Nominal, Ordinal, Interval, Ratio

Nominal, Ordinal, Interval, Ratio

The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. Not every statistical operation can be used with every set of data. Data can be classified into four levels of measurement. They are (from lowest to highest level) nominal, ordinal, interval, and ratio:

Nominal Data

Data that is measured using a nominal scale is qualitative. Categories, colors, names, labels and favorite foods along with yes or no responses are examples of nominal level data. Nominal scale data are not ordered. For example, we could ask people to indicate their favorite food and create categories, but putting these categories in order (e.g. putting pizza first and sushi second) is not meaningful.

Smartphone companies are another example of nominal scale data. Some examples are Sony, Motorola, Nokia, Samsung and Apple. This is just a list and there is no inherent order. Some people may favor Apple but that is a matter of opinion. Nominal scale data cannot be used in calculations.

Ordinal Data

Data that is measured using an ordinal scale is data that can be ordered. An example of ordinal scale data is a list of the top five national parks in the United States. The top five national parks in the United States can be ranked from one to five but, importantly, we cannot measure differences between the data.

Another example of ordinal scale data are the place racers finish in a race. We know that the first place finisher finished ran faster than the second place finisher, and the second place finisher ran faster than the third place finisher, but we do not know the difference between how fast the first place finisher ran compared to how fast the second place finisher ran. All we know is that the first place finisher completed the race first. Therefore, we can order our data from the fastest racer to least fastest racer, but the differences between our data cannot be measured. Like the nominal scale data, ordinal scale data cannot be used in calculations.

Interval Data

Data that is measured using the interval scale has and order, however this time, the differences between the data can be measured. Importantly, in interval data, 0 does not represent the absence of the thing being measured..

Temperature scales like Celsius (C) and Fahrenheit (F) are measured by using the interval scale. In both temperature measurements, 40° is equal to 100° minus 60°. Differences make sense. But 0 degrees does not mean the absence of temperature. We can still feel temperature at 0 degrees and we can even have temperatures like -10° F and -15° C that are colder than 0.

Interval level data can be used in calculations, but we cannot do operations like multiplication and division since there is not a true 0 point. For example, one cannot say that 80° C is four times as hot as 20° C (nor is 80° F four times as hot as 20° F). There is no meaning to the ratio of 80 to 20 (or four to one) if there is not a true zero point.

Ratio Data

Data that is measured using the ratio scale has all the properties of interval data, but it has a true 0 point which means ratios can be calculated. For example, four multiple choice statistics final exam scores are 80, 68, 20 and 92 (out of a possible 100 points). The exams are machine-graded.

The data can be put in order from lowest to highest: 20, 68, 80, 92.

The differences between the data have meaning. The score 92 is more than the score 68 by 24 points. Ratios can be calculated. There is a true 0; if you receive a 0, this means you did not score on the test. Because there is a true zero, we can make statements like an 80 on an exam means you received a score that is four times better than a 20.

Click here to go back to main chapter page