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An interval scale is a measurement in which the differences between numbers are meaningful. It includes the same information as do nominal and ordinal scales; however, with interval data, the differences between the numbers are of equal size. For example, you have probably at some point been asked to complete a customer satisfaction survey, such as those in Figure 2.3. For these items, we can easily assign numeric values to each response. We can give a 1 to a mark of “Highly Satisfied,” a 2 for “Satisfied,” and so on, with a 5 for “Highly Dissatisfied.”

Interval scale: distance (interval) between each number is of the same magnitude.

Figure 2.3 Example Items From a Grocery Store Customer Satisfaction Survey

When we ask people to respond to questions such as these, which use a response range, this is an interval scale. The rule for assigning numbers on an interval scale is that equal differences between the numbers on the scale must represent equal psychological differences between the events or objects.

Returning to our example of vegetable preferences, we could have collected such data using an interval scale. Here is how. You could have asked me how much I liked each one of the five vegetables, perhaps using an interval scale such as this one:

If I gave red peppers a 7, asparagus a 4, and carrots a 3, it would mean my liking of red peppers is quite a bit stronger than my liking of asparagus even though asparagus is my second favorite vegetable. My liking of carrots is closer to my liking of asparagus more than my liking of asparagus is to my liking of red peppers. The interval scale gives us more details than does an ordinal scale.

It is important to note that the interval scale does not contain a meaningful zero point. That is, a score of zero, when using an interval scale, does not indicate the absence of a variable being measured. Temperature is an example of an interval scale. A temperature of 0 degrees Fahrenheit does not mean that there is no temperature outside. Without a meaningful zero point, we cannot form ratios using interval data. So when it is 80 degrees Fahrenheit outside, we cannot say it is twice as warm as when it is 40 degrees Fahrenheit outside.

Just as with nominal and ordinal data, there are different statistical tools we can calculate and statistical tests we can perform on interval data. We can calculate all measures of central tendency and all measures of variability (Chapter 4). We can also use t tests (Chapters 7 and 8), analyses of variance (ANOVAs; Chapters 9–11), and correlational analyses (Chapters 12 and 13). As you can see, there are a lot more statistical tools available for interval data than there are for nominal and ordinal data.

Unlike an interval scale, a ratio scale has a meaningful zero point, as well as all of the characteristics of nominal, ordinal, and interval scales. The rule for assigning numbers on a ratio scale is that the ratios between the numbers on the scale must represent the psychological ratios between the events or objects. Examples of ratio data include many physical measures, such as time or weight. With a ratio scale and its meaningful zero point, it is possible to form ratios to make comparisons. For instance, the two minutes it takes someone to solve a statistics problem is half the time it took the person needing four minutes to solve the problem. So, we can conclude that the second person took twice as long. Someone who weighs 150 pounds is twice as heavy as someone who weighs 75 pounds.

Ratio scale: interval data that has a meaningful zero point.

The same sort of statistical tools can be used with ratio data as are used on interval data. That is why you might encounter a type of data called scale data. In practice, th e distinction between interval and ratio data is not nearly as important as the differences they have with nominal and ordinal data. The reason we care about scales of measurement is that some statistical techniques can only be used on interval or ratio scales. If all of your data are measured at a nominal level, then you are limited in what you can do with your data. This will be clear as we talk about how to present data in various parts of the book. Table 2.3 contains a summary of our scales of measurement.

Scale data: refers to interval and ratio data without making a distinction between them.

Table 2.3