# Adjustment of the protonorms to norms conversion

© 2 February 2023 Paul Cooijmans

## 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); homogeneous tests are excluded because they do not provide a good enough indication of I.Q. in their own right;
• Score distribution not distorted by strong floor or ceiling effects (Isis Test and Evens are left out therefore).

The combined score distribution thus obtained is meant to be representative for candidates on serious high-range intelligence tests that, each on their own, provide a fair indication of one's I.Q. 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 the numbers of female and male candidates on this sample of tests. The male/female ratio here is close to 17, while on high-range tests in general it is closer to 11; this is because females avoid heterogeneous tests more than do males.

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.

ScoreProp.# scores (* = 1 score)
970.004 (0.007) *
1350.011 (0.015) *
1550.018 (0.022) *
2070.026 (0.029) *
2400.033 (0.037) *
2640.040 (0.044) *
2670.048 (0.051) *
2680.055 (0.059) *
2720.063 (0.066) *
2810.074 (0.081) **
2820.085 (0.088) *
2830.103 (0.118) ****
2860.121 (0.125) *
2910.129 (0.132) *
2970.136 (0.140) *
2980.143 (0.147) *
2990.151 (0.154) *
3000.162 (0.169) **
3020.176 (0.184) **
3030.191 (0.199) **
3040.202 (0.206) *
3050.210 (0.213) *
3070.217 (0.221) *
3080.232 (0.243) ***
3090.246 (0.250) *
3100.261 (0.272) ***
3130.276 (0.279) *
3140.287 (0.294) **
3160.298 (0.301) *
3180.305 (0.309) *
3210.313 (0.316) *
3280.320 (0.324) *
3330.335 (0.346) ***
3350.349 (0.353) *
3400.360 (0.368) **
3440.371 (0.375) *
3490.379 (0.382) *
3570.386 (0.390) *
3610.393 (0.397) *
3620.404 (0.412) **
3640.423 (0.434) ***
3650.438 (0.441) *
3670.445 (0.449) *
3680.460 (0.471) ***
3700.474 (0.478) *
3740.482 (0.485) *
3760.493 (0.500) **
3790.504 (0.507) *
3800.515 (0.522) **
3810.529 (0.537) **
3860.540 (0.544) *
3870.555 (0.566) ***
3890.570 (0.574) *
3900.577 (0.581) *
3930.585 (0.588) *
3950.592 (0.596) *
3960.603 (0.610) **
3970.625 (0.640) ****
4010.643 (0.647) *
4040.662 (0.676) ****
4140.680 (0.684) *
4160.688 (0.691) *
4250.699 (0.706) **
4260.713 (0.721) **
4280.728 (0.735) **
4330.739 (0.743) *
4360.746 (0.750) *
4390.754 (0.757) *
4400.761 (0.765) *
4410.768 (0.772) *
4420.776 (0.779) *
4430.783 (0.787) *
4460.794 (0.801) **
4530.805 (0.809) *
4570.816 (0.824) **
4580.827 (0.831) *
4590.835 (0.838) *
4780.842 (0.846) *
4840.849 (0.853) *
4860.857 (0.860) *
4870.868 (0.875) **
4930.879 (0.882) *
4940.886 (0.890) *
4980.897 (0.904) **
5100.908 (0.912) *
5180.915 (0.919) *
5290.923 (0.926) *
5410.930 (0.934) *
5550.938 (0.941) *
5630.945 (0.949) *
5690.952 (0.956) *
5800.960 (0.963) *
5880.967 (0.971) *
6100.974 (0.978) *
6500.982 (0.985) *
6590.989 (0.993) *
6740.996 (1.000) *

