Assignment 3: Scales of Measurement
For each measure or attribute in the following list, create a realistic example (for example, weight = 150 pounds) and indicate the scale of measurement (nominal, ordinal, interval, or ratio). Please note the example given is usually called a value, and the term “value” is used in a generic sense; the answer does not have to be a number; some of the answers might be words:
Attribute Example Scale
The amount of time it takes you to run a mile
Gender
The number of times a dog barks before eating
The order in which first-grade kids learn to read
The number of cell phone numbers in an address book
After deciding on the scale of measurement for the above attributes, change all the examples or values so they will fit into a different scale of measurement. For example, weight can be made into an ordinal scale of measurement by calling it weight group and a realistic measurement would be thin. Then, state what scale this new measurement would fit into. The most challenging one is gender. Can this scale be altered? Why?
Last, but not the least, explain why many scientists believe most data labeled as ratio are really interval data.
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Created a realistic value and indicated the scale of measurement for the given attributes.
Changed the current scale of measurement to fit into a different scale of measurement and explained what scale the new measurement would fit into.
Analyzed and justified whether the scale for measuring gender can be altered.
Analyzed and explained why many scientists believe most data labeled as ratio data are really interval data.
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Let’s start by reviewing each of the four scales of measurement.
Nominal data are data that we assign numbers to, but those numbers are meaningful only for coding. They don’t indicate anything about the relative performance or value of the scores. For example, if you had males and females in your study, you might code males as 1 and females as 2. Note that these codes are arbitrarily assigned; you could just as well code females as 1 and males as 2. The numbers are used only to identify groups.
Ordinal data are data that are ranked, so we know that one score is higher than another, but we don’t know that the intervals between the scores are equivalent. For example, breast cancer can be classified into 4 stages in terms of its severity. We know that Stage 4 is worse than Stage 3, and Stage 3 is worse than Stage 2, but we wouldn’t say that there are twice as many cancer cells in Stage 4 as in Stage 2, or that the increase in the number of cancer cells is the same for each stage transition. With this scale, we can talk meaningfully about relative position (rank) only.
Interval data are data that follow a number scale, so we can talk meaningfully about the intervals between scores, but …
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