The first step in data analysis is simply understanding what the data mean. This is facilitated by classifying each variable according to its measurement level. Standard textbooks distinguish four such measurement levels: nominal, ordinal, interval and ratio.

## Measurement Levels - Classical Approach

Quick Overview of Measurement Levels## 1. Nominal Measurement Level

The nominal measurement level implies that there's **no undisputable order** in what's represented by the data values. An easy example is country. We may sort countries alphabetically, according to their sizes or to numbers of inhabitants. Different orders make equal sense for a list of countries.

Now don't overlook the phrase *“what's being represented”*. It's not the data values that matter. It's what they represent in the real world. So a tricky example are ZIP codes. These actually represent geographical areas, which don't have an undisputable order. This renders ZIP code a nominal variable.

## 2. Ordinal Measurement Level

The ordinal measurement level implies that there's a **clear order but no fixed unit of measurement** in what's represented by the data values. Typical examples are attitude scales like

- Bad;
- Neutral;
- Good.

known as **Likert scales**. There's a clear order in the sentiments represented by these values. "Neutral" is clearly between "Bad" and "Good". However, we've no clue just *where* between those. For instance, a demanding respondent who rates almost everything "Bad" may feel "Neutral" is actually closer to "Good" than to "Bad". This is illustrated by the figure below.

A different way to state this is that the sentiments represented here don't have any **fixed unit of measurement**. This renders their data values rather arbitrary. We used "1", "2" and "3" to represent "Bad", "Neutral" and "Good" but we may just as well use "1", "1.5" and "3" instead.

Note that this arbitrary choice dictates the outcomes of **calculations** on this variable. This is why calculations on ordinal variables are **not meaningful**. Less strictly though, calculations on ordinal variables are quite common under the Assumption of Equal Intervals.

Note that monthly income measured as

- Less than 1000 Euros;
- 1000 to 2000 Euros;
- 2000 Euros or over.

is ordinal as well. These three values really represent income *categories* and these don't have a fixed unit of measurement. We'll say that “income was *measured* at the ordinal level”.

We could measure it at ratio level too by asking the exact income in Euros. The point here is that a single variable (income) can sometimes be measured at different measurement levels.

## 3. Interval Measurement Level

The interval measurement level implies a **fixed unit of measurement** but **no natural zero point**. True interval variables are rare but one of the few examples is temperature in degrees Celsius.

The measurement unit is fixed because every degree Celsius represents the same amount (“**interval**”) of temperature. However, zero degrees Celsius does *not* mean “nothing” with regard to temperature.With regard to temperature, we'd probably say that "nothing" corresponds to -273.15 degrees Celsius.

Without a natural zero point, **multiplication is not meaningful**. It doesn't make sense to say that 40 degrees Celsius is “twice as warm” as 20 degrees.

## 4. Ratio Measurement Level

The ratio measurement level implies a **fixed unit of measurement** and a **natural zero point**. An example is weight in kilos. A kilo is a fixed unit of measurement because it always represents the exact same weight.

So what is meant by "a natural zero point"? A natural zero point means that **zero represents “nothing”**. This holds because zero kilos corresponds to “nothing” with regard to weight.

We rather avoid “absolute zero point” because ratio variables may hold **negative values**; the balance of my bank account may be negative but is has a fixed unit of measurement -Euros in my case- and zero means “nothing”.

This natural zero point is what really renders multiplication - and therefore **ratios** - of values meaningful; it makes perfect sense to say that € 2000,- is two times € 1000,- or four times € 500,-.

## Classical Measurement Levels - Shortcomings

We argued that measurement levels matter because they **facilitate data analysis**. However, when we look at the most common statistical techniques, we see that

- dichotomous variables are treated differently from all other variables but classical measurement levels fail to distinguish them;
- metric variables (interval and ratio) are always treated identically;
- categorical variables (nominal and ordinal) are sometimes treated similarly and sometimes not.

In order to fix these issues, we propose a more useful classification below.

## Measurement Levels - Modern Approach

**Dichotomous variables**are variables that have**precisely two distinct values**. It is useful to distinguish dichotomous variables as a separate measurement level because they require different analytical procedures than other variables, such as SPSS Independent Samples T Test and SPSS Binomial Test.

Dichotomous variables are sometimes known as**binary variables**.**Categorical variables**are variables on which**calculations are not meaningful**. They thus comprise nominal and ordinal variables. We sometimes do and sometimes don't distinguish these.

Categorical variables are also known as**qualitative variables**because they express a*quality*rather than a quantity.**Metric variables**are variables on which**calculations are meaningful**. They thus comprise interval and ratio variables. We never distinguish these and we always use the same analytical procedures for them.

Metric variables are also known as**quantitative variables**because they express a*quantity*of something rather than a qualtity.

Well, that's about it. Whether or not you agree with my opinion on measurement levels, I hope you found it useful anyway. Thanks for reading!

## This tutorial has 21 comments

## By Eileen Potter on June 9th, 2017

Lovely, clear discussion. Percentages are my problem and I have been bounced around with 'ordinal', 'ratio' and 'interval' explanations. Metric would be so much more useful.

## By Ruben Geert van den Berg on March 29th, 2017

I know, the CMS is not entirely tidy. I was confident nobody would notice or care about the wrong comment count but I didn't take you into account ;-) Ok, I'll fix it.

## By Jon Peck on March 29th, 2017

The site says "This Tutorial has 11 Comments", but I can only see the first. Maybe that means that the others have not been approved.

## By Jon Peck on March 27th, 2017

Thanks for contributing to this rather confusing topic. There are a few places to go next.

- the variable role. Measurement level has a different impact depending on how a variable will be used, e.g., as a predictor in regression, in a tree analysis, or in, say, t tests and in graphics and tables.

- Calculating with combinations of variables. It may be perfectly okay to multiply a dichotomous variable by another type depending on the coding but not appropriate to add them.

We once considered trying to assign a measurement level to a computed quantity but decided that it was too hard to get this right in the general case.

- Simple addition might not be okay even with interval or ratio variables depending on the units.

As you doubtless know, Statistics can attempt to guess the measurement level for a variable if it is unknown. This happens both in Data > Define Variable Properties and in more recent versions when the data are passed, but it can certainly be fooled. The heuristics use the number and type of values, the variable format, and other properties to guess. The user can, of course, override this.

## By lukwago umar on October 21st, 2016

interesting but being my first time am still confused if you can reccomend me for books i can read in my free time its better. send them via my email thanks