Adjustment of the protonorms to norms conversion (males)

© January 2022 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. 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.

ScoreProp.# scores (* = 1 score)
950.0003 (0.0005) *
970.0008 (0.0011) *
1070.0014 (0.0016) *
1140.0019 (0.0022) *
1310.0025 (0.0027) *
1350.0030 (0.0033) *
1360.0035 (0.0038) *
1440.0044 (0.0049) **
1490.0052 (0.0055) *
1500.0063 (0.0071) ***
1560.0076 (0.0082) **
1570.0090 (0.0098) ***
1650.0104 (0.0109) **
1670.0115 (0.0120) **
1690.0134 (0.0147) *****
1730.0150 (0.0153) *
1760.0161 (0.0169) ***
1790.0180 (0.0191) ****
1900.0194 (0.0197) *
1910.0199 (0.0202) *
1920.0205 (0.0208) *
1980.0216 (0.0224) ***
2000.0229 (0.0235) **
2060.0238 (0.0240) *
2080.0243 (0.0246) *
2110.0248 (0.0251) *
2160.0254 (0.0257) *
2190.0259 (0.0262) *
2200.0265 (0.0268) *
2500.0270 (0.0273) *
2510.0276 (0.0279) *
2530.0281 (0.0284) *
2540.0287 (0.0289) *
2550.0303 (0.0317) *****
2600.0319 (0.0322) *
2610.0330 (0.0339) ***
2620.0341 (0.0344) *
2640.0355 (0.0366) ****
2670.0369 (0.0371) *
2680.0382 (0.0393) ****
2690.0401 (0.0410) ***
2700.0412 (0.0415) *
2720.0418 (0.0421) *
2730.0423 (0.0426) *
2760.0429 (0.0431) *
2780.0451 (0.0470) *******
2790.0478 (0.0486) ***
2800.0497 (0.0508) ****
2810.0527 (0.0546) *******
2820.0552 (0.0557) **
2830.0568 (0.0579) ****
2840.0587 (0.0595) ***
2870.0598 (0.0601) *
2880.0603 (0.0606) *
2900.0609 (0.0612) *
2910.0620 (0.0628) ***
2920.0631 (0.0634) *
2930.0647 (0.0661) *****
2940.0669 (0.0677) ***
2960.0680 (0.0683) *
2970.0696 (0.0710) *****
2980.0713 (0.0715) *
2990.0729 (0.0743) *****
3000.0778 (0.0814) *************
3010.0855 (0.0896) ***************
3020.0904 (0.0912) ***
3030.0915 (0.0918) *
3040.0923 (0.0928) **
3050.0934 (0.0939) **
3060.0942 (0.0945) *
3070.0948 (0.0950) *
3080.0953 (0.0956) *
3090.0961 (0.0967) **
3100.0975 (0.0983) ***
3110.0997 (0.1010) *****
3120.1019 (0.1027) ***
3130.1032 (0.1038) **
3140.1046 (0.1054) ***
3150.1079 (0.1103) *********
3170.1111 (0.1120) ***
3180.1133 (0.1147) *****
3200.1150 (0.1152) *
3210.1161 (0.1169) ***
3220.1171 (0.1174) *
3230.1185 (0.1196) ****
3240.1202 (0.1207) **
3250.1210 (0.1212) *
3270.1229 (0.1245) ******
3280.1248 (0.1251) *
3290.1267 (0.1283) ******
3300.1294 (0.1305) ****
3310.1322 (0.1338) ******
3320.1349 (0.1360) ****
3330.1395 (0.1431) *************
3340.1442 (0.1453) ****
3350.1480 (0.1507) **********
3360.1510 (0.1513) *
3370.1521 (0.1529) ***
3390.1540 (0.1551) ****
3400.1592 (0.1633) ***************
3410.1674 (0.1715) ***************
3420.1745 (0.1775) ***********
3430.1778 (0.1780) *
3440.1808 (0.1835) **********
3450.1846 (0.1857) ****
3460.1860 (0.1862) *
3470.1901 (0.1939) **************
3480.1969 (0.1999) ***********
3490.2010 (0.2021) ****
3500.2067 (0.2114) *****************
3520.2119 (0.2125) **
3530.2135 (0.2146) ****
3540.2152 (0.2157) **
3550.2176 (0.2196) *******
3560.2209 (0.2223) *****
3570.2258 (0.2294) *************
3580.2299 (0.2305) **
3590.2313 (0.2321) ***
3600.2351 (0.2381) ***********
3610.2389 (0.2398) ***
3620.2441 (0.2485) ****************
