LEVEL OF MEASUREMENT

Level of measurement

Refers to the kind of data you collect when you are creating a variable. 

Can be: Ratio, interval, ordinal or nominal.

Let us take a look at each of these four:

Ratio:

The ratio level of measurement is the "highest" level of measurement--generally speaking you can do the most with variables that are collected at the ratio level. You can add, subtract, divide and multiply ratio level variables which means you can do almost any kind of analysis.

Ratio level variables have a meaningful ("real") 0. Age 0 is the complete absence of years, and hours worked per week =0 means the complete absence of hours.

Additionally, the steps from one number to the next are evenly spaced: There is the same distance between 1 and 2 as the distance between 5 and 6. 

Discrete vs. continuous

Collecting at the ratio level means collecting "actual numbers". 

These numbers can be continuous (like pi 3.14159...) or discrete (as is often the case with age. You usually report a your age at your last birth day in whole years, like 18 or 22 instead of reporting your actual, exact age like 18.2263480 years). 

Continuous: the exact number with however many decimal places the value actually has (or reporting it as an exact fraction). 

Discrete: reporting only certain numbers--like whole numbers for age.

Ratio level measures can be continuous or discrete. 

Examples of common ratio level variables:

Age
Height
Weight
GPA
Years of education

Interval:

In practice, interval level variables are sort of rare. There are actually only a few examples that we see in practice with any frequency. 

EXAMPLES:

Interval means basically the same thing as ratio except that the 0 is not "real"--it is not really the absence of the thing being measured: 0 degrees Fahrenheit is not the absence of temperature, the year 0 AD is not the absence of time, and a shoe size of 13 comes before a shoe size of 1. 

You can basically use interval data like ratio data (add, subtract, multiply, divide) except that you have to watch out for non-mathematically-meaningful zeros. If you have data on temperature and two of the observations are 0 and 10 degrees Fahrenheit, is the 10 really infinitely warmer than the 0? No. This can lead to deceptive outputs in your analysis, so USE WITH CAUTION!

Interval level observations also have equal spacing like with ratio level. The difference between 0 to 1 degree Fahrenheit is the same as the difference between 200 and 201. 

Ordinal:

Ordinal level of measurement means that there is a clear order to the data, but the spacing is not equal. 

In some cases this is clear, like in Likert Scale data: "do not agree, somewhat agree, strongly agree, very strongly agree".

In other cases, it can be confusing: "0-1 children, 2-4 children, 5+ children". Many students would say that this is ratio level data because there is equal spacing from 0 to 1 to 2...children. BUT THAT IS NOT HOW THE VARIABLE IS REPORTED. And in fact, we cannot with certainty say that there is the same gap from "0-1" to "2-4" as there is from "2-4" to "5+" (If for no other reason than "5+" could include someone with 10 children!).

Ordinal level variables are limited to analysis that uses "greater than/less than" functions, or difference (saying whether there is a difference between the group with 0-1 children and the group with 5+ children for example).

Nominal:

Nominal means "name" and that is pretty much the limit to this level of measurement. The different values the variable can take are simply names or categories. 

For example, you may create a variable that is called TRANSPORTATION that asks how people most often get to school. The options may be: Bus, car, bike, walk and "other". 

These categories do not have a clear order and your analysis is limited to the examination of differences. 

In certain cases, it may be unclear if there is an order or not. For example, in the TRANSPORTATION variable, could you place the values in increasing size of the mode of transportation, like this: walk, bike, car, bus? You might argue for that (even if it is probably unrelated to your analysis and may sound a little silly), but many examples are very clear. Do you want to try to place SEX in order (male, female) or RACE (black, white, indigenous, Asian...)? 

Analysis:

It is critical to be able to identify what type of variable you have because most statistical packages do not (ACCURATELY) identify level of measurement (unless you manually tell the software the level of measurement). You need to know what kind of variable you are working with. 

There are many types of analysis so we cannot list all the ways you can use each level of measurement. BUT, if you need division or multiplication, you know you will be limited to RATIO (or INTERVAL with caution about the non-meaningful zeros). If you need to add or subtract, you are again limited to RATIO and INTERVAL. If you only need to perform greater than/less than operations, ORDINAL, RATIO or INTERVAL will be fine. If you are only showing differences, than you can use any.

This table summarizes it:

	add, subtract, multiply, divide…	Greater than/less than	Difference
Ratio	X	X	X
Interval	X (w caution)	X	X
Ordinal	-	X	X
Nominal	-	-	X