n = 136

## 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.

ScoreProp.# scores (* = 1 score)
970.0002 (0.0004) *
1070.0007 (0.0009) *
1100.0011 (0.0013) *
1130.0015 (0.0017) *
1140.0020 (0.0022) *
1310.0024 (0.0026) *
1470.0028 (0.0031) *
1490.0033 (0.0035) *
1500.0039 (0.0044) **
1510.0048 (0.0052) **
1530.0054 (0.0057) *
1550.0063 (0.0070) ***
1560.0074 (0.0078) **
1570.0085 (0.0092) ***
1610.0094 (0.0096) *
1650.0098 (0.0100) *
1670.0107 (0.0113) ***
1730.0116 (0.0118) *
1790.0126 (0.0135) ****
1900.0142 (0.0148) ***
1910.0150 (0.0153) *
1920.0155 (0.0157) *
2000.0161 (0.0166) **
2060.0168 (0.0170) *
2100.0172 (0.0174) *
2110.0177 (0.0179) *
2200.0187 (0.0196) ****
2330.0209 (0.0222) ******
2450.0224 (0.0227) *
2490.0229 (0.0231) *
2520.0233 (0.0235) *
2530.0238 (0.0240) *
2540.0242 (0.0244) *
2550.0251 (0.0257) ***
2590.0259 (0.0262) *
2610.0268 (0.0275) ***
2630.0277 (0.0279) *
2640.0283 (0.0288) **
2660.0290 (0.0292) *
2670.0294 (0.0296) *
2680.0310 (0.0323) ******
2690.0331 (0.0340) ****
2710.0342 (0.0344) *
2720.0349 (0.0353) **
2730.0357 (0.0362) **
2740.0364 (0.0366) *
2750.0371 (0.0375) **
2760.0377 (0.0379) *
2770.0381 (0.0384) *
2780.0403 (0.0423) *********
2790.0429 (0.0436) ***
2800.0453 (0.0471) ********
2810.0482 (0.0493) *****
2820.0499 (0.0506) ***
2830.0530 (0.0554) ***********
2860.0562 (0.0571) ****
2870.0575 (0.0580) **
2900.0582 (0.0584) *
2910.0586 (0.0588) *
2920.0591 (0.0593) *
2930.0599 (0.0606) ***
2940.0608 (0.0610) *
2950.0615 (0.0619) **
2960.0621 (0.0623) *
2970.0639 (0.0654) *******
2980.0656 (0.0658) *
2990.0680 (0.0702) **********
3000.0724 (0.0745) **********
3020.0756 (0.0767) *****
3030.0769 (0.0772) *
3050.0776 (0.0780) **
3060.0787 (0.0793) ***
3070.0802 (0.0811) ****
3080.0844 (0.0876) ***************
3090.0898 (0.0920) **********
3100.0933 (0.0946) ******
3110.0957 (0.0968) *****
3120.0970 (0.0972) *
3130.0976 (0.0981) **
3140.0994 (0.1007) ******
3150.1033 (0.1059) ************
3160.1064 (0.1068) **
3170.1075 (0.1081) ***
3180.1092 (0.1103) *****
3200.1109 (0.1116) ***
3210.1118 (0.1120) *
3220.1122 (0.1125) *
3230.1131 (0.1138) ***
3240.1140 (0.1142) *
3250.1144 (0.1146) *
3260.1157 (0.1168) *****
3270.1188 (0.1207) *********
3280.1210 (0.1212) *
3290.1214 (0.1216) *
3300.1218 (0.1221) *
3310.1231 (0.1242) *****
3320.1253 (0.1264) *****
3330.1297 (0.1330) ***************
3340.1332 (0.1334) *
3350.1351 (0.1369) ********
3360.1382 (0.1395) ******
3370.1412 (0.1430) ********
3380.1432 (0.1434) *
3390.1463 (0.1491) *************
3400.1539 (0.1587) **********************
3410.1611 (0.1635) ***********
3420.1654 (0.1674) *********
3430.1678 (0.1683) **
3440.1698 (0.1713) *******
3450.1724 (0.1735) *****
3460.1748 (0.1761) ******
3470.1776 (0.1792) *******
3480.1811 (0.1831) *********
3490.1857 (0.1883) ************
3500.1942 (0.2001) ***************************
3520.2003 (0.2005) *
3530.2018 (0.2031) ******
3540.2044 (0.2058) ******
3550.2079 (0.2101) **********
3560.2110 (0.2119) ****
3570.2145 (0.2171) ************
3580.2173 (0.2175) *
3590.2184 (0.2193) ****
3600.2228 (0.2262) ****************
3610.2282 (0.2302) *********
3620.2343 (0.2384) *******************
3630.2391 (0.2398) ***
3640.2441 (0.2485) ********************
3650.2522 (0.2559) *****************
3660.2583 (0.2607) ***********
3670.2661 (0.2716) *************************
