominal

4.  The appropriate measure of central tendency of a nominal scale is mode, and neither the mean
nor the median can be defined.
 Permissible statistical operations- Frequency, percentage, mode, chi-square test etc.

5.  In ordinal measurement the attributes can be rank-ordered.
 Here, distances between attributes do not have any meaning.
 Ordinal scales are those that measure rank-ordered data, such as the ranking of students in a class as first, second,
third, and so forth, based on their grade point average or test scores.
 The actual or relative values of attributes or difference in attribute values cannot be assessed.
 In ordinal level of measurement, numbers are assigned to objects or events which can be placed
into mutually exclusive categories and be ordered into a greater or less than scale.
 At the ordinal level of measurement, numbers are assigned to objects or events not only to categorize
them but also to indicate a greater than or less than relationship.
 The scale has no absolute zero point and there are unequal distances between scale values.
 Numbers assigned at the ordinal level provides more information than at the nominal level because
they also establish an ordering of the objects or events.
Ordinal

6. For example, Various television programs may be categorized according to popularity.
Classification of upper, middle and lower classes in the socio- economic status.
Categories may be made on the basis of land holding.
The central tendency measure of an ordinal scale can be its median or mode, and means are uninterpretable.
Hence, statistical analyses may involve percentiles and non-parametric analysis, but more sophisticated
techniques such as correlation, regression, and analysis of variance, are not appropriate.
The most suitable statistical tests for ordinal data (e.g., Likert scale) are non-parametric tests, such as Mann-
Whitney U test (one variable, no assumption on distribution), Wilcoxon signed rank sum test (two variables,
normal distribution), Kruskal Wallis test (two or more groups, no assumption on distribution).
Statistical operations- median, percentile, correlation coefficient based on rankings etc.

7.  In interval level of measurement, numbers are assigned to objects or events which can be categorized,
ordered and assumed to have an equal distance between scale values.
 The zero point is set arbitrarily.
 Addition and subtraction are permissible operations but because of the arbitrary zero, multiplication
and division are not permissible.
 Example- measuring the temperature with thermometer, measuring the time from selecting a starting
moment, measuring the altitude from mean sea level etc.
 In interval measurement the distance between attributes does have meaning.
 For example, when we measure temperature (in Fahrenheit), the distance from 30-40 is same as distance
from 70-80. The interval between values is interpretable.
 But in interval measurement ratios don’t make any sense - 80 degrees is not twice as hot as 40 degrees
(although the attribute value is twice as large).
Interval

8.  Interval scale allows us to examine “how much more” is one attribute when compared to another,
which is not possible with nominal or ordinal scales.
 Permissible statistical operations are mean, range, standard deviation, Pearson product moment correlation,
T test, F- test etc.
 Permissible statistical analyses include all of those allowed for nominal and ordinal scales, plus
correlation, regression, analysis of variance, and so on.

9.  In ratio level of measurement, numbers are assigned to objects or events which can be categorized, ordered,
assumed to have equals intervals between scale points and have a real zero point.
 It is highest level of measurement and has all the properties of nominal, ordinal and interval plus an
absolute or true zero point.
 These scales are called “ratio” scales because the ratios of two points on these
measures are meaningful and interpretable.
 The salient feature of the ratio scale is that the ratio of any two numbers is independent of the unit of
measurement and therefore, it can meaningfully be equated.
 Ratio scale represents the actual amounts of variables.
Ratio

10.  Example- Adoption quotient
 Measures of physical dimensions such as height, weight, distance etc. are examples.
 Generally all statistical techniques, multiplication and division can be used with the scale.
 Permissible statistical operations- central tendency and coefficient of variation.

11. Scale Central Tendency Statistics
Nominal Mode Chi-Square
Ordinal Median Percentile, Non
parametric statistics
Interval Arithmetic mean, Range,
Standard deviation
Correlation, regression,
analysis of variance
Ratio Geometric mean, Harmonic
mean
Coefficient of variation

12.  Social Science Research- Principles, methods, and practices by Anol Bhattacherjee
 Foundations of behavioral research- Kerlinger F. N.
 Extension in Research- John. W. Best
References