Exercise: Identifying scales of measurement
Each of the following scenarios involves measuring one or more variables. Decide whether the various
measurements reflect nominal, ordinal, interval, or ratio scales, and justify your choices. Be careful, as
the answers are not always as obvious as they might initially appear.
1. An environmental scientist collects water samples from screams and rivers near large
industrial plants and saves exactly 1 liter of water from each sample. Then, back at the lab,
the researcher determines the amounts of certain health-jeopardizing bacteria in each sample.
What measurement scale does the measurement of bacteria content reflect?
2. A market researcher is studying the relationship between (a) a country's average annual
relative humidity levels and (b) the number of raincoats sold in the country during the year.
What scales underlie the two variables in this study?
3. A sports journalist in Spain wants to determine whether a football club's fan club membership
correlates to the frequency with which the club has won in the Spanish football league during
the past five years. The researcher can easily obtain information about fan club membership
and wins from the club's records. To simplify data collection, the researcher uses the following
coding scheme for the fan club membership: 1 = FC Barcelona, 2 = Real Madrid, and 3 =
Atletico de Madrid. What measurement scale(s) underlie (a) fan club membership and (b)
frequency of wins?
4. A new audio system was installed in a theatre that has a seating capacity of 500 people. The
seating area has been divided int three distinct areas: platinum, gold, and silver. At the end of
every show m one week the audience was asked to fill out a questionnaire to determine the
effectiveness of the new audio system. What measurement scale does the researcher’s coding
scheme for the seating are represent?
5. An advertiser is studying the impact of a chocolate commercial on different age groups. He
puts the age groups in four categories: group 1 includes 3-to 12-year-olds, group 2 includes
teenagers aged 13 to 19, group 3 includes adults aged 20 to 49, and group 5 includes people
aged 50 and above, what kind of scale is the classification of age groups in this study?
6. A car manufacturer is studying car patterns over five years of four different types of car that
vary in size and available utilities: hatchbacks (small cars with no trunk space), midsized
sedans (cars with limited trunk space and more utilities compared to hatchbacks), sedans
(proper trunk space and all utilities), and luxury sedans (big trunk space and luxurious
interiors). Based on size and available utilities, which measurement scale does the type of car
reflect?
7. A child psychologist is developing an instrument designed to measure the social etiquette of
small children. The instrument includes 25 statements, for example, “wishes elders when they
meet them”, “courteous to their sibling”, and “says please when asking for something or thank
you when someone has helped”. Parents must rate each of these statements on a 5-point scale
as follows:

0 never
1 rarely
2 sometimes
3 often
4 always

Parents who answer ‘never’ to each of the 25 questions get the lowest possible score of 0 on
the instrument. Parents who answer ‘always’ to each of the 25 questions get the highest
possible score of 100 on the instrument. Thus, scores on the instrument range from 0 to 100.
What kind of scale do the scores represent?

Question

Exercise: Identifying scales of measurement
Each of the following scenarios involves measuring one or more variables. Decide whether the various
measurements reflect nominal, ordinal, interval, or ratio scales, and justify your choices. Be careful, as
the answers are not always as obvious as they might initially appear.
1. An environmental scientist collects water samples from screams and rivers near large
industrial plants and saves exactly 1 liter of water from each sample. Then, back at the lab,
the researcher determines the amounts of certain health-jeopardizing bacteria in each sample.
What measurement scale does the measurement of bacteria content reflect?
2. A market researcher is studying the relationship between (a) a country's average annual
relative humidity levels and (b) the number of raincoats sold in the country during the year.
What scales underlie the two variables in this study?
3. A sports journalist in Spain wants to determine whether a football club's fan club membership
correlates to the frequency with which the club has won in the Spanish football league during
the past five years. The researcher can easily obtain information about fan club membership
and wins from the club's records. To simplify data collection, the researcher uses the following
coding scheme for the fan club membership: 1 = FC Barcelona, 2 = Real Madrid, and 3 =
Atletico de Madrid. What measurement scale(s) underlie (a) fan club membership and (b)
frequency of wins?
4. A new audio system was installed in a theatre that has a seating capacity of 500 people. The
seating area has been divided int three distinct areas: platinum, gold, and silver. At the end of
every show m one week the audience was asked to fill out a questionnaire to determine the
effectiveness of the new audio system. What measurement scale does the researcher’s coding
scheme for the seating are represent?
5. An advertiser is studying the impact of a chocolate commercial on different age groups. He
puts the age groups in four categories: group 1 includes 3-to 12-year-olds, group 2 includes
teenagers aged 13 to 19, group 3 includes adults aged 20 to 49, and group 5 includes people
aged 50 and above, what kind of scale is the classification of age groups in this study?
6. A car manufacturer is studying car patterns over five years of four different types of car that
vary in size and available utilities: hatchbacks (small cars with no trunk space), midsized
sedans (cars with limited trunk space and more utilities compared to hatchbacks), sedans
(proper trunk space and all utilities), and luxury sedans (big trunk space and luxurious
interiors). Based on size and available utilities, which measurement scale does the type of car
reflect?
7. A child psychologist is developing an instrument designed to measure the social etiquette of
small children. The instrument includes 25 statements, for example, “wishes elders when they
meet them”, “courteous to their sibling”, and “says please when asking for something or thank
you when someone has helped”. Parents must rate each of these statements on a 5-point scale
as follows:

0 never
1 rarely
2 sometimes
3 often
4 always

Parents who answer ‘never’ to each of the 25 questions get the lowest possible score of 0 on
the instrument. Parents who answer ‘always’ to each of the 25 questions get the highest
possible score of 100 on the instrument. Thus, scores on the instrument range from 0 to 100.
What kind of scale do the scores represent?

Accepted Answer

Hello! As you have posted 2 different questions, we are answering the first question. In case you…