Levels of Measurement | Introduction to Statistics

Opening

You're analyzing a survey where customers rate a cruise as "excellent," "good," "satisfactory," or "unsatisfactory." Can you average those ratings to get a mean satisfaction score? The answer depends on the level of measurement of your data.

The idea

Data can be classified into four levels of measurement—nominal, ordinal, interval, and ratio—which determine what statistical operations are meaningful.

Four levels of measurement

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, from lowest to highest: nominal, ordinal, interval, and ratio.

Vocabulary· 2 terms

Examples of each level

Let's look at examples of each level. Nominal: smartphone company names—there's no agreed-upon order, even if people have personal preferences. Ordinal: a list of the top five national parks—you can rank them 1 to 5, but you can't measure the difference between ranks. Interval: temperature in Celsius or Fahrenheit—differences make sense (40°C is 100°C minus 60°C), but 0° is not the absolute lowest, so 80°C is not four times as hot as 20°C. Ratio: data with a true zero, like height or weight—covered in the Levels of Measurement unit.

Vocabulary· 2 terms

Easily confused

Looks like

Ordinal and interval data both have an order, so they seem similar.

Actually

Ordinal data can be ordered but differences between values are not measurable; interval data has measurable differences.

The key difference is whether the gaps between values carry meaning—that's what allows calculations.

Definition

ordinal scale level

A scale of measurement for data that can be ordered, but where differences between data cannot be measured; like nominal scale data, ordinal scale data cannot be used in calculations.

It's data you can rank, but the gaps between ranks aren't meaningful, so you can't do arithmetic on it.

The levels

Ordinal example: cruise survey

A cruise survey asks passengers to rate their experience as "excellent," "good," "satisfactory," or "unsatisfactory." These responses are ordered from most desired to least desired, but the differences between two responses cannot be measured. Like nominal data, ordinal data cannot be used in calculations.

Recap

Say each point to yourself, then tap it to check.

Nominal: categories with no order; no calculations.
Ratio: true zero, so ratios are meaningful.