This document discusses the different scales of measurement in statistics: nominal, ordinal, interval, and ratio scales. It defines each scale and provides examples. The nominal scale provides categorization without rank ordering. The ordinal scale allows for ranking but not quantifying differences. The interval scale quantifies and compares differences but lacks a true zero point. The ratio scale has all properties of interval plus an absolute zero. The scales determine which statistical tests can be used, with nominal being the weakest and ratio being the strongest.

1. By:
Mrs.Keerthi Samuel,
Associate Professor,
Vijay Marie College of Nursing
SCALES
OF
MEASUREMENT
IN
STATISTICS

2. Statistics deals with
• Collection
• Organization
• Presentation
• Analysis
• Interpretation

3. INTRODUCTION
DEFINITION:
Levels of measurement is a classification that describes the
nature of information within the numbers assigned to the variables.
USES:
 In any study the researcher makes some measurements to map properties ,
characteristics and attributes of an object on some scale.
 For example to know the educational level , income and occupation it is
mapped onto some scale of socio economic status, like low, ,middle and
higher class
 Knowing the level of measurement helps the researcher to decide how to
interpret the data from the variable.
 These scales play an important role in determining the statistical tests that has
to be carried out on the data.
 In ascending order there are 4 scales remembered by an acronym NOIR

4. Nominal scale (‘Name’ in Latin)
• It is the weakest scale of measurement.
• Provides simple, non overlapping categorization of observations based
on characteristics possessed by an object.
• We cannot rank order those categories
• Ex: gender of a patient, numbers for players
• The number assigned is ARBITARY like 1 can be assigned for male and
2 can be assigned for female

5. Nominal Scale
Used as measures of identity.
Examples:
 Religion
 Sex

6. Ordinal scale(‘Order’ in Latin)
• Provides categorization based on the characteristics possessed by
an object.
• Though the characteristics can be ranked in ascending or
descending order of magnitude, it does not tell how much more or
how much less.
• Ex: ask a person how u feel after marriage , he can say unhappy,
happy or very happy. We cannot say how much more or less the
person is feeling.
• So here it is the order of the values that is important but not the
differences between each one which is unknown.

7. Ordinal Scales
Used in measurement
wherein numbers reflect
the rank order of the
individual or objects

8. INTERVAL SCALE
• It allows not only the rank order but also to quantify and compare the
sizes of differences between them.
• Ex: measurement of temperature in F or C . The mercury in the
thermometer indicates temperature .how many units of mercury
corresponds to the temperature measured.
• The number Zero is present here but it remains arbitrary because it is
not a true zero.
• The zero point does not indicate the absence of temperature .
• One can perform addition or substraction but not multiplication and
division on the data measured on interval scale.

9. Interval Scale
 Provides numbers that reflect differences
among items.
 Measurement units are equal.
 Has no reference to zero
 AS has meaning

10. Ratio scale
• It is the ultimate , the highest level of measurement and most
important
• It has an ABSOLUTE ZERO
• It tells the exact value between the units.
• With a ratio scale we can compare both differences in scores
• Ex: the difference between 10 and 20 kgs is the same AS that of
20 and 30 kgs.
• Similarly money is measured on a ratio scale. Money has a true
zero, like if a person has zero money it indicates the absence of
money.
• It has all the mathematical properties of the number system.

11. Ratio Scale
 It has absolute zero.

12. OVERVIEW
Ratio-
absolute
Zero
Interval –
Distance Is
Meaningful
Ordinal-
Attribute
Can Be
Ordered
Nominal –
Attributes
Are Only
Named ,
Weakest

13. Table showing the criteria met by various
scales…..
SCALE INDICATES
DIFFERENCE
INDICATES
DIRECTION
OF
DIFFERENCE
INDICATES
AMOUNT OF
DIFFERENCE
ABSOLUTE
ZERO
NOMINAL YES - - -
ORDINAL YES YES - -
INTERVAL YES YES YES -
RATIO YES YES YES YES

14. SUMMARY OF PROPERTIES OF
FOUR LEVELS OF MEASURMENT
DESCRIPTION CAHRACTERIS
TICS
EXAMPLE PERMISSABLE STATS GRAPHS
NOMINAL Organized into
categories but not
in order
Contains no
magnitude,
just names
Eye
color(black
/brown),ge
nder(male
/female)
DS: Freq & %,Mode
IS:Chisquare
Bar and
pie
ORDINAL Organized and
arranged in rank
order, however
difference
between data
values cannot be
organized
Reflects only
magnitude,
doesn’t have
intervals or an
absolute zero.
Has a rank
order.
Levels of
depression
, stages of
cancer
DS: Freq & %,Mode,
Median
IS: Rank order
correlation
Bar and
pie

15. DESCRIPTION CAHRACTERIS
TICS
EXAMPLE PERMISSABLE STATS GRAPHS
INTERVAL Categorized and
ranked with
meaningful
intervals between
measurements.
No true zero
point.
Possess
magnitude,
fixed size of
intrvals
between data
points , but no
absolute zero.
Temperatu
re on F or
C , IQ
scores.
DS: Freq & %,Mean,
Mode,Median,SD,Ske
wness and kurtosis.
IS:ANOVA,t test
Bar and
pie,
histogra
m
RATIO Categorized and
ranked with
meaningful
intervals between
measurements.
And has an
inherent zero
point.
Reflects only
magnitude,
have intervals
has an
absolute zero.
Has a rank
order.
Height ,
weight,
currency
DS:
Mean,SD,skewness,
kurtosis.
IS: Coefficient of
variation and t test
Histogra
m
SUMMARY OF PROPERTIES OF FOUR LEVELS
OF MEASURMENT