Levels of Measurement (Also Called Scales of Measurement) First read the material in the book. Then think about these examples to solidify the concepts. Examples of Measurement at the Nominal Level Sex - male/female Ethnicity - Hispanic/Caucasian/Indonesian/Black Yes/No - Own Home or not; Pass or not; Have driver's license or not; text while driving or not Examples of Measurement at the Ordinal Level Good/Better/Best; Low/Medium/High etc 0-5/6-10/11-15 and similar categories Disagree Strongly/Disagree/Neither Agree nor Disagree/Agree/Agree Strongly Rating on a scale from 1 to 10 Examples of Measurement at the Interval Level Score on a personality inventory IQ score Score on a survey Examples of Measurement at the Ratio Level Number of dollars earned in a year Amount of time required to complete a task Number of times a particular behavior is exhibited The Same Concept Can Be Measured in Different Ways We can't talk about scales of measurement until we've selected our operational definition. Remember that the operational definition tells us how to measure our variable. Let's use income as our example. We can measure income using several different operational definitions and each one results in a different level of measurement This operational definition generates a nominal level of measurement: 1. Had income in 2012 2. Did not have income in 2012 3. Prefer not to answer Note that each of these numbers (1,2,3) is just a label for the category; the numbers have no real numerical meaning. This operational definition generates an ordinal level of measurement 1. 0 to 19,999 (low) 2. 20,000 to 39,999 (med/low) 3. 40,000 to 59,999 (med) 4. 60,000 to 79,999 (med/high) 5. 80,000 to 99,9999 (high) The numbers 1 - 5 have limited numerical value. See the discussion below. This operational definition generates a ratio scale of measurement: Record the exact number of dollars earned by each participant. Consider this example of income data: Joe: 39,900 Sue: 61,000 Dave: 78,000 Using our operational definition above that generates a nominal scale of measurement, here is what we would record: Joe: 1 Sue: 1 Dave: 1 Those numbers have no real numerical meaning. Using our operational definition above that generates an ordinal scale of measurement, here is what we would record: Joe: 2 Sue: 4 Dave: 4 These numbers also have limited meaning. Did Sue and Dave earn twice as much as Joe? No. Are the intervals between each measurement equal? No. The interval between Sue and Joe appears to be 2 and the interval between Dave and Joe appears to be 2 in this particular scheme - but those appearances are deceiving. The real interval between Sue and Joe and between Sue and Dave can only be seen if we use a different scale of measurement. The real interval between Sue and Joe is 21,100 and the real interval between Dave and Joe is 38,100 - those intervals are clearly not equal. Using our operational definition that generates a ratio scale of measurement, here is what we would record: Joe: 39,900 Sue: 61,000 Dave: 78,000