Measurement scale, or scale of measurement, is a construct developed by S. S. Stevens in an attempt to put psychological measurement on the same firm footing as measurement in the physical sciences. His measurement scales are outlined in the following table.

scale characteristics examples operations allowed
nominal places observations into categories
• gender
• political party affiliation
• gun ownership (yes/no)
• seatbelt usage (yes/no)
• equal to
• not equal to
ordinal ranks; places observations into an ordered ranking (ideally without ties)
• class rank (senior, junior, etc.)
• class rank (1st in class, 2nd in class, etc.)
• letter grade
• Likert scale responses
• seatbelt usage (never/sometimes/always)
• equal to
• not equal to
• greater than
• less than
interval equal units of measurement on all parts of the scale but no true zero
• temperature in degrees centigrade or fahrenheit
• most scores given by psychological tests (e.g., IQ scores), or at least we would like to assume so
• dates (time) as measured by the Gregorian calendar
• equal to
• not equal to
• greater than
• less than
• addition
• subtraction
ratio equal units of measurement on all parts of the scale and a true zero
• most physical measurements, e.g.:
• height
• weight
• volume
• electric current
• degrees Kelvin
• time (elapsed)
• but also counts (number of ...)
• equal to
• not equal to
• greater than
• less than
• addition
• subtraction
• multiplication
• division

A common misconception about some of these examples has to do with "no true zero" versus "no zero possible." If we are measuring height and weight, for example, we will never get a measurement of zero ("no zero possible"), but the measurement scale still has a true zero on it. If we did get a measurement of zero (use your imagination!), it would mean the person being measured has no height or weight (absence of height or weight), whereas a measurement of zero degrees fahrenheit does NOT indicate the absence of temperature (or heat), and year zero on the Gregorian calendar was not the beginning of time. (In fact, there was no year zero on the Gregorian calendar.)

The important discussion centers around the role of measurment scales in statistics. My opinion on this (which is, of course, correct) is that if you have numbers, you can do anything you want with them. I.e., you can do a t-test on ordinal data as long as the data are in numerical form and you've met the assumptions of the t-test. The difficulty comes with the meaning or interpretation of the result.

For our purposes, we will differentiate between numerical data (interval or ratio measurement), ranked data (ordinal measurement), and categorical data (nominal measurement) for the purposes of deciding upon a statistical procedure. We will have to take some care with the interpretation of the result of that procedure, but then don't we always? If group one has a mean IQ score of 110, and group two has a mean IQ score of 95, and the two means are significantly different by t-test, does that indicate that people in group one are, on the average, more "intelligent" than people in group two? Similarly, if two instructors are rated on a Likert-type rating scale by 30 students each, and then means are taken of those 30 ratings for each instructor, is the instructor with the higher mean necessarily the better instructor? (NO!)

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