Statisticians sometimes refer to four levels of measurement for data: nominal, ordinal, interval, and ratio. This typology was proposed over 60 years ago by psychologist S. S. Stevens. The allowable statistical tests depend on the measurement level. The criteria are summarized in Figure 2.3.
Nominal Measurement
Nominal measurement is the weakest level of measurement and the easiest to recognize. Nominal data (from Latin nomen, meaning “name”) merely identify a category. “ Nominal” data are the same as “qualitative,” “categorical,” or “classifi cation” data. To be sure that the categories are collectively exhaustive, it is common to use Other as the last item on the list.
For example, the following survey questions yield nominal data:
Did you fi le an insurance claim last month?
1. Yes 2. No
Which cell phone service provider do you use?
1. AT&T 2. Sprint-Nextel 3. T-Mobile 4. Verizon 5. Other
We usually code nominal data numerically. However, the codes are arbitrary placeholders with no numerical meaning, so it is improper to perform mathematical analysis on them.
This may seem obvious, yet people have been known to do it. Once the data are in the computer, it’s easy to forget that the “numbers” are only categories. With nominal data, the only permissible mathematical operations are counting (e.g., frequencies) and a few simple statistics such as the mode.
Ordinal Measurement
Ordinal data codes connote a ranking of data values. For example:
What size automobile do you usually drive?
1. Full-size 2. Compact 3. Subcompact
How often do you use Microsoft Access?
1. Frequently 2. Sometimes 3. Rarely 4. Never
Thus, a 2 (Compact) implies a larger car than a 3 (Subcompact). Like nominal data, these ordinal numerical codes lack the properties that are required to compute many statistics, such as the average. Specifi cally, there is no clear meaning to the distance between 1 and 2, or between 2 and 3, or between 3 and 4 (what would be the distance between “Rarely” and “Never”?). Other examples of ordinal scales can be found in a recruiter’s rating of job candidates(outstanding, good, adequate, weak, unsatisfactory), S&P credit ratings (AAA, AA1, AA, AA2, A1, A, A2, B1, B, B2, etc.) or job titles (president, group vice president, plant manager, department head, clerk). Ordinal data can be treated as nominal, but not vice versa. Ordinal data are especially common in social sciences, marketing, and human resources research. There are many useful statistical tests for ordinal data.
Ratio Measurement
Ratio measurement is the strongest level of measurement. Ratio data have all the properties of the other three data types, but in addition possess a meaningful zero that represents the absence of the quantity being measured. Because of the zero point, ratios of data values are meaningful (e.g., $20 million in profi t is twice as much as $10 million). Balance sheet data, income statement data, fi nancial ratios, physical counts, scientifi c measurements, and most engineering measurements are ratio data because zero has meaning (e.g., a company with zero sales sold nothing). Having a zero point does not restrict us to positive data. For example, profi t is a ratio variable (e.g., $4 million is twice $2 million), yet fi rms can have negative profi t (i.e., a loss).
Zero does not have to be observable in the data. Newborn babies, for example, cannot have zero weight, yet baby weight clearly is ratio data (i.e., an 8-pound baby is 33 percent heavier than a 6-pound baby). What matters is that the zero is an absolute reference point. The Kelvin temperature scale is a ratio measurement because its absolute zero represents the absence of molecular vibration, while zero on the Celsius scale is merely a convenience (note that 30°C is not “twice as much temperature” as 15°C).
Lack of a true zero is often the quickest test to defrock variables masquerading as ratio data. For example, a Likert scale (12, 11, 0, 21, 22) is not ratio data despite the presence of zero because the zero (neutral) point does not connote the absence of anything. As an acid test, askyourself whether 2 (strongly agree) is twice as much “agreement” as 1 (slightly agree). Some classifi cations are debatable. For example, college GPA has a zero, but does it represent the absence of learning? Does 4.00 represent “twice as much” learning as 2.00? Is there an underlying reality ranging from 0 to 4 that we are measuring? Most people seem to think so, although the conservative procedure would be to limit ourselves to statistical tests that assume only ordinal data. Although beginning statistics textbooks usually emphasize interval or ratio data, there are textbooks that emphasize other kinds of data, notably in behavioral research (e.g., p sychology, sociology, marketing, human resources).
We can recode ratio measurements downward into ordinal or nominal measurements (but not conversely). For example, doctors may classify systolic blood pressure as “normal” (under 130), “elevated” (130 to 140), or “high” (140 or over). The recoded data are ordinal, since the ranking is preserved. Intervals may be unequal. For example, U.S. air traffi c controllers classify planes as “small” (under 41,000 pounds), “large” (41,001 to 254,999 pounds), and “heavy” (255,000 pounds or more). Such recoding is done to simplify the data when the exact data magnitude is of little interest; however, we discard information if we map stronger measurements into weaker ones.
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