The IQ scale: the official Swiss classification of intelligence values

An IQ table is quickly found, and most of the ones circulating online are either copied out inaccurately or come from another country. For Switzerland there is an official professional recommendation: the classification of intelligence values published by SPILK in 2023. To this day it exists only as a PDF. Here it is as a readable table, with all three figures that belong to it.

After that come the questions a table on its own does not answer: why 100 and 15 are conventions, what a percentile rank does better than an IQ score, why the broad middle band is called a normal variant of all things, and why any value without a confidence range is incomplete.

The Swiss classification of intelligence values

The classification further provides for the band from 85 to 114 to be split into a lower, a middle and an upper part. That is not a detail. Between 85 and 114 lie 29 points, and within that span lie two thirds of all results. Without the split, the statement “average” would be the only thing the table yields for most people.

Where this table comes from

The publisher is SPILK, the inter-cantonal leadership conference of Swiss school psychology, which brings together the heads of the cantonal school psychology services and publishes on schulpsychologie.ch. This matters for placing the document. In Switzerland education is a cantonal matter, and each of the 26 cantons runs its own Schulpsychologischer Dienst, the school psychology service that assesses pupils free of charge. SPILK is the body through which those cantonal services agree on common professional practice. The table is therefore a professional recommendation for the working practice of Swiss services, not a private compilation.

Anyone reading a classification out of a Swiss report reads it against this table. If your child has been assessed by the cantonal service and the report places the result in a band, that band is almost certainly one of the five above.

Two things stand out on a close look. First, the classification rounds: arithmetically an IQ of 130 corresponds to percentile rank 97.7, not to “above 98”. Second, the boundaries are set rather than found. There is no natural edge between 114 and 115. The categories are a means of communication between professionals, not a property of the thing being measured.

Why a table on its own is not enough

A classification places values, but it does not produce them. For a value to fit into a row at all, three pieces of information are needed that the table does not contain: which instrument was used, on which reference sample that instrument was normed, and from which year that norm dates.

If one of the three is missing, a number cannot be placed. In practice this affects the most common situation of all: someone has received a value online somewhere, then looks for a table and lays the two on top of each other. The outcome looks like a classification but is not one, because the reference quantity is unknown.

The classification is therefore not a tool for interpreting a number you happen to have found. It is a tool for reading a value that arrived together with its details.

Splitting the middle band

The classification provides for the band from 85 to 114 to be divided in three, but the table itself sets no cut-off points. So if a report says “lower average range”, that is a sensible refinement, but not one that can be recalculated from outside.

From this follows a concrete question for a feedback session: which boundaries underlie this assignment. Two reports can use the same wording and mean different cut-off points, and the difference can amount to several points.

The usefulness of the three-way split is nonetheless considerable. Without it, a span of 29 points and two thirds of all people collapses into a single word. A result of 87 and one of 113 then carry the same label, although about 60 percentile rank points lie between them. Anyone reading a classification that says only “average” has received less information than the classification actually offers.

Why 100 and 15 are conventions

A metre is defined, but it is also measurable: you can measure a distance with it and arrive at the same result regardless of the measuring device. For intelligence there is no such unit. There is no zero point, no reference length and no way of stating an absolute quantity.

The IQ scale therefore works differently. An instrument is tried out on a sample, the raw points are counted, and the distribution is then converted so that its mean is 100 and its spread 15 points. Both numbers are conventions inherited from habit. Had a spread of 10 become established historically, the same position would carry a different number today.

Two consequences follow, and you have to keep both in mind whenever you read an IQ table. First, an IQ score always measures relative to a reference sample, never absolutely. Second, an average of 100 is not a finding but a precondition: it is put in during norming, not discovered.

What the T value in the table means

Swiss reports often give sub-results as T values rather than IQ scores. The T value carries the same information in a different unit: mean 50, spread 10. The conversion is one line:

T = 50 + 10 * (IQ - 100) / 15

An IQ of 115 lies one spread above the mean and therefore gives a T value of 60. An IQ of 85 lies one spread below and gives 40. That is exactly what the table above says, and anyone who knows the conversion can see at once whether a table they have found is internally consistent. Many of the ones in circulation are not.

The reason for the second unit is practical. For sub-areas of an instrument, an IQ-like value would be misleading, because it looks like an overall result. The T value signals that a single area is being described.

