After measuring two individuals, a researcher can say that Tom's score is 4 points higher than Bill's. The measurements must come from a(n) _______ scale.

After measuring two individuals, a researcher can say that Tom's score is 4 points higher than Bill's. The measurements must come from a(n) _______ scale.

• A. Nominal
• B. Ordinal
• C. Interval
• D. Interval or ratio

Answer: (D)

The key idea is that talking about how much higher one score is than another requires a scale with meaningful numeric differences between values. You can subtract one score from another only if the scale has equal units and meaningful intervals. Nominal scales have only category labels with no order or distance between categories, and ordinal scales preserve order but not equal intervals between ranks, so you cannot say one score is 4 points higher than another on those scales. Interval scales have equal intervals between points, so a difference like 4 points is meaningful. Ratio scales also have this property and even include a true zero, which lets you discuss ratios as well. Since the statement involves a precise difference between two scores, the measurement must come from an interval or ratio scale.

The key idea is that talking about how much higher one score is than another requires a scale with meaningful numeric differences between values. You can subtract one score from another only if the scale has equal units and meaningful intervals. Nominal scales have only category labels with no order or distance between categories, and ordinal scales preserve order but not equal intervals between ranks, so you cannot say one score is 4 points higher than another on those scales. Interval scales have equal intervals between points, so a difference like 4 points is meaningful. Ratio scales also have this property and even include a true zero, which lets you discuss ratios as well. Since the statement involves a precise difference between two scores, the measurement must come from an interval or ratio scale.