Adjustment of the protonorms to norms conversion

© 2 February 2023 Paul Cooijmans

The procedure

A sample of tests is selected by these criteria:

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