The percentile rank says more than the IQ score

The percentile rank names the share of the reference group that reaches the same result or a lower one. Percentile rank 84 means: 84 out of 100 people in the comparison group reach this value or less, 16 lie above it. That can be read without any knowledge of scales and spreads, and it is the figure that actually carries meaning in a conversation.

The IQ score, by contrast, has a property that almost everyone underestimates: equal distances on the scale mean very unequal distances in rank.

Between 100 and 110 lie ten points, and whoever takes that step leaves about 25 people in 100 behind. Between 130 and 140 there are likewise ten points, but the step corresponds to only about two in 100. The same number means something entirely different at the two ends of the scale. The percentile rank shows that immediately; the IQ score hides it.

Why 85 to 114 is called a normal variant

The wording of the Swiss classification is more careful at this point than what everyday use makes of it. The band from 85 to 114 is not called merely “average” there but Normvariante, durchschnittliche Intelligenz, a normal variant, average intelligence. Normal variant means an expression within the ordinary range of spread: something that calls for no explanation because it is the rule.

Arithmetically this band covers roughly two thirds of all people, from percentile rank 16 to 83. It is therefore not the middle of a table but the table itself, for the great majority. Everything outside it is the special case.

In everyday speech “average” sounds like a verdict, like a label between good and bad. In the classification it is a pure statement of position within a distribution, nothing more. Someone who receives a value of 103 does not have a weak result. They have a result that sits, together with two thirds of all people, in the band the professional recommendation expressly calls the normal case.

That is precisely why the intended split into a lower, middle and upper part is useful. It stops a span of 29 points collapsing into a single word.

A value without a confidence range is incomplete

This is our core position, and it is the reason the result page at Kognita looks different from that of most online tests. It holds regardless of the provider: even a carefully obtained value from a long, supervised procedure remains an estimate. The only difference is how wide the range turns out to be, not whether there is one.

What a confidence range is

A test result is an estimate, not a reading off a gauge. The same person, tested on two days with the same instrument, gets two different numbers. That is not down to a fault in the procedure but to the fact that a limited number of tasks can only approximate an ability. On top of that come daily form, tiredness, distraction and practice from an earlier run.

The confidence range makes this blur visible. A 95 per cent interval says: if you repeated the measurement very often and formed such an interval each time, 95 out of 100 of those intervals would contain the true value. It is not a cautious formula and not small print; it is as much part of the result as the number in front of it.

A comparison helps in placing it. Nobody would take an election forecast without a margin of error seriously, and with a survey of 1000 respondents everyone expects the note that the value may move by a few points. With a test result that note is almost always missing, although the uncertainty there is greater.

How wide the interval actually is

For our short test with 30 tasks the standard error is 6.4 points, measured across 4‘000 simulated runs. The 95 per cent interval is therefore about 25 points wide. Someone who scores 112 lies, with 95 per cent confidence, roughly between 100 and 124. Even reporting a single standard error width still gives a span of around 13 points.

These figures are not a guess into the blue. The procedure was recalculated on 4,000 simulated people with known true values: the mean deviation between the true and the estimated value is about 6.5 points, and the reported 95 per cent interval contains the true value in 94.3 per cent of cases against a nominal 95. It therefore covers slightly less than its name promises, and that belongs here too. The full set-up is on the method page.

Anyone who then quotes a point value to the nearest unit is acting as though this uncertainty did not exist. A result of “118” reads like a reading off an instrument. A result of “118, confidence range 103 to 133” reads like what it is.

What that means for placing a value in the table

The blur affects not only the number but the label as well. A measured value of 112 falls in the normal variant band. Its confidence range, however, reaches up to 127 and therefore well into the band of high, above average intelligence. The category is thus exactly as uncertain as the value.

The least load-bearing statements are those close to a category boundary. A result of 114 and one of 115 sit in different rows of the table. Yet they differ by a single point, while the standard error of the procedure is 6.4 points. Anyone who draws a conclusion from that one point is reading noise.

From this follows a simple rule for reading: check first whether the confidence range crosses a category boundary. If it does, the category is not information but a rounding.

Why the edges of the scale carry less than the middle

A bell curve is thick in the middle and thin at the edges, and that has a consequence most tables do not show: an instrument measures most precisely where most people and most tasks are, that is in the middle. The further a result moves outwards, the fewer tasks of matching difficulty are available and the coarser the estimate becomes.

That is why we do not report values below 55 and above 145 as numbers but as “below 55” and “above 145”, with the note that a test with 30 tasks no longer separates there. A reported 152 would be no more precise than “above 145”; it would only look that way.

