Level of measurement refers to the degree to which variables can be compared and mathematically manipulated. There are four levels of measurement: nominal, ordinal, interval, and ratio. Nominal measurement involves categorizing variables without mathematical relationships between categories. Ordinal measurement allows ranking but not precise measurement of distances between ranks. Interval measurement assigns real numbers with equal units of measurement and mathematical properties. Ratio measurement has all interval properties plus an absolute zero point.

1. Level of Measurement
Debra Wallace

2. Level of Measurement
Level of measurement is the extent or degree to
which the values of variables can be compared
and mathematically manipulated.

3. Level of Measurement
The level of measurement depends on the type of
information the measurement contains.
The relationship between the variables and the
numbers is key.

4. Levels of Measurement
Ratio
Interval
Ordinal
NominalNominal
Ordinal
Interval
Ratio

5. Nominal Level
Nachmias-Nachmias (2000)
The nominal level of measurement refers to the
most basic level of measurement.
At the nominal level, numbers or symbols are used
to classify objects or events into categories that
are names or classes of other characteristics.
There is no mathematical relationship between
categories. Each category has an equivalent
relationship.

6. Nominal Level
or

7. Ordinal Level
Nachmias-Nachmias (2000)
Ordinal level measurement allows for a complete
ranking of all observations, though the distance
between observations cannot be precisely
measured.
Rank values indicate rank but do not indicate that
the intervals or size of the difference between the
ranks are equal, nor do they indicate absolute
quantities.

8. Ordinal Level
Nachmias-Nachmias (2000)
Has three important logical properties:
1. Irreflexive
For any value of a, a > a
For any a, it is not true that a > a
2. Asymmetry
If a > b, then b > a
3. Transitivity
If a > b and b > c, then a > c

9. Ordinal Level

10. Ordinal Level

11. Ordinal Level

12. Ordinal Level
Nachmias-Nachmias (2000)
● Surveys use ordinal
scales.
● Ex: Political efficacy
question: Do you
agree with the
following statement?
“People like me
have a lot of
influence on gov't
decisions.”

13. Interval Level
Nachmias-Nachmias (2000)
Interval level measurements are characterized by a
common and constant, fixed and equal unit of
measurement that assigns a real number to all the
objects in the ordered set.

14. Interval Level
Nachmias-Nachmias (2000)
Interval level measurements are isomorphic,
meaning there is similarity or identity in structure
between the properties of a variable and the
properties of the instrument used to measure it.

15. Properties of interval measures
Nachmias-Nachmias (2000)
1. Uniqueness: If a and b stand for real numbers,
then a + b and a * b represent only one real
number.
2. Symmetry: If a = b, then b = a
3. Commutation: If a and b denote real numbers,
then a + b = b + a.

16. Properties of interval measures
Nachmias-Nachmias (2000)
4. Substitution: If a = b and a + c = d, then b + c =
d; and if a = b and ac = d, then bc = d
5. Association: If a, b and c stand for real numbers,
then (a + b) + c = a + (b + c), and (ab)c = a(bc)
Examples: Income, SAT scores, years

17. Ratio Level
Nachmias-Nachmias (2000)
The ratio level of measurement has the same
properties as the interval level with one exception:
the absolute zero point.
In other words, we apply the arithmetic operations
and numbers to the total amount measured from
the absolute zero point, not some arbitrary point.
Examples: Weight, age, unemployment rate, % vote