3630.2493 (0.2501) ***
3640.2540 (0.2578) **************
3650.2605 (0.2632) **********
3660.2671 (0.2709) **************
3670.2764 (0.2818) ********************
3680.2897 (0.2977) *****************************
3690.3012 (0.3048) *************
3700.3061 (0.3075) *****
3710.3097 (0.3119) ********
3720.3127 (0.3135) ***
3730.3138 (0.3140) *
3740.3170 (0.3200) ***********
3750.3239 (0.3277) **************
3760.3288 (0.3299) ****
3770.3329 (0.3359) ***********
3780.3362 (0.3364) *
3790.3419 (0.3474) ********************
3800.3553 (0.3632) *****************************
3810.3667 (0.3703) *************
3820.3727 (0.3752) *********
3830.3760 (0.3768) ***
3840.3793 (0.3818) *********
3850.3826 (0.3834) ***
3860.3883 (0.3932) ******************
3870.4044 (0.4156) *****************************************
3880.4189 (0.4222) ************
3890.4230 (0.4238) ***
3900.4263 (0.4287) *********
3910.4312 (0.4336) *********
3920.4391 (0.4446) ********************
3930.4500 (0.4555) ********************
3940.4631 (0.4708) ****************************
3950.4782 (0.4855) ***************************
3960.4863 (0.4872) ***
3970.4877 (0.4883) **
3980.4918 (0.4954) *************
3990.4978 (0.5003) *********
4000.5030 (0.5057) **********
4010.5074 (0.5090) ******
4020.5112 (0.5134) ********
4030.5164 (0.5194) ***********
4040.5213 (0.5232) *******
4050.5259 (0.5287) **********
4060.5289 (0.5292) *
4070.5298 (0.5303) **
4080.5325 (0.5347) ********
4090.5371 (0.5396) *********
4100.5412 (0.5429) ******
4110.5434 (0.5440) **
4120.5467 (0.5494) **********
4130.5579 (0.5664) *******************************
4140.5683 (0.5702) *******
4150.5729 (0.5756) **********
4160.5800 (0.5844) ****************
4170.5857 (0.5871) *****
4180.5874 (0.5877) *
4190.5893 (0.5909) ******
4200.5972 (0.6035) ***********************
4210.6046 (0.6057) ****
4220.6070 (0.6084) *****
4230.6095 (0.6106) ****
4250.6109 (0.6111) *
4260.6128 (0.6144) ******
4270.6161 (0.6177) ******
4280.6237 (0.6297) **********************
4290.6300 (0.6303) *
4300.6319 (0.6335) ******
4310.6349 (0.6363) *****
4320.6371 (0.6379) ***
4330.6464 (0.6548) *******************************
4340.6578 (0.6608) ***********
4350.6619 (0.6630) ****
4360.6644 (0.6658) *****
4370.6668 (0.6679) ****
4380.6707 (0.6734) **********
4390.6750 (0.6767) ******
4400.6854 (0.6942) ********************************
4410.6947 (0.6952) **
4420.6977 (0.7002) *********
4430.7026 (0.7051) *********
4440.7067 (0.7084) ******
4450.7105 (0.7127) ********
4460.7135 (0.7144) ***
4470.7174 (0.7204) ***********
4480.7239 (0.7275) *************
4490.7294 (0.7313) *******
4500.7324 (0.7335) ****
4510.7346 (0.7357) ****
4520.7376 (0.7395) *******
4530.7441 (0.7488) *****************
4540.7510 (0.7531) ********
4550.7540 (0.7548) ***
4560.7561 (0.7575) *****
4570.7591 (0.7608) ******
4580.7627 (0.7646) *******
4590.7660 (0.7673) *****
4600.7682 (0.7690) ***
4610.7717 (0.7744) **********
4630.7780 (0.7815) *************
4640.7818 (0.7821) *
4650.7840 (0.7859) *******
4670.7865 (0.7870) **
4680.7881 (0.7892) ****
4690.7897 (0.7903) **
4740.7906 (0.7908) *
