The Data: The 4 Scales of Measurement

A question: how many times have we seen — or made — the mistake of calculating the average SERP position for a set of keywords and then using that number as if it were any other piece of data?
The average position is 4.3, keyword A is at 3 and keyword B at 7, “on average we are fourth”.
The problem is that a ranking position is not a number: it is ordinal data. The distance between position 1 and position 3 is not the same as between 3 and 5, and averaging numbers that do not have an interpretable distance — that is truly a meaningless operation.

Before performing any calculation on data, we must ask ourselves: what type of data is this? The answer determines everything we can — and cannot — do downstream. The answer comes from a classification that, although dating back to 1946, remains the foundation of every respectable statistical analysis: the 4 scales of measurement by Stanley Smith Stevens.

The scale of measurement does not serve to describe data: it serves to establish which operations are meaningful on that data. The more information a scale contains, the greater the number of statistical analyses we can apply. This is the criterion that makes Stevens’ classification so powerful and enduring in practice.

The 4 Levels of Measurement

Data can be measured at different levels, depending on the type of variable and the level of detail recorded.
American psychologist Stanley Smith Stevens proposed a classification of 4 levels of measurement (or scales of measurement) in 1946, which is still widely used today.

So we are talking about:

• Nominal Measurement
• Ordinal Measurement
• Interval Measurement
• Ratio Measurement

The difference between these 4 types of measurement scales is based on some salient characteristics:

• The order
• The distance between observations
• The presence and inclusion of a zero with a real meaning

Quantitative and Qualitative Data

Let’s start with some fundamental concepts that will always be with us.

Data can be classified into 2 main types:

• Quantitative
• Qualitative (or Categorical)

Important
In statistics, the entire group we are studying is called the population.
The individuals (which can be living beings or things) in the population are called units.
The characteristics of the units we are studying are called variables.

These variables can be quantitative or qualitative (also called categorical).

Nominal Scale

A nominal measurement is one in which the values of the variables are names. In this case we have:

• The order of observations does not matter
• The distance is not maintained
• There is no true zero

Let’s use examples from the world of web traffic data analysis, as it’s “daily bread” for those involved in SEO.

Think of the country of origin of visits to a website. Simplifying greatly, I consider visits coming from 4 countries:

Italy
France
UK
USA

We can count the visits from each of these countries:

Country        Visits
Italy        3305
France       1850
UK            1938
USA           2214

We are clearly dealing with a nominal measurement.
This is because:

• The order doesn’t matter (the table is readable even if I change the position of the various countries).
• The distance between categories is not relevant. (It would be if we were treating the data in terms of ratios).
• Zero is not needed (indicating the complete absence of views, and therefore that country would not appear in the report…).

For this type of measurement, the suitable chart type is the bar chart, or the histogram.

Ordinal Measurement

An ordinal measurement involves collecting information in which the order is important.

In terms of salient characteristics:

• The order of observations matters.
• Ordinal measurement does not preserve distance. The distance between two consecutive values has no meaning. (For example, the distance between the first and second observation can be in the order of thousands of units, while that between the fifth and sixth may be only a few units…).
• There is no meaningful zero.

Returning to our example of website visits by country:

Country        Position
Italy        1
USA           2
UK            3
France       4

We have established an order. The distance between the values of the various countries is unknown. Zero does not exist.

The appropriate chart type for ordinal measurements is the histogram or the bar chart.

Common mistake
Calculating the arithmetic mean on ordinal data — such as average SERP position, star ratings (4.2 out of 5), or satisfaction level on a Likert scale — is a serious methodological error.
The mean assumes that the distance between values is interpretable: between “satisfied” and “very satisfied” there is not the same distance as between “dissatisfied” and “very dissatisfied”, yet the mean treats them all as if they were numbers on a ruler.
What to use instead? For ordinal data, the median is the correct measure of position: it tells us the central value of the ordering without assuming equal distances between categories.