Shrinkage towards the middle

There is a second effect. The estimation procedure assumes that the ability is normally distributed in the population, and that assumption feeds into the estimate. Extreme results are therefore reported more cautiously than the raw answers suggest.

This becomes visible in the spread of the reported values: it comes out at 12.8 rather than 15. So someone who solves 30 out of 30 tasks does not get the highest conceivable value but one that takes the thin data at the edge into account. That is intentional, because an extreme value out of 30 tasks is usually noise and not signal.

The same shrinkage explains a result we publish gladly, because it protects the reader: anyone who clicks through at random does not get an average value. The median of such runs is IQ 67 with a spread of 4.6 points, and in 85.3 per cent of these cases the scoring additionally reports chance level. A test that hands 100 to somebody who read nothing measures nothing at all. These figures come from the same simulation as those above and are on our method page, which also gives the date of the last measurement.

For reading a table this means something that runs against intuition. A striking value far out looks like the most interesting piece of the whole result. In fact it is the most uncertain, and the further out it lies, the more that holds.

Comparing two instruments: only through the percentile rank

The most common question after a second test is why the number has changed. Usually it is not the day that differs, but the fact that the two numbers do not mean the same thing at all.

Three things differ between two instruments. First the reference sample: people who voluntarily fill in an online test form a different group from a sample drawn for norming. Second the norming year, because norms shift across decades. Third the content, because a purely figural test measures something other than one with a language section.

Each of these three can move the result by several points, and they act independently of one another. Subtracting two numbers from two sources and interpreting the difference assumes that all three agree. That is almost never the case, and usually nowhere does it say whether it is.

Why the spread shifts the rank

There is a fourth point that is easy to miss: not every instrument works with the same spread. A worked example makes it clear. Suppose an instrument sets the spread to 24 instead of 15. A value of 130 then lies only 1.25 spreads above the mean and corresponds to percentile rank 89, not 98. The same number, an entirely different position.

This is not hair-splitting. It is the most frequent reason why a value from one source does not fit a table from another. Anyone wanting to place a number therefore always needs to know which spread it refers to. If that is stated nowhere, the number cannot be placed, however precise it looks.

The percentile rank sidesteps the problem because it is defined without a scale unit. It names a position in a group, and positions can be compared even when the measuring devices differ. That is not entirely clean either, since the groups themselves remain different. But it is the only comparison that has any shared meaning at all.

Reading a result in five steps

1. Look for the percentile rank, not just the IQ score. If it is missing, the most important figure has not been reported.
2. Look for the confidence range. If it is missing, the result is incomplete, no matter how precise the number looks.
3. Check the reference group and the norming year. Without both, the value can neither be placed nor compared with another.
4. Check what was measured. Five areas including a language section give a different picture from a purely figural short test.
5. Watch for edge positions. If the value sits near a category boundary, the label says less than the number.

These five points double as a usable checklist for the provider’s page itself. An offer that makes none of the five statements usually does so because it cannot.

What our test reports

Kognita has 30 tasks in 25 minutes, across five areas: figural matrices, number series, verbal analogies, spatial imagination and deductive reasoning. Scoring runs through an item response theory model with a guessing correction, which means that the difficulty of each individual task enters the estimate.

Every result is reported with a percentile rank and a 95 per cent confidence range. We do not report values below 55 or above 145, because a test with 30 tasks no longer separates there. Sub-areas are rounded to steps of five, because a precise number based on six tasks would be invented precision.

And the most important limitation: our reference quantity is a provisional reference distribution and not a representative Swiss norming sample. People who voluntarily fill in an intelligence test on the internet are not randomly selected. As long as that is the case, the reference quantity remains an assumption, and we write that on every result. Mensa Schweiz, the Swiss branch of the international high-IQ society, does not accept unsupervised online tests in any case, ours included.

We should also say plainly what we are. Kognita is an editorial team with a test procedure we built ourselves. In Switzerland an intelligence test may only be administered by someone with a recognised psychology degree, the professional title is protected by law, and the FSP specialist title of the Federation of Swiss Psychologists marks a recognised practitioner. We hold none of that, we carry out no assessments, and nothing from us can be submitted anywhere.

A table is a tool for placing a result, not a verdict on a person. It says where a result sits in a distribution. It says nothing beyond that, and the good reports are exactly the ones that write that down as well.