For example, an arbitrary zero is assigned to the Fahrenheit temperature scale and equal temperature differences equate to equal volumes of expansion in the liquid used in the thermometer. Therefore, it is not correct to state that any value on a specific interval scale is a multiple of another (50°F is not twice as hot as 25°F). Most ordinary statistical measures (such as arithmetic mean, standard deviation, and correlation coefficient) require only interval scales for their computation.
To provide some idea of the relationships among nominal, ordinal, interval, and ratio scales, marketing researchers who use descriptive statistics (arithmetic mean, standard deviation) and tests of significance (t-test, F-test) should require that the data are (at least) interval-scaled. From a purely mathematical point of view, you can obviously do arithmetic with any set of numbers—and any scale. What is at issue is the interpretation and meaningfulness of the results. As we select more powerful measurement scales, our abilities to predict, explain, and otherwise understand respondent ratings also increase.
Scales provide the measurement for survey research. Rather than asking respondents a basic yes or no question, scales measure the direction and intensity. Scales also fulfill the level of measurement required by your selected statistical analysis technique. This is critical for research. Imagine the owner of a small-town retail store. She thinks she has a great relationship with all of her customers. In fact, she’d be surprised if more than 5% of her customers are dissatisfied with her store. But she wants to make sure. She asks 100 customers if they are satisfied or dissatisfied with the store. She gets this breakdown.
These two charts paint completely different pictures of the store’s customer satisfaction, but an unscaled “Are you satisfied? “Question with yes-no answer choices doesn’t reveal the answer. That’s why researchers use scales for their studies.
Not only can they run basic percentages like the ones above, they can also assign each option a value and find a mean, median, range, and variance. Means enable quick evaluations of results across multiple questions. For example, the same store owner could use a 7-point Satisfied – Dissatisfied scale to ask about satisfaction with four attributes of her store.