Interval Scale

In interval scales, the distance between two values has specific meaning.
A typical example is a questionnaire where the answers are coded on a scale ranging, for example, from:

1 = I like it very little
to
10 = I like it very much

The characteristics of interval measurements are:

• The order of responses/observations is relevant.
• The distance is relevant.
• There is no zero with a real meaning. (Although the data could be scaled so that 0 could be counted).

This type of measurement is very common in surveys.

Appropriate chart types for representation are bar charts, line charts, and scatterplots.

The most appropriate statistics for interval measurements are the mean, median, variance, standard deviation, skewness, and kurtosis.

Note
In practice, many questionnaires are analyzed as interval scales, even though this is a widely accepted simplification that is not without debate.

Ratio Scale

Now we come to the most common type of measurement in web data analysis: the ratio.

A ratio measurement expresses the relationship between the magnitude of a continuous quantity and a unit magnitude of the same kind.

A variable measured in this way includes not only the concept of order and interval, but also the idea of “nothing,” or absolute zero. Therefore:

• The order of responses/observations matters.
• Differences and ratios between values are interpretable.
• There is a true zero.

Staying within the field of web metrics, a typical example is the ratio between the number of visits and goals.

Appropriate charts are: histograms, bar or line charts, and scatterplots.

Appropriate statistics are: median, mean, variance, standard deviation, skewness, and kurtosis.

The scales of measurement form a hierarchy

Stevens’ categorization of measurement scales shows us an increase in the amount of information available at each level. Schematically:

Or in a table:

	Nominal	Ordinal	Interval	Ratio
Order	No	Yes	Yes	Yes
Interpretable Distance	No	No	Yes	Yes
True Zero	No	No	No	Yes

Some types of measurement levels can be transformed into others. The transformation can take place from the most complex to the least complex, never vice versa. And in the transformation, of course, we lose information.

Working with Data Using the Correct Tools

Here is a table that summarizes, for each scale, the allowed operations:

Scale	Can I order?	Differences?	Ratios?	Mean?
Nominal	✗	✗	✗	✗
Ordinal	✓	✗	✗	generally no
Interval	✓	✓	✗	✓
Ratio	✓	✓	✓	✓

We have seen how nominal or ordinal data are, in the traditional classification, qualitative data. Therefore, we cannot perform normal arithmetic operations on them or directly use statistical indices such as the mean, standard deviation, skewness, or kurtosis. However, we can use a series of non-parametric tools, such as contingency tables or the chi-squared test of independence.

For quantitative data, we obviously have the possibility to operate with the tools of basic arithmetic (we can add, subtract, multiply, divide), as well as take advantage of the possibility of calculating the mean, variance, standard deviation, kurtosis, and skewness. We also have parametric analysis tools at our disposal, such as correlation indices, regression calculations, and ANOVA.

For the distinction between parametric and non-parametric analysis tools, I refer you to this article.

Try it yourself

Now it’s your turn. Here are 5 common GA4 metrics. For each one, try to identify the corresponding scale of measurement:

• Users
• Country of origin
• Average SERP position
• Pages per session
• Bounce rate

Solution: Users and Pages per session are ratio measurements (they have a real zero and ratios make sense). Country of origin is nominal (categories cannot be ordered). Average SERP position is ordinal (there is an order but distance is not interpretable). Bounce rate is ratio (it is a ratio between two quantities, with a real zero).

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Before even choosing a statistical test, we must ask ourselves what type of data we have in front of us. Almost all errors in data analysis arise from this question asked too late.

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Now that we know how to distinguish the type of data we have in front of us, we can finally ask: how do we summarize a set of data into a single representative value?
This is the topic of measures of position (mean, median, mode), which we will cover in the next article. And — after the mistake we have seen today — one question is worth more than a thousand formulas: when does it make sense to use the mean, and when is the median the only correct choice?

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Further Reading

To dig deeper into how data is classified and measured — and why getting it right changes every analysis downstream — The Art of Statistics by David Spiegelhalter devotes remarkably clear pages to data and its collection.

For those who prefer a comprehensive university textbook with exercises and in-depth coverage of measurement scales and descriptive statistics, Statistica by Newbold, Carlson and Thorne (Italian MyLab edition) is the reference text for the foundations of statistical inference.