## What is Level of Measurement?

In statistics, level of measurement is a classification that relates the values that are assigned to variables with each other. In other words, level of measurement is used to describe information within the values. Psychologist Stanley Smith is known for developing four levels of measurement: nominal, ordinal, interval, and ratio.

### Four Measurement Levels

The four measurement levels, in order, from the lowest level of information to the highest level of information are as follows:

#### 1. Nominal scales

Nominal scales contain the least amount of information. In nominal scales, the numbers assigned to each variable or observation are only used to classify the variable or observation. For example, a fund manager may choose to assign the number 1 to small-cap stocks, the number 2 to corporate bonds, the number 3 to derivatives, and so on.

#### 2. Ordinal scales

Ordinal scales present more information than nominal scales and are, therefore, a higher level of measurement. In ordinal scales, there is an ordered relationship between the variable’s observations. For example, a list of 500 managers of mutual funds may be ranked by assigning the number 1 to the best-performing manager, the number 2 to the second best-performing manager, and so on.

With this type of measurement, one can conclude that the number 1-ranked mutual fund manager performed better than the number 2-ranked mutual fund manager.

#### 3. Interval scales

Interval scales present more information than ordinal scales, in that they provide assurance that the differences between values are equal. In other words, interval scales are ordinal scales but with equivalent scale values from low to high interval.

For example, temperature measurement is an example of an interval scale: 60°C is colder than 65°C and the difference in temperature is the same as the difference between 50°C and 55°C. In other words, the difference of 5°C in both intervals have the same interpretation and meaning.

Consider why the ordinal scale example is not an interval scale: A fund manager that is ranked 1 probably did not outperform the fund manager ranked 2 by the exact same amount that a fund manager ranked 6 outperformed a fund manager ranked 7. Ordinal scales provide a relative ranking, but there is no assurance that the differences between the scale values are the same.

A drawback in interval scales is that they do not have a true zero point. Zero does not represent an absence of something in an interval scale. Consider that the temperature -0°C does not represent the absence of temperature. For this reason, interval-scale-based ratios fail to provide some insights – for example, 50°C is not twice as hot as 25°C.

#### 4. Ratio scales

Ratio scales are the most informative scales. Ratio scales provide rankings, assure equal differences between scale values, and have a true zero point. In essence, a ratio scale can be thought of as nominal, ordinal, and interval scales combined as one.

For example, the measurement of money is an example of a ratio scale. An individual with $0 has an absence of money. With a true zero point, it would be correct to say that someone with $100 has twice as much money as someone with $50.

### More Resources

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