1. There are four levels of measurement for variables: nominal, ordinal, interval, and ratio. 2. Nominal scales classify variables into categories while ordinal scales allow variables to be rank-ordered. 3. Interval and ratio scales indicate equal distances between variables and have a true zero point, respectively. 4. Different statistics can be applied depending on the level of measurement, with more advanced statistics used for higher levels.

2. Measurement
Scales
Presented by: Farah Ahmad

3. What are Variables and Measurements?
 Variables: Characteristics that cantake on different values for
different members ofa group.Forexample height
 Measurements:Assignment of numbers to Characteristics
(variables) of objects, persons orevents according to a set of rules.

4. Introduction to Levels of Measurement
Refers to the way that a variable is measured.
In statistics and quantitative research methodology, levels of measurement
are developed by the psychologist Stanley Smith Stevens in 1946.

5. LEVELS OF MEASUREMENT
• Stevens (1946) classified variables into four levels.
These are referred to as levels of measurement, or
levels of data.
1. Nominal
2. Ordinal
3. Interval
4. Ratio

6. Qualitative
Data
Nominal Ordinal
Quantitative
Data
Interval Ratio

7. NOMINAL SCALE
 The nominal scales are used to classify/categorize objects,
individuals, groups or events.
 Nominal scales are mere codes assigned to objects as labels,
they are not measurements.
 A nominal scale represents lower level of measurement.
 Such scales classifies persons or objects in to two or more
categories.
Examples:includeGender,Nationality,Religion, Language,Biological species,ABO
bloodgroupsystemandEyecolor: blue,brown,green, etc.

8. WHAT STATISTICS CAN BE APPLIED?
Frequency
distribution
and mode
Chi-
square

9. ORDINAL SCALE
 At this level, variables can be ranked-ordered.
 Ordinal scale can determine whether an object has more or less of a
characteristic than some other object. The exact measurement is not
available like student A is taller than student B but their actual heights
are not available.
 Designates an ordering: greater than, less than.
 Does not assume that the intervals between numbers are equal.

10. Examples:
 Position (1st, 2nd, 3rd etc.)
 Rating (poor, good, excellent)
 Socio-economic status (lower class, middle class, upper class)
 Grades (A, B, C, D, F) etc.

11. WHAT STATISTICS CAN BE APPLIED?
Frequency
Distribution
Median, Mode
and Percentiles

12. INTERVAL SCALE
 A measurement scale possessing a constant interval size (distance)
but not a true zero point, is called an interval scale.
 Designates an equal-interval ordering.
 Interval scales indicate order and also the distance in the order
 Zero point on the interval scale is arbitrary zero, it does not mean the
complete absence of anything.

13. Examples:
 Celsius temperature is an interval variable. It is
meaningful to say that 40 degrees Celsius is 10
degrees hotter than 50 degrees Celsius, and that 60
degrees Celsius is the same amount hotter (10
degrees) than 70 degrees Celsius. Notice, however,
that 0 degrees Celsius does not have a natural
meaning. That is, 0 degrees Celsius does not mean
the absence of heat!
 Temperature in Fahrenheit
 Common IQ tests are assumed to use an interval scale.
 pH etc.

14. WHAT STATISTICS CAN BE
APPLIED?
 Frequency Distribution
 Median And Percentiles
 Mean
 Standard Deviation
 Correlation, Regression
 Analysis Of Variance
 T-test
 F-test
 Add, Subtract

15.  It is a special kind of scale where the scale of measurement has a
true zero point as its origin.
 This is the highest level of measurement and has the properties of
other three levels.
 This scale has a unique or fixed beginning or true zero point.
(complete absence of the phenomenon being measured).
Ratio Scale

16. Examples:
 Weight (in grams) is also a ratio variable. Again, the zero value is
meaningful, zero grams means the absence of weight.
 heart beats per minute has a very natural zero point. Zero means no
heart beats.
 Temperature in Kelvin (zero is the absence of heat, can’t get colder)
 Height
 Age
 Time
 Distance
 Length
 Salary
 Volume

17. WHAT STATISTIC CAN BE APPLIED?
 Frequency Distribution
 Median And Percentiles
 Mean
 Standard Deviation
 Correlation, Regression
 Analysis Of Variance
 Ratio, Or Coefficient Of Variation
 F-test, T-test
 Add, subtract
 Multiply, Division etc.

19. THANK YOU

20. Reference:
Introduction to statistical theory by Prof. Sher Muhammad
Chaudhry and Prof. Dr.Shahid Kamal.