Statistics and probability lesson 4

Lesson 4 – Levels of Measurement
Ms. Maria Christita Polinag
Miriam College Adult Education

1. Plan or design the collection of data
to verify the validity of the statement in
a way that maximizes information
content and minimizes bias;
2. Collect the data as required in the
plan;
3. Verify the quality of the data after it
was collected;

4. Summarize the information
extracted from the data; and
5. Examine the summary statistics
so that insight and meaningful
information can be produced to
support your decision whether to
believe or not the given statement.

 Students who eat a healthy
breakfast will do best on a quiz,
students who eat an unhealthy
breakfast will get an average
performance, and students who
do not eat anything for breakfast
will do the worst on a quiz

1. Nominal Level of measurement
arises when we have variables that are
categorical and nonnumeric or where
the numbers have no sense of
ordering
e.g. gender, marital status, religious
affiliation and numbers on the
uniforms of basketball players

2. Ordinal level also deals with
categorical variables like the nominal
level, but in this level ordering is
important, that is the values of the
variable could be ranked
 e.g. socio economic status (A to E,
where A is wealthy, E is poor), difficulty
of questions in an exam (easy, medium
difficult), rank in a contest (first place,
second place, etc.), and perceptions in
Likert scales.

Statistics and probability lesson 4

 While there is a sense or ordering, there is
no zero point in an ordinal scale
 There is no way to find out how much
“distance” there is between one category
and another
In a scale from 1 to 10, the difference
between 7 and 8 may not be the same
difference between 1 and 2

3. Interval level tells us that one unit
differs by a certain amount of degree
from another unit
 e.g. Celsius scale, Intelligence
Quotient (IQ) of a person

 Interval level allows addition and
subtraction
operations, but it does not possess an
absolute zero.
 Zero is arbitrary as it does not mean
the value does not exist
 Zero only represents an additional
measurement point

4. Ratio level also tells us that one
unit has so many times as much of
the property as does another unit
 possesses a meaningful (unique and
non-arbitrary) absolute,
 fixed zero point and allows all
arithmetic operations
 e.g. mass, heights, weights, energy
and electric charge

Level Property Basic Empirical
Operation
Nominal No order, distance,
or origin
Determination of
equivalence
Ordinal Has order but no
distance or unique
origin
Determination of
greater or lesser
values
Interval Both with order and
distance but no
unique origin
Determination of
equality of intervals
or difference
Ratio Has order, distance
and unique origin
Determination of
equality of ratios or
means

1. Objective - uses any or combination of
the five senses (sense of sight, touch, hearing,
taste and smell) to measure the variable
2. Subjective - obtains data by getting
responses through a questionnaire
Primary data - obtained the data directly from
the source

3. Use of existing records – data collected by
other entities for certain purposes these data
are Secondary data
e.g.
data from the Philippine Statistics Authority,
administrative records, news articles, internet

 we must be confident of the quality of the
data we are using by knowing how the data
were gathered
 we must remember to request permission
and acknowledge the source of the data when
using data gathered by other agency or
people

a. The website of Philippine Airlines provides a
questionnaire instrument that can be answered
electronically.
b. The latest series of the Consumer Price
Index (CPI) generated by the Philippine
Statistics Authority was downloaded from PSA
website.

c. A reporter recorded the number of minutes
to travel from one end to another of the Metro
Manila Rail Transit (MRT) during peak and off-
peak hours.
d. Students getting the height of the plants
using a meter stick.
e. PSA enumerator conducting the Labor Force
Survey goes around the country to interview
household head on employment-related
variables.

a. The website of Philippine Airlines provides a
questionnaire instrument that can be answered
electronically. (subjective method, primary
data)
b. The latest series of the Consumer Price
Index (CPI) generated by the Philippine
Statistics Authority was downloaded from PSA
website. (use of existing record,secondary
data)

c. A reporter recorded the number of minutes
to travel from one end to another of the Metro
Manila Rail Transit (MRT) during peak and off-
peak hours. (objective method, primary data)
d. Students getting the height of the plants
using a meter stick. (objective method, primary
data)
e. PSA enumerator conducting the Labor Force
Survey goes around the country to interview
household head on employment-related
variables. (subjective method, primary data)

 TEACHING GUIDE FOR SENIOR HIGH SCHOOL - Statistics
and Probability by CHED in collaboration with the
Philippine Normal University

Statistics and probability lesson 4

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