3680.2788 (0.2860) *********************************
3690.2890 (0.2921) **************
3700.2929 (0.2938) ****
3710.2966 (0.2995) *************
3720.3008 (0.3021) ******
3740.3067 (0.3112) *********************
3750.3123 (0.3134) *****
3760.3165 (0.3195) **************
3770.3215 (0.3235) *********
3780.3248 (0.3261) ******
3790.3311 (0.3361) ***********************
3800.3429 (0.3496) *******************************
3810.3518 (0.3540) **********
3820.3568 (0.3596) *************
3830.3607 (0.3618) *****
3840.3636 (0.3653) ********
3850.3657 (0.3662) **
3860.3710 (0.3758) **********************
3870.3884 (0.4010) **********************************************************
3880.4032 (0.4054) **********
3890.4082 (0.4111) *************
3900.4137 (0.4163) ************
3910.4174 (0.4185) *****
3920.4196 (0.4207) *****
3930.4265 (0.4324) ***************************
3940.4401 (0.4477) ***********************************
3950.4562 (0.4647) ***************************************
3960.4701 (0.4756) *************************
3970.4771 (0.4786) *******
3980.4819 (0.4852) ***************
3990.4854 (0.4856) *
4000.4878 (0.4900) **********
4010.4911 (0.4922) *****
4020.4943 (0.4965) **********
4030.4989 (0.5013) ***********
4040.5031 (0.5048) ********
4050.5061 (0.5074) ******
4060.5078 (0.5083) **
4070.5087 (0.5092) **
4080.5183 (0.5275) ******************************************
4090.5290 (0.5305) *******
4100.5316 (0.5327) *****
4110.5340 (0.5353) ******
4120.5368 (0.5384) *******
4130.5464 (0.5545) *************************************
4140.5558 (0.5571) ******
4150.5612 (0.5654) *******************
4160.5669 (0.5684) *******
4170.5697 (0.5711) ******
4180.5721 (0.5732) *****
4190.5739 (0.5745) ***
4200.5835 (0.5924) *****************************************
4210.5933 (0.5942) ****
4220.5957 (0.5972) *******
4230.5983 (0.5994) *****
4250.6009 (0.6024) *******
4260.6083 (0.6142) ***************************
4270.6173 (0.6203) **************
4280.6247 (0.6290) ********************
4290.6314 (0.6338) ***********
4300.6371 (0.6404) ***************
4310.6415 (0.6425) *****
4320.6434 (0.6443) ****
4330.6521 (0.6600) ************************************
4340.6602 (0.6604) *
4350.6609 (0.6613) **
4360.6626 (0.6639) ******
4370.6650 (0.6661) *****
4390.6680 (0.6700) *********
4400.6768 (0.6835) *******************************
4410.6840 (0.6844) **
4420.6861 (0.6879) ********
4430.6905 (0.6931) ************
4440.6938 (0.6944) ***
4450.6946 (0.6949) *
4460.6973 (0.6997) ***********
4470.7038 (0.7079) *******************
4480.7108 (0.7136) *************
4490.7151 (0.7167) *******
4500.7177 (0.7188) *****
4510.7210 (0.7232) **********
4520.7236 (0.7241) **
4530.7282 (0.7323) *******************
4540.7343 (0.7363) *********
4550.7369 (0.7376) ***
4560.7389 (0.7402) ******
4570.7413 (0.7424) *****
4580.7443 (0.7463) *********
4590.7509 (0.7554) *********************
4600.7568 (0.7581) ******
4610.7605 (0.7629) ***********
4620.7637 (0.7646) ****
4630.7659 (0.7672) ******
4640.7692 (0.7711) *********
4650.7722 (0.7733) *****
4670.7740 (0.7746) ***
4680.7748 (0.7751) *
4690.7755 (0.7759) **
4700.7762 (0.7764) *
4740.7772 (0.7781) ****
4750.7786 (0.7790) **
4760.7805 (0.7820) *******
4770.7836 (0.7851) *******
4780.7857 (0.7864) ***
4790.7888 (0.7912) ***********
4800.7932 (0.7951) *********
4810.7956 (0.7960) **
4820.7988 (0.8017) *************
