Adjustment of the protonorms to norms conversion - Old reports

Adjustment of the protonorms to norms conversion (males)

The procedure

A sample of tests is selected by these criteria:

• Heterogeneous contents (at least two different item types out of verbal, numerical, spatial, logical);
• Score distribution not distorted by strong floor or ceiling effects;
• There is confidence that the test's norms have a minimum quality.

The combined score distribution thus obtained is meant to be representative for candidates on serious high-range intelligence tests. A score distribution is derived, using all of the scores on the selected tests. "Proportions outscored" are computed for each protonorm, within-sex, to the number of decimals needed to retain the information of the distribution. Sex-combined proportions outscored are computed by taking for each protonorm the weighted mean of the female and male proportions outscored (weighted by numbers that form [a reduced fraction of] the female/male ratio among candidates on this sample of tests).

Below is the distribution.

Test-combined protonorm histogram with proportions outscored for males

In parenthesis the proportion outscored value for scores above the present score but lower than the next-higher score in the table.

n = 1831

Tests used

• Test of the Beheaded Man
• Cooijmans Intelligence Test - Form 3
• A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude
• The Nemesis Test
• The Sargasso Test
• Reflections In Peroxide
• Problems In Gentle Slopes of the third degree
• Combined Numerical and Spatial sections of Test For Genius - Revision 2010
• Reason Behind Multiple-Choice - Revision 2008
• The Marathon Test
• Test For Genius - Revision 2010
• Associative LIMIT
• Numerical and spatial sections of The Marathon Test
• Labyrinthine LIMIT
• Psychometrically Activated Grids Acerbate Neuroticism
• Narcissus' last stand
• Problems In Gentle Slopes of the second degree
• Cooijmans Intelligence Test - Form 4
• The Alchemist Test
• The Bonsai Test - Revision 2016
• Cooijmans Intelligence Test 5
• Test For Genius - Revision 2016
• Combined Numerical and Spatial sections of Test For Genius - Revision 2016
• The Piper's Test
• Dicing with death
• De Laatste Test - Herziening 2019
• Divine Psychometry
• Cartoons of Shock
• Low Countries Aptitude Test
• Problems In Gentle Slopes of the first degree
• The Hammer Of Test-Hungry
• Test of Shock and Awe
• Short Test For Genius
• Reason Behind Multiple-Choice
• Long Test For Genius
• Long Test For Genius (French)
• Long Test For Genius (Netherlandic)
• Test For Genius - Revision 2004
• Cooijmans On-Line Test
• Bonsai Test
• Cooijmans Intelligence Test - Form 1
• Cooijmans Intelligence Test - Form 2
• Giga Test
• Grail Test
• The Hammer Of Test-Hungry - Revision 2013

Adjustment of the protonorms to norms conversion (females)

The procedure

A sample of tests is chosen by these criteria:

• Heterogeneous contents (at least two different item types out of verbal, numerical, spatial, logical);
• The score distribution is not distorted by strong floor or ceiling effects;
• There is confidence that the test's protonorms have a minimum quality.

The combined score distribution thus obtained is meant to be representative for candidates on serious high-range intelligence tests. A score distribution is derived using all of the scores on the chosen tests. "Proportions outscored" are computed for each protonorm, within-sex, to the number of decimals needed to retain the information of the distribution (three in this case). Sex-combined proportions outscored are computed by taking, for each protonorm, the weighted mean of the female and male proportions outscored, weighted by numbers that form [a reduced fraction of] the female/male ratio among candidates on this sample of tests, which is 1/13. This ratio is somewhat smaller than it is in high-range tests on the whole (about 1/11) because females have a slightly higher tendency than males to prefer homogeneous over heterogeneous tests, while the latter make up most of this sample. To arrive at a more sizeable sample of female scores, three tests by other authors have been included in this adjustment (Bultas, Forsström, Meyers; the latter is the only exception to the "heterogeneous contents" rule).

Below is the distribution.

