Scales of Measurement

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Measurement is the process by which numbers are assigned to variables of individual population units. In statistics, when we speak of scales of measurement we are often referring to classification of data. Possibly, this is where your confusion is stemming from in that scales of measurement are often referred to types of data but yet considered scales of measurement as well. Keep this in mind. We generally classify data using one of four types of measurement scales: nominal, ordinal, interval, or ratio.

NOMINAL SCALE (categorical data)

Nominal data are measurements that simply classify the units of the sample (or population) into categories.

Often in terms of labels rather than numbers.

The following are examples of nominal data:

1.The political party affiliation of each individual in a sample of 50 registered voters.

2.The gender of each individual in a sample of seven applicants for a computer-programming job

3.The brand toothpaste preferred by each individual in a sample of 100 consumers.

Note that in each case-political party, gender, and brand--the measurement is no more than a categorization of each sample unit. Nominal data are often reported as nonnumerical labels, such as Democrat, women, and Crest. Even if the labels are converted to numbers, as they often are for ease of computer entry and analysis, the numerical values are simply codes. They cannot be meaningfully added, subtracted, multiplied, or divided. For example, we might code Democrat = 1, Republican = 2, and other = 3. They are simply numerical codes for each of the categories into which units mat fall and have no utility beyond that.

ORDINAL SCALE

Ordinal data are measurements that enable the units of the sample (or population) to be ordered with respect to the variable of interest. Ordinal data are measurements that indicate the relative amount of a property possessed by the units. The following are examples of ordinal data:

1. The size of car rented by each individual in a sample of 30 business travelers: compact, subcompact, midsize, or full-size.
2. A taste-tester's ranking of four brands of barbecue sauce for a panel of 10 tasters
3. A supervisor's annual performance rating of 1 (lowest) to 10 (highest) for each of 20 employees.

Note that in each case--size, flavor preference, and ...