4750.7911 (0.7914) *
4760.7919 (0.7925) **
4770.7927 (0.7930) *
4780.7938 (0.7946) ***
4790.7985 (0.8023) **************
4800.8034 (0.8045) ****
4810.8053 (0.8061) ***
4820.8119 (0.8176) *********************
4830.8195 (0.8214) *******
4840.8217 (0.8220) *
4850.8241 (0.8263) ********
4860.8271 (0.8280) ***
4870.8312 (0.8345) ************
4880.8348 (0.8351) *
4890.8362 (0.8372) ****
4900.8392 (0.8411) *******
4910.8427 (0.8443) ******
4930.8454 (0.8465) ****
4950.8476 (0.8487) ****
4980.8514 (0.8542) **********
5000.8564 (0.8585) ********
5010.8599 (0.8613) *****
5030.8621 (0.8629) ***
5040.8646 (0.8662) ******
5050.8678 (0.8695) ******
5060.8697 (0.8700) *
5070.8708 (0.8717) ***
5080.8725 (0.8733) ***
5090.8752 (0.8771) *******
5100.8788 (0.8804) ******
5110.8809 (0.8815) **
5120.8826 (0.8837) ****
5130.8839 (0.8842) *
5150.8850 (0.8859) ***
5160.8872 (0.8886) *****
5170.8889 (0.8891) *
5180.8900 (0.8908) ***
5200.8916 (0.8924) ***
5210.8935 (0.8946) ****
5230.8949 (0.8951) *
5240.8954 (0.8957) *
5250.8960 (0.8962) *
5270.8965 (0.8968) *
5280.8973 (0.8979) **
5290.8981 (0.8984) *
5300.8987 (0.8990) *
5320.8998 (0.9006) ***
5330.9017 (0.9028) ****
5340.9044 (0.9061) ******
5350.9063 (0.9066) *
5360.9069 (0.9072) *
5370.9077 (0.9082) **
5380.9088 (0.9093) **
5400.9123 (0.9153) ***********
5420.9156 (0.9159) *
5430.9164 (0.9170) **
5440.9175 (0.9181) **
5470.9194 (0.9208) *****
5480.9216 (0.9224) ***
5490.9233 (0.9241) ***
5510.9246 (0.9252) **
5520.9268 (0.9285) ******
5530.9287 (0.9290) *
5540.9295 (0.9301) **
5550.9306 (0.9312) **
5560.9320 (0.9328) ***
5570.9334 (0.9339) **
5580.9347 (0.9356) ***
5590.9361 (0.9366) **
5600.9383 (0.9399) ******
5610.9402 (0.9405) *
5620.9407 (0.9410) *
5630.9421 (0.9432) ****
5650.9437 (0.9443) **
5670.9446 (0.9448) *
5680.9451 (0.9454) *
5690.9457 (0.9459) *
5700.9462 (0.9465) *
5730.9468 (0.9470) *
5780.9473 (0.9476) *
5800.9478 (0.9481) *
5810.9484 (0.9487) *
5830.9489 (0.9492) *
5840.9498 (0.9503) **
5850.9525 (0.9547) ********
5880.9549 (0.9552) *
5890.9555 (0.9558) *
5900.9566 (0.9574) ***
5930.9577 (0.9579) *
5940.9582 (0.9585) *
5950.9593 (0.9601) ***
5960.9604 (0.9607) *
5970.9610 (0.9612) *
6000.9615 (0.9618) *
6030.9623 (0.9629) **
6050.9640 (0.9650) ****
6060.9656 (0.9661) **
6070.9664 (0.9667) *
6080.9670 (0.9672) *
6100.9678 (0.9683) **
6120.9686 (0.9689) *
6140.9700 (0.9711) ****
6170.9721 (0.9732) ****
6180.9735 (0.9738) *
6200.9749 (0.9760) ****
6220.9765 (0.9771) **
6270.9776 (0.9782) **
6300.9790 (0.9798) ***
6320.9803 (0.9809) **
6360.9812 (0.9814) *
6400.9817 (0.9820) *
6410.9823 (0.9825) *
6440.9828 (0.9831) *
6460.9836 (0.9842) **
6470.9844 (0.9847) *
6500.9853 (0.9858) **
6530.9869 (0.9880) ****
6550.9883 (0.9885) *
6590.9894 (0.9902) ***
6620.9904 (0.9907) *
6650.9910 (0.9913) *
6660.9915 (0.9918) *
6670.9926 (0.9934) ***
6680.9937 (0.9940) *
6690.9943 (0.9945) *
6720.9948 (0.9951) *
6750.9954 (0.9956) *
6800.9959 (0.9962) *
6810.9965 (0.9967) *
6850.9970 (0.9973) *
6900.9975 (0.9978) *
7000.9981 (0.9984) *
7050.9986 (0.9989) *
7300.9992 (0.9995) *
7310.9997 (1.0000) *