Test-combined protonorm histogram with proportions outscored for females

In parenthesis the proportion outscored value for scores above the present score but lower than the next-higher score in the table.

n = 160

Tests used

• Test of the Beheaded Man
• Cooijmans Intelligence Test - Form 3
• A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude
• The Nemesis Test
• Gliaweb Riddled Intelligence Test - Revision 2011
• The Sargasso Test
• Problems In Gentle Slopes of the first degree
• Reflections In Peroxide
• Problems In Gentle Slopes of the third degree
• Combined Numerical and Spatial sections of Test For Genius - Revision 2010
• Reason Behind Multiple-Choice - Revision 2008
• The Marathon Test
• Test For Genius - Revision 2010
• Associative LIMIT
• Numerical and spatial sections of The Marathon Test
• Labyrinthine LIMIT
• Psychometrically Activated Grids Acerbate Neuroticism
• Narcissus' last stand
• Problems In Gentle Slopes of the second degree
• Cooijmans Intelligence Test - Form 4
• The Alchemist Test
• The Bonsai Test - Revision 2016
• Cooijmans Intelligence Test 5
• Test For Genius - Revision 2016
• Combined Numerical and Spatial sections of Test For Genius - Revision 2016
• The Hammer Of Test-Hungry - Revision 2013
• Cartoons of Shock
• Female Intelligence Test
• Low Countries Aptitude Test
• The Hammer Of Test-Hungry
• Test of Shock and Awe
• Short Test For Genius
• Reason Behind Multiple-Choice
• Long Test For Genius
• Long Test For Genius (French)
• Long Test For Genius (Netherlandic)
• Test For Genius - Revision 2004
• Cooijmans On-Line Test
• Bonsai Test
• Cooijmans Intelligence Test - Form 1
• Cooijmans Intelligence Test - Form 2
• Giga Test
• Gliaweb Riddled Intelligence Test (old version)
• Chimera Test
• Culture Fair Numerical Spatial Examination - Final version
• Advanced Intelligence Test

Adjustment of the protonorms to norms conversion (males)

The procedure

A sample of tests is selected by these criteria:

• Heterogeneous contents (at least two different item types out of verbal, numerical, spatial, logical);
• Score distribution not distorted by strong floor or ceiling effects;
• There is confidence that the test's norms have a minimum quality.

The combined score distribution thus obtained is meant to be representative for candidates on serious high-range intelligence tests. A score distribution is derived, using all of the scores on the selected tests. "Proportions outscored" are computed for each protonorm, within-sex, to the number of decimals needed to retain the information of the distribution. Sex-combined proportions outscored are computed by taking for each protonorm the weighted mean of the female and male proportions outscored (weighted by numbers that form [a reduced fraction of] the female/male ratio among candidates on this sample of tests).

The Protonorms table shows the resulting norms. Below is the distribution.

Test-combined protonorm histogram with proportions outscored for males

In parenthesis the proportion outscored value for scores above the present score but lower than the next-higher score in the table.

n = 1237

Tests used

• Test of the Beheaded Man
• Cooijmans Intelligence Test - Form 3
• A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude
• Cooijmans On-Line Test - Two-barrelled version
• Laaglandse Aanlegtest - Herziening 2016
• The Nemesis Test
• The Sargasso Test
• Problems In Gentle Slopes of the first degree
• Reflections In Peroxide
• Problems In Gentle Slopes of the third degree
• Combined Numerical and Spatial sections of Test For Genius - Revision 2010
• Reason Behind Multiple-Choice - Revision 2008
• The Marathon Test
• Test For Genius - Revision 2010
• Associative LIMIT
• Numerical and spatial sections of The Marathon Test
• Labyrinthine LIMIT
• Psychometrically Activated Grids Acerbate Neuroticism
• Narcissus' last stand
• Problems In Gentle Slopes of the second degree
• Cooijmans Intelligence Test - Form 4
• The Alchemist Test
• The Bonsai Test - Revision 2016
• Cooijmans Intelligence Test 5
• Test For Genius - Revision 2016
• Combined Numerical and Spatial sections of Test For Genius - Revision 2016
• Cartoons of Shock
• The Hammer Of Test-Hungry
• Test of Shock and Awe
• Short Test For Genius
• Reason Behind Multiple-Choice
• Long Test For Genius
• Long Test For Genius (French)
• Long Test For Genius (Netherlandic)
• Test For Genius - Revision 2004
• Bonsai Test
• Cooijmans Intelligence Test - Form 1
• Cooijmans Intelligence Test - Form 2
• Giga Test
• Grail Test

Adjustment of the protonorms to norms conversion (females)

The procedure

A sample of tests is chosen by these criteria:

• Heterogeneous contents (at least two different item types out of verbal, numerical, spatial, logical);
• The score distribution is not distorted by strong floor or ceiling effects;
• There is confidence that the test's protonorms have a minimum quality.

