NOIR Part 3: Interval Measurements

An introduction into interval measurements, what they are, how and when to use them.

November 17, 2019 Ryan Sanchez

4 minutes read

Measurement NOIR

This is the third in a series of four posts discussing the common measurement types used within social sciences. An easy acronym to help you remember the 4 measurement types is:

NOIR (No-are)

Today’s post will discuss interval measurements, what they are, how and when to use them. Identifying your data’s measurement type is an important step when deciding what type of statistical analyses can be done.

Speaking of NOIR, check out 9 Great Noir Books.

Interval Measurements

Interval measurements are characterized by knowing both the ordering and difference between the ordering in the measurement. However, interval measurements do not have a meaningful ‘zero’ value.

Interval measurements occur frequently in our everyday lives, though we don’t usually recognize them as such. Every time we check the temperature, take a dreaded standardized test or countdown the days until our birthday we are using an interval measurement.

Days are interval measurements since ordering and space between days are known.

Looking at a calendar, it’s easy to see that Tuesday the 6^th comes after Monday the 5^th and the spacing between the days is 24 hours. These are the two important properties of interval measurements, a defined ordering and spacing. This is true for all measurements of time including hours, minutes and seconds.

Notice that days do not have a true ‘zero’. In easier words, the concept of an “absence of days” doesn’t make sense (contrast this concept with an ‘absence of money’ which makes perfect sense). Instead, days are always counted from an arbitrary starting point. Your birthday is a measurement of days from your birth, but imagine trying to manage schedules if everyone used their own birthday to define a calendar! Instead the ‘zero’ date of a calendar was set as roughly 2019 years ago.

Analysis

Addition and subtraction are valid mathematical operations for interval measurements. Think about adding 5 days to the current date, 5 degrees to the current temperature or 5 points to your SAT/ACT score, each of these examples have an identifiable value. Contrast this with an ordinal measurement of water temperature: cold, warm, and hot. Adding 5 degrees doesn’t mean anything since it’s unknown if 5 degrees is enough to move cold to warm or keep cold at cold?

Multiplication and division are not valid operations for interval measurements. This can be difficult to understand since the measurements are numbers and you can usually multiply and divide numbers, but not with interval measurements.

To see why this is the case, consider the average high and low temperature for several cities measured in both degrees Fahrenheit and Celsius:

City	High ^oF	Low ^oF	Ratio ^oF	High ^oC	Low ^oC	Ratio ^oC
Seattle	79	55	1.45x	26	13	2x
Atlanta	90	70	1.28x	32	21	1.52x

Notice that in the month of July, the average high in Seattle was 26 Celsius while the average low was 13 Celsius resulting in a ratio of 2. It might be tempting to conclude the average high is twice as hot as the average low temperature, this is incorrect. The same temperature measured in Fahrenheit results in a ratio of 1.45. This leads to a confusing situation where ratios depend on the interval used. This is the reason multiplication and division are not proper operations with interval measurements.

Review

Properties of interval measurements include:

Defined Order
- Measurements can be classified as bigger/smaller, better/worse, later/earlier, etc. than other measurements and ordered accordingly.
Known Spacing
- The spacing between the orders is defined and known.
Yes - Addition/Subtraction ; No - Multiplication/Division
- Addition and subtraction can be used freely but don’t use multiplication or division. The output of multiplication or division is dependent on the interval scale used.
Use the Mean
- Since addition and subtraction are valid operations, use the mean to describe the average member of the measurements. The mode and median are also valid with interval measurements.

GoFactr

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