Any statistics you calculate requires knowing what the level of measurement is, which means that you gotta know this to get very far with statistics. So what it is? I might say that level of measurement refers to the degree of quantification of a variable. In other words, how much any particular variable ranges from having an arbitrary relationship to numbers to being a fully meaningful number.
There are four main levels of measurement from least to most quantitative:
1. Nominal
2. Ordinal
3. Interval
4. Ratio
1. NOMINAL VARIABLES are those where the possible responses have no inherent numeric value and they also cannot be ranked or ordered in any meaningful way. Examples might be:
Religion
a. Muslim
b. Jewish
c. Catholic
d. Protestant
e. Other Christian
f. Other
Or
Marital Status
a. Married
b. Common-Law
c. Divorced
d. Widowed
e. Separated
f. Single and ready to mingle
g. Happily single
Or
Favorite Ice Cream Flavor
a. Vanilla
b. chocolate
c. strawberry
d. chunky monkey
e. other
Even though YOU might be able to rank your favorite ice cream flavors, there is no inherent ranking for ice cream that would lead a researcher to put one flavor before another when designing a survey. I could have put chunky monkey for a, b, or c, just as easily as in spot d.
2. If you CAN rank the possible answers to a survey question, but you don’t know the exact or precise distance between the responses, then you’re in the land of ORDINAL VARIABLES. Examples might include something like:
How much do you agree the country is headed in the right direction?
a. strongly agree
b. agree
c. disagree
d. strongly disagree
(Note: A scale of agreement or disagreement on a four or five point scale from strongly agree/approve/etc. to strongly disagree/disapprove/etc. is called a Likert Scale)
Ordinal variables don’t have to have equidistant categories like that and can also be a bit “lumpier” in terms of knowing how far away one category is from the next, such as with education:
What is your highest level of education?
a. Less than high school
b. High school diploma
c. Some college/university
d. Community college degree
e. University degree
f. Some graduate school without a degree
g. Graduate degree
Notice that this variable is rankable in that we know that less than high school is less than high school diploma. However, we don’t know if you select (a) if that means that you went to school for 11 years or 3 years. We can’t say exactly how many years of school you’ve been to or know how much more or less one participant went to school compared to another participant.
3. INTERVAL VARIABLES are where the real statistical action can start to take place (hot damn interval variables!). These are rank-able, like ordinal variables, but they also have the added benefit of having numeric values that tell us the precise distance between categories. So, for instance, dress sizes are numeric and, if we buy women’s clothing in North America, we know that a size 12 is a size smaller than a size 14.
However, although it sounds like interval variables are the MOST quantified you can get, they actually still have one limitation in that they do not have a meaningful zero point. Going back to the dress size example, if I were a size zero, this would not mean that suddenly I no longer have a size. Zero doesn’t mean zero, in this instance, zero just means another possible size a person could be (zero also does not mean better or worse #bodypositivemovement).
Because of this, you can see why some people treat Likert Scales as though they are interval scales, since with Likert scales we know that strongly agree is one unit more than agree and two units more than disagree. And, really, dress size isn’t a meaningful number any more than the sizes Small, Medium, Large, X-Large and so. When I went to Indonesia last year, I went from a Large/X-large in Canada to being somewhere between an XXXL-XXXXXL, because Indonesians tend to be much smaller than people of European origin like myself. Still, I’d probably still call clothing size interval if there’s a number associated with it and ordinal if it has a word associated with it.
Another interval variable that looks, at first glance, like a truly meaningful number would be temperature. Temperature IS measured with a number, however, think about what the temperature is when it is zero degrees outside. Have we entered into some kind of alternate time and space continuum in which temperature ceases to be? NO, it just means it’s really cold outside. However, even there, it doesn’t universally mean it’s the same amount of coldness. If you’re in celsius, it means that it’s the point at which water freezes, but if you’re in fahrenheit (I’m talking to you, United States) zero is much colder than that.
Because of this, although we can say that 10 degrees is 5 degrees hotter than 5 degrees, we can’t really say that 10 degrees is twice as hot as 5 degrees. Temperature just doesn’t work that way. Or a size four isn’t twice as big as a size two, they’re actually pretty darn close in size if you held up two pieces of clothing next to each other.
So, now that your mind is blown that some numbers aren’t actually really numbers but just a measure of some abstract concept like size or temperature, is there no God? Are there no meaningful numbers?
4. RATIO VARIABLES are the most numeric or quantified of the levels of measurement. These variables’ values are rank-able, have a measurable distance between each value, and there is a meaningful zero point. Counts are a particular kind of ratio variable which are the clearest to see. For example, number of pets participants own would be a ratio variable. I have two, so if you have 4 pets, you have twice as many as I do. (Although, according to my husband, this would mean that you are worse off because zero is the normatively ideal number of pets one should have, but I digress.)
Other ratio variables would be money–if you have zero dollars, you broke! You got no money, honey. Percentages, proportions, and ratios are all measured at the ratio level because 0%, 0.00, and 0:0 all mean none.
Often, textbooks and researchers will treat interval and ratio variables the same way in a data analysis, or even ordinal variables with equidistant categories. Much of the time this is not a problem, but sometimes, especially with more advanced methods, this can give you results that don’t really represent the data. Because of this, any quality research should always pay attention to the level of measurement when preparing analyse data, to make sure that the results actually mean what we think they mean.