The combined score distribution thus obtained is meant to be representative for candidates on serious high-range intelligence tests. A score distribution is derived, using all of the scores on the chosen tests. "Proportions outscored" are computed for each protonorm, within-sex, to the number of decimals needed to retain the information of the distribution. Sex-combined proportions outscored are computed by taking for each protonorm the weighted mean of the female and male proportions outscored (weighted by numbers that form a reduced fraction of the female/male ratio among candidates on this sample of tests; this ratio is 74/872, reduced to 37/436).

The Protonorms table shows the resulting norms. Below is the distribution.

Test-combined protonorm histogram with proportions outscored for females

In parenthesis the proportion outscored value for scores above the present score but lower than the next-higher score in the table.

n = 74

Tests used

• Test of the Beheaded Man
• Cartoons of Shock
• Cooijmans Intelligence Test - Form 3
• A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude
• Female Intelligence Test
• Cooijmans On-Line Test (Two-barrelled)
• Low Countries Aptitude Test
• The Nemesis Test
• Gliaweb Riddled Intelligence Test - Revision 2011
• The Sargasso Test
• Problems In Gentle Slopes of the first degree
• Intelligence Quantifier by assessment
• Reflections In Peroxide
• Reason Behind Multiple-Choice - Revision 2008
• The Marathon Test
• Test For Genius - Revision 2010
• Associative LIMIT
• Labyrinthine LIMIT Test
• Psychometrically Activated Grids Acerbate Neuroticism
• Narcissus' last stand
• The Hammer Of Test-Hungry
• Test of Shock and Awe
• Short Test For Genius
• Reason Behind Multiple-Choice
• Long Test For Genius
• Long Test For Genius (French)
• Long Test For Genius (Netherlandic)
• Test For Genius - Revision 2004
• Cooijmans On-Line Test
• Bonsai Test
• Cooijmans Intelligence Test - Form 1
• Cooijmans Intelligence Test - Form 2
• Giga Test
• Grail Test

Adjustment of the protonorms to norms conversion

The procedure

A sample of tests is chosen by these criteria:

• Heterogeneous contents (at least two different item types out of verbal, numerical, spatial, logical; in this criterion lies the main difference with the previous adjustment, wherein homogeneous tests were used as well as heterogeneous ones);
• The score distribution is not distorted by strong floor or ceiling effects;
• There is confidence that the test's protonorms have a minimum quality.

The combined score distribution thus obtained is meant to be representative for candidates on serious high-range intelligence tests. Separate score distributions are derived for females and males, using all of the scores on the chosen tests. "Proportions outscored" are computed for each protonorm, within-sex, to the number of decimals needed to retain the information of the distribution. Sex-combined proportions outscored are computed by taking for each protonorm the weighted mean of the female and male proportions outscored (weighted by numbers that form a reduced fraction of the female/male ratio).

The Protonorms table shows the resulting norms. Below are the distributions.

Test-combined protonorm histogram with proportions outscored for females

In parenthesis the proportion outscored value for scores above the present score but lower than the next-higher score in the table.

n = 54

Test-combined protonorm histogram with proportions outscored for males

In parenthesis the proportion outscored value for scores above the present score but lower than the next-higher score in the table.

n = 730

Tests used

• Test of the Beheaded Man
• Cartoons of Shock
• Cooijmans Intelligence Test - Form 3
• A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude
• Cooijmans On-Line Test (Two-barrelled)
• The Nemesis Test
• The Sargasso Test
• Problems In Gentle Slopes of the first degree
• Intelligence Quantifier by assessment
• Reason Behind Multiple-Choice - Revision 2008
• The Marathon Test
• Test For Genius - Revision 2010
• Associative LIMIT Test
• Numerical and spatial sections of The Marathon Test
• Labyrinthine LIMIT Test
• Psychometrically Activated Grids Acerbate Neuroticism
• Narcissus' last stand
• The Hammer Of Test-Hungry
• Test of Shock and Awe
• Short Test For Genius
• Reason Behind Multiple-Choice
• Long Test For Genius
• Long Test For Genius (French)
• Long Test For Genius (Netherlandic)
• Test For Genius - Revision 2004
• Bonsai Test
• Cooijmans Intelligence Test - Form 1
• Cooijmans Intelligence Test - Form 2
• Giga Test
• Grail Test

Adjustment of the relation between protonorms and I.Q.