4830.8027 (0.8038) *****
4840.8041 (0.8043) *
4850.8056 (0.8069) ******
4860.8078 (0.8086) ****
4870.8110 (0.8134) ***********
4880.8136 (0.8139) *
4890.8158 (0.8178) *********
4900.8200 (0.8221) **********
4910.8228 (0.8235) ***
4920.8248 (0.8261) ******
4930.8269 (0.8278) ****
4960.8287 (0.8296) ****
4970.8306 (0.8317) *****
4980.8389 (0.8461) *********************************
4990.8463 (0.8466) *
5000.8494 (0.8522) *************
5010.8529 (0.8535) ***
5020.8540 (0.8544) **
5030.8548 (0.8553) **
5040.8570 (0.8588) ********
5050.8603 (0.8618) *******
5070.8620 (0.8622) *
5080.8636 (0.8649) ******
5090.8657 (0.8666) ****
5100.8677 (0.8688) *****
5140.8697 (0.8705) ****
5150.8707 (0.8710) *
5160.8721 (0.8731) *****
5170.8745 (0.8758) ******
5180.8764 (0.8771) ***
5200.8795 (0.8819) ***********
5210.8821 (0.8823) *
5220.8840 (0.8858) ********
5240.8860 (0.8862) *
5250.8864 (0.8867) *
5260.8873 (0.8880) ***
5270.8882 (0.8884) *
5290.8904 (0.8923) *********
5300.8925 (0.8928) *
5310.8930 (0.8932) *
5320.8936 (0.8941) **
5330.8949 (0.8958) ****
5340.8965 (0.8971) ***
5360.8973 (0.8976) *
5370.8978 (0.8980) *
5380.8982 (0.8984) *
5400.9017 (0.9050) ***************
5410.9056 (0.9063) ***
5420.9069 (0.9076) ***
5430.9078 (0.9080) *
5440.9087 (0.9093) ***
5450.9095 (0.9098) *
5460.9100 (0.9102) *
5470.9115 (0.9128) ******
5480.9130 (0.9133) *
5490.9135 (0.9137) *
5500.9139 (0.9141) *
5510.9146 (0.9150) **
5520.9156 (0.9163) ***
5530.9167 (0.9172) **
5540.9176 (0.9180) **
5550.9185 (0.9189) **
5560.9194 (0.9198) **
5570.9202 (0.9207) **
5580.9211 (0.9215) **
5590.9224 (0.9233) ****
5600.9244 (0.9255) *****
5610.9257 (0.9259) *
5620.9261 (0.9263) *
5630.9270 (0.9276) ***
5650.9279 (0.9281) *
5660.9283 (0.9285) *
5670.9287 (0.9289) *
5690.9292 (0.9294) *
5700.9298 (0.9303) **
5730.9305 (0.9307) *
5770.9309 (0.9311) *
5780.9313 (0.9316) *
5800.9327 (0.9337) *****
5810.9342 (0.9346) **
5830.9348 (0.9350) *
5840.9355 (0.9359) **
5850.9372 (0.9385) ******
5880.9392 (0.9398) ***
5900.9418 (0.9438) *********
5940.9440 (0.9442) *
5950.9457 (0.9473) *******
5960.9477 (0.9481) **
5970.9483 (0.9486) *
5980.9488 (0.9490) *
6000.9499 (0.9507) ****
6010.9510 (0.9512) *
6020.9518 (0.9525) ***
6030.9531 (0.9538) ***
6050.9547 (0.9555) ****
6060.9560 (0.9564) **
6070.9566 (0.9568) *
6080.9595 (0.9621) ************
6100.9627 (0.9634) ***
6120.9638 (0.9643) **
6140.9649 (0.9656) ***
6160.9660 (0.9664) **
6170.9673 (0.9682) ****
6190.9684 (0.9686) *
6200.9693 (0.9699) ***
6210.9701 (0.9704) *
6220.9710 (0.9717) ***
6260.9719 (0.9721) *
6270.9725 (0.9730) **
6300.9732 (0.9734) *
6310.9736 (0.9738) *
6320.9743 (0.9747) **
6330.9749 (0.9752) *
6360.9754 (0.9756) *
6400.9760 (0.9765) **
6410.9769 (0.9773) **
6460.9780 (0.9786) ***
6470.9789 (0.9791) *
6500.9793 (0.9795) *
6510.9797 (0.9799) *
6520.9802 (0.9804) *
6530.9813 (0.9821) ****
6550.9826 (0.9830) **
6560.9832 (0.9834) *
6570.9837 (0.9839) *
6580.9841 (0.9843) *
6590.9852 (0.9861) ****
6620.9863 (0.9865) *
6630.9867 (0.9869) *
6640.9871 (0.9874) *
6660.9876 (0.9878) *
6670.9882 (0.9887) **
6680.9893 (0.9900) ***
6710.9904 (0.9908) **
6720.9911 (0.9913) *
6740.9922 (0.9930) ****
6760.9932 (0.9935) *
6800.9937 (0.9939) *
6810.9943 (0.9948) **
6870.9952 (0.9956) **
6970.9963 (0.9969) ***
7050.9972 (0.9974) *
7100.9976 (0.9978) *
7250.9980 (0.9983) *
7300.9991 (1.0000) ****

