Data Types & Measurement Levels

The first split: qualitative and quantitative

Qualitative data sorts things into groups; quantitative data measures how much of something there is. Blood type and region are qualitative. Height and revenue are quantitative. You count the first kind and you measure the second.

Quantitative data then splits again, into discrete and continuous. Number of children is discrete — there is nothing between two and three. Body weight is continuous, because there are infinitely many values between 62.4 kg and 62.5 kg.

The four levels of measurement

The more useful distinction is the four-rung ladder Stevens laid out. Each rung up, the number promises you more.

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  Nominal — a label, nothing else. Blood type, region, brand, sex. No order, no spacing.
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  Ordinal — order is real, spacing is unknown. Rank, letter grade, satisfaction, income bracket.
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  Interval — the gaps are equal but zero was chosen by someone. Celsius, calendar year, IQ, z-scores.
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  Ratio — zero means "none at all". Length, weight, duration, revenue, counts.

What each level lets you do

Every rung unlocks one more operation, and the unlocks are cumulative: anything legal lower down stays legal higher up, never the reverse.

The level decides the method

"Which test should I use?" is almost always answered by the measurement level of the variables. This is precisely why software cannot choose for you: from the digits alone, nothing distinguishes a ZIP code from a revenue figure.

What goes wrong, and how quietly

Assume the wrong level and the computation still succeeds. That silence is the dangerous part. The output is a plausible-looking number, so nobody thinks to question it.

You can go down the ladder, never up

Age is ratio; bucket it into 20s, 30s and 40s and it becomes ordinal. You lose information, but nothing breaks. The reverse is impossible. From "in their 20s" you cannot recover the age, and the moment you assume "call it 25" you have invented data that was never collected.

The same rules govern machine learning

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  Nominal — one-hot encode. Feed the raw codes in and the model will read an order that was never there.
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  Ordinal — integer-encode in a way that preserves the order. One-hot encoding throws that order away.
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  Interval and ratio — use as they are, or standardise. Distance-based algorithms need the scaling.
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  High-cardinality nominal — with thousands of categories, like ZIP codes or SKUs, one-hot stops being viable and target encoding takes over.

1. Three questions, in order

Ask them in sequence and every column lands on exactly one rung.

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  Can the values be ranked? If not, you are done — it is nominal.
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  Are the gaps equal? Is the distance from 1st to 2nd the same as from 2nd to 3rd? If not, it is ordinal.
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  Does zero mean "none"? If not, interval. If so, ratio.

2. The columns that pretend to be numbers

Almost every real-world mistake happens in one of two places: columns stored as numbers that are not quantities at all, and columns that look interval but are only ordinal.

3. What to do about Likert scales

A "1 = strongly disagree … 5 = strongly agree" scale is, strictly, ordinal: nothing guarantees that the distance from 1 to 2 matches the distance from 4 to 5. And yet everybody averages them. So what should you actually do?

The question is not really whether to use a mean. It is whether to use only a mean. Show the distribution alongside it and most of the objection evaporates.

4. Settle it once, at the start

Write down the level of every column the moment the data lands, and every later decision falls out of that table on its own.

In practice: three restaurants, all rated 3.0

Three restaurants on a delivery app hold an average rating of exactly 3.00, from thirty reviews each. On the app they are indistinguishable.

Shop A disappointed nobody and delighted nobody. Shop C is half five-star, half one-star. Filing those two under "a three-star place" is plainly wrong — and that is exactly what the mean does.

A distribution like C's usually means something specific: quality that depends on which dish you order, food that survives some delivery zones and not others, or a batch of planted reviews. Reading only the mean, you would have filed the whole thing under "average".

In practice: taking one survey apart

Sort the questions on an ordinary customer survey by level, and the available analyses assign themselves.

Notice that "age bracket" and "age in years" sit side by side. Same underlying fact, different level, different toolkit. Always collect the raw age if you can — bucketing it later is free, and unbucketing it is impossible.

Common misunderstandings

Find out where each scale keeps its zero

Below, three units are drawn along a single physical axis. Choose temperature and their three zeros land in three different places; choose weight and they land on the same one. The B ÷ A column is the consequence.

What to look for

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  With A = 10°C and B = 20°C, what multiple does each unit report?
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  Why is the Kelvin multiple the one closest to 1?
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  Switch to weight — why do all three multiples become identical?
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  Swap A and B around and check the property still holds.
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  B − A differs by unit too, so why are differences still safe to compare?