A smoothening toward linearity has been applied on the local scale without significantly changing the norms on cardinal points or on the larger scale. As a result, the I.Q. distribution has regained its original irregularity (which had been retained by the protonorm distribution), with locally sharp differences between occurrence frequencies of neighbouring I.Q.s. In the 2009 adjustment these irregularities had been straightened out by forcing the distribution into a shape (the "10 000 model", which incidentally is not a "normal" distribution or "bell curve") with (above the mode) gradually declining numbers of scores per I.Q. slot. This approach has been discontinued in anticipation of a better way to norm protonorms to I.Q.s.

For clarity, note the paradox: A more linear relation between protonorm and I.Q. results in an irregular I.Q. distribution; a less linear relation between protonorm and I.Q. is needed to obtain a regular I.Q. distribution.

Adjustment of the protonorms to norms conversion

The procedure

A large sample of tests is chosen, such that the 1455 scores thereon are representative for the performance of candidates on true, serious high-range intelligence tests. Separate score distributions are derived for females and males, using all of the scores on the chosen tests. "Proportions outscored" are computed for each protonorm, within-sex, to four decimals to retain the full information of the distributions. Sex-combined proportions outscored are computed by taking for each protonorm the weighted mean of the female and male proportions outscored (weighted by the numbers of females [110] and males [1345]).

The sex-combined proportions outscored are linked to I.Q.s using the "10 000" model of the high-range population. General population proportions outscored are linked to the I.Q.s using the "normal distribution". Note that the I.Q.s obtained such are fully liberated from those of regular psychology, childhood tests, or other high-range test designers. They are normed directly on the high-range population, and any required correction to a score level needs to be made in one place only (the "10 000" model).

The Protonorms table shows the current norming.

Female distribution

Male score distribution

The tests used

Abbreviations are used to save space:

a_10, an1, an1_nl, ass, ass_nl, bonsai, cart, cit, cit2, dlt, fin, gat, giga, lcat, limit, ltfg, ltfg_f, ltfg_nl, nem, nit, num, odds, pigs1, pq, qmc4, reason, shock, sit, stfg, sth, tfg, tteat.

The March 2007 adjustment

From 1995 to early 2007, the IQ norms of my tests have been established by anchoring tests to each other and to other tests through rank equation of their shared score pairs. The statistical reports have always given full insight into that procedure. As a result, the IQs from the tests have become comparable across tests, and more or less in accordance with IQs from American high-range tests. I have no way to verify the absolute height of the IQs against any population.

Next to IQ norms, I have in more recent years provided high-range norms based directly on the group of high-range candidates, in the form of "proportion outscored". These are obtained by combining all of the scored IQs from a representative selection of my tests. The advantage of these norms over IQs is that they do indicate a score's standing among a population with certainty.

To allow for readjustment of the height of the IQ norms, I have in March 2007 invented protonorms as a step in between raw scores and norms. Protonorms are generalized raw scores that allow comparison between scores on all of my tests, but do not contain information as to where that score stands in any population; they are not standard scores or quantiles. From now on, tests will be normed to protonorms in exactly the same way as they have been normed to IQs before. The initial formula to derive protonorms from the IQs of the before-protonorm era is as follows:

Protonorm = ((IQ - 80)/15) × 100

Thanks to this, a readjustment of the protonorm-IQ relation requires change in one table only, and not in every singly test norm table that still contains IQs. To avoid confusion: the above formula will NOT change when the protonorm to IQ conversion table is adjusted.

Mid-March 2007 I have adjusted the relation between protonorms and IQs, and renormed the proportion of high-range candidates outscored. For this purpose I have combined the protonorms from a number of my tests, yielding exactly 1200 scores in total. The used tests are:

• Test of the Beheaded Man
• Cartoons of Shock
• CIT Forms 1 and 2
• De Laatste Test
• The Final Test
• Genius Association Test
• Reason Behind Multiple-Choice
• LIMIT
• The Nemesis Test
• Numbers
• Odds
• QMC #4
• Reason
• Test For Genius (Short, Long, Revision 2004, Netherlandic and French)
• The Test To End All Tests
• Spatial Insight Tests
• Space, Time and Hyperspace
• A-10
• Analogies #1
• Bonsai Test
• De Gigatest
• Numerical Insight Test

The proportion of high-range candidates outscored in the protonorms to norms conversion table is based directly on these 1200 scores. The number of decimals to which the proportion is expressed is always chosen so that each value is distinguished from the previous and next different values, and the proportions therefore form a true reflection of the score distribution.

