What level of measurement shows an order but not the magnitude of differences?

The correct choice is ordinal measurement because it captures the essence of ranking or ordering items based on some characteristic while not conveying the exact differences between those ranks. For example, in a survey asking respondents to rate their satisfaction on a scale from "unsatisfied" to "very satisfied," the responses can be ordered from least to most satisfied, indicating that one response is better than another. However, the ordinal scale does not quantify the difference between "satisfied" and "very satisfied" or how much more one is satisfied compared to another.

In contrast, nominal measurement categorizes data without any order or ranking, while interval and ratio measurements provide both order and a quantifiable difference between values. Interval data, like temperature in Celsius, allows for measurement of differences (e.g., the difference between 20°C and 30°C is the same as between 30°C and 40°C). Ratio measurement further includes a true zero point, allowing for meaningful comparison of magnitudes. Thus, ordinal measurement uniquely identifies the order without indicating how much greater or lesser one option is compared to another.