Interval Level of Measurement

The interval level of measurement falls between the ordinal and ratio levels on the hierarchy of measurement and is considered the second “highest” or second most precise measurement scale. Interval scales are less exact than only ratio-level data. Interval data are more precise than nominal and ordinal data because the interval scale contains meaningful distances.

For instance, whereas in a nominal scale we can say only that certain traits or values belong to different mutually exclusive categories, and in an ordinal scale we can say only that a score or performance ranks above or below another one, with the interval scale, we can conclude how much higher one score is than another score. The unique characteristic of the scale that allows this determination of meaningful distances (or the quantification of “how much”) is the equidistance of the intervals it contains.

To conceptualize the use of an interval scale, let's explore an example that compares interval-level measurement to the two less precise measurement levels.

Five students took a 10-question true-or-false history quiz, and each question was worth one point. The students received the following scores:

• Kevin—10 points
• Jaime—6 points
• Sara—5 points
• Jen—3 points
• Bill—0 points

In this example, the teacher could grade the students using a nominal scale and give each student a score of either “pass” or “fail” that corresponds to the student's score. If the teacher decided to grade this way, Kevin and Jaime would receive the same grade, even though Kevin correctly answered four more questions than Jaime. Sara, Jen, and Bill would also earn equal grades of “fail” even though Sara got five more questions correct than did Bill and even though Sara's score was only 1 point below Jaime's.

The teacher could also decide to grade the quizzes using an ordinal scale. With this method, she would rank the students and give Kevin an “A” because he obtained the highest score, Jaime a “B,” Sara a “C,” Jen a “D,” and Bill an “F.”

However, the most precise way to grade the history quizzes would be to use an interval scale that corresponds directly to the number of questions the students answered correctly. Each interval along the scale would be worth the same amount: one point. Kevin would receive 10 points (100%), since he answered all questions correctly, Jaime would receive 6 points (60%), and so on. In this respect, we can say that Kevin's score of 10 is 4 points higher than Jaime's score of 6. An important point to remember, though, is that we are unable to say that Jaime has “twice” as much knowledge of history as Jen even though Jaime earned a 6 and Jen earned a 3. Because the interval scale has an arbitrary zero point (i.e., a score of 0 on the quiz does not indicate a complete [Page 487]lack of knowledge about history), we cannot produce this ratio.

Using this interval scale for grading would highlight the most variability among the five students, telling us more about their knowledge of history than would nominal or ordinal grading methods. As Kevin would likely agree, the interval scale is probably the fairest grading method as well, because it clearly distinguishes the scores of 10 and 6 in a meaningful way. In the social sciences, especially because true ratio-level data are rare, interval-level data are desirable because of the amount of information they can provide.

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