The main features of the distribution are the mode (protonorm 367) and the top (673). Really there is a modal range from 367 to 387. The modal range corresponds to IQs 135 to 138. The top to IQ 181. These are old IQs, from before the present adjustment.

Also characteristic are certain near-vacuums, such as that from 513 to 547. I have been looking at those vacuums for years already, and they have remained stable. I have been wondering if they are a real phenomenon in the population or an artifact of the tests, and for the moment I am assuming they are an artifact. I am not going into the possible exact causes of such an artifact in this report.

Below the modal range there are clearly less scores in a steeply declining curve, as a result of the tests' being too difficult for people below a certain level. In the past I would have thought this could be due to people being preselected through Mensa membership, but nowadays with everything going via the Internet this does not apply any more, so it must be the test difficulty. The modal range is apparently where the high-range distribution "touches" the Bell curve of the total population, and starts declining gradually. The high-range distribution itself is NOT a Bell curve, but an asymmetric wedge, whereby the decline from mode to top is close to linear and not significantly concave or convex.

I adjusted the modal range downward by about three IQ points, so to 132-135. I cannot verify this with certainty but I believe this brings the IQs in line with the Western European population, which is a few points of IQ smarter than the US population, that (the latter) formed the basis of the norms of a lot of high-range tests in the past. Support for this three-point correction lies in the reported scores of candidates on the Nonverbal Cognitive Performance Examination - E, by Xavier Jouve. These scores show that my old IQs are about one to two points too high in the range below about IQ 146. I put it at three to compensate for the fact (observed by me) that candidates tend to withhold their lower scores and only report their higher scores. Naturally, this correction pushes the scores below the mode down by a few points as well.

Also, I adjusted the top IQs downward to 175. Again I have no way to verify this at this moment, but a consideration is that, as I have learnt over the past years, the distribution of intelligence over the world is uneven, and the world average IQ is not is not 100 but probably below 90. This means that the highest IQs to expect with norms based on a Western population are much lower than I thought in the past, and probably between 180 and 185. So the lowering to 175 is conservative, and if in say five years from now no one has scored above the current top scores, I will adjust them upward again to around 180. There is no other way of finding out the correct height of those top scores; I will have to wait and see if the current top scores are already from the smartest people, or if the real top dogs are still to come. After some time I will conclude that the then top scores are from the smartest people, and norm them accordingly. Until then I will keep the norms conservative.

Then, I smoothened the decline from mode to top. That is, I redistributed the protonorms over the IQs so that the number of scores in each IQ slot declines smoothly by about .9 score per IQ point. It could not be made perfectly smooth on the level of single IQs, but by balancing out adjacent IQs it is close to smooth on the level of two-IQ classes. As a result of this smoothening, IQs have not come down three points rigidly, and in fact in the range of roughly 140-169 they have at some points remained about the same or even got higher. The Glia Society admission level has stayed virtually the same (protonorm 442, IQ 147).

Above the top scores I kept the initial protonorm-IQ relation from IQ 190 on, and made a smooth path to that from 176 upward. So for the Giga and Grail Societies and Isis, all of the old IQ norms remain valid.

Below the mode I smoothened the decline similarly to that from mode to top, except that there are four different slopes there instead of one: there is a steep slope from IQ 132 to 121 (a drop of about three scores per IQ point); a gradual slope from 121 to 116 (about one score per point); a shallow slope from 116 to 106 (about .2 scores/point); and a very shallow slope from 106 to the low 90s (about .04 scores/point).

Below the actual distribution of 1200 scores in protonorms; protonorms with no scores are left out.

Finally, here is a model of the high-range population by IQ (not the actual current distribution):

The "10 000" model of the high-range population

To show in more detail how the high-range distribution may lie relative to adult population IQ, here is a table of a hypothetical sample of 10 000 candidates representative for the high-range test-taking population. The columns show the number of candidates out of these 10 000 for each IQ, the cumulative number up to that IQ, and the (range of) "proportion outscored" that would belong to that IQ.

For better understanding: The purpose of a table like this is to aid in providing an IQ as additional information next to the proportion of high-range candidates outscored, which (the latter) I see now as the primary and most important score from my tests. These high-range proportions are now obtained directly from the protonorm distribution, independently of possible IQs from prior tests. The protonorms have been "liberated" from the concept of "IQ".

The high-range proportions obtained from the protonorm distribution can be looked up in the fourth column of a table as below to find an IQ for additional information, the exact relation between proportions and IQs being less important than the proportions themselves.

[Older reports on the high-range score distribution] [Old report on the sex score difference]