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.

[Old versions of this report]