n = 2294

### Tests used

1. Test of the Beheaded Man
2. Cooijmans Intelligence Test - Form 3
3. A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude
4. Cooijmans On-Line Test - Two-barrelled version
5. Laaglandse Aanlegtest - Herziening 2016
6. The Nemesis Test
7. De Golfstroomtest - Herziening 2019
8. Gliaweb Riddled Intelligence Test - Revision 2011
9. The Sargasso Test
10. Only idiots
11. Reflections In Peroxide
12. Problems In Gentle Slopes of the third degree
13. Random Feickery
14. Combined Numerical and Spatial sections of Test For Genius - Revision 2010
15. Reason Behind Multiple-Choice - Revision 2008
16. The Marathon Test
17. Test For Genius - Revision 2010
18. Associative LIMIT
19. Numerical and spatial sections of The Marathon Test
20. Labyrinthine LIMIT
21. Psychometrically Activated Grids Acerbate Neuroticism
22. Narcissus' last stand
23. Problems In Gentle Slopes of the second degree
24. Cooijmans Intelligence Test - Form 4
25. The Alchemist Test
26. The Bonsai Test - Revision 2016
27. Cooijmans Intelligence Test 5
28. Test For Genius - Revision 2016
29. Combined Numerical and Spatial sections of Test For Genius - Revision 2016
30. The Piper's Test
31. Dicing with death
32. De Laatste Test - Herziening 2019
33. Divine Psychometry
34. A Relaxing Test
35. Cartoons of Shock
36. Female Intelligence Test
37. Low Countries Aptitude Test
38. Problems In Gentle Slopes of the first degree
39. The Hammer Of Test-Hungry
40. Test of Shock and Awe
41. Short Test For Genius
42. Reason Behind Multiple-Choice
43. Long Test For Genius
44. Long Test For Genius (French)
45. Long Test For Genius (Netherlandic)
46. Test For Genius - Revision 2004
47. Cooijmans On-Line Test
48. Bonsai Test
49. Cooijmans Intelligence Test - Form 1
50. Cooijmans Intelligence Test - Form 2
51. Giga Test
52. Grail Test
53. Gliaweb Riddled Intelligence Test (old version)
54. The Hammer Of Test-Hungry - Revision 2013