n = 1831

Tests used

Adjustment of the protonorms to norms conversion (females)

© 15 October 2019 Paul Cooijmans

The procedure

A sample of tests is chosen by these criteria:

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).

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.

Prot.Prop.# scores (* = 1 score)
970.003 (0.006) *
1350.009 (0.013) *
2070.016 (0.019) *
2330.025 (0.031) **
2400.034 (0.037) *
2550.041 (0.044) *
2610.047 (0.050) *
2670.053 (0.056) *
2690.059 (0.063) *
2710.066 (0.069) *
2720.072 (0.075) *
2790.091 (0.106) *****
2810.109 (0.113) *
2820.116 (0.119) *
2830.122 (0.125) *
2840.131 (0.138) **
2850.141 (0.144) *
2870.147 (0.150) *
2910.153 (0.156) *
2950.169 (0.181) ****
2970.184 (0.188) *
2990.191 (0.194) *
3000.203 (0.212) ***
3030.222 (0.231) ***
3040.234 (0.237) *
3100.244 (0.250) **
3120.253 (0.256) *
3130.259 (0.263) *
3150.266 (0.269) *
3160.278 (0.287) ***
3210.291 (0.294) *
3270.300 (0.306) **
3280.309 (0.313) *
3330.322 (0.331) ***
3390.338 (0.344) **
3400.359 (0.375) *****
3420.378 (0.381) *
3460.388 (0.394) **
3470.397 (0.400) *
3500.403 (0.406) *
3510.412 (0.419) **
3530.425 (0.431) **
3550.434 (0.438) *
3570.441 (0.444) *
3580.447 (0.450) *
3620.463 (0.475) ****
3650.487 (0.500) ****
3660.503 (0.506) *
3670.509 (0.512) *
3680.519 (0.525) **
3700.528 (0.531) *
3710.537 (0.544) **
3740.547 (0.550) *
3790.559 (0.569) ***
3800.575 (0.581) **
3810.588 (0.594) **
3820.597 (0.600) *
3840.609 (0.619) ***
3860.622 (0.625) *
3890.628 (0.631) *
3910.634 (0.637) *
3920.641 (0.644) *
3930.647 (0.650) *
3960.653 (0.656) *
3970.666 (0.675) ***
4000.678 (0.681) *
4030.684 (0.688) *
4040.706 (0.725) ******
4050.731 (0.738) **
4060.741 (0.744) *
4140.750 (0.756) **
4160.759 (0.762) *
4190.766 (0.769) *
4240.772 (0.775) *
4280.778 (0.781) *
4290.784 (0.787) *
4330.794 (0.800) **
4370.803 (0.806) *
4380.809 (0.813) *
4390.816 (0.819) *
4400.828 (0.838) ***
4410.841 (0.844) *
4420.847 (0.850) *
4430.853 (0.856) *
4480.859 (0.863) *
4530.869 (0.875) **
4570.878 (0.881) *
4580.884 (0.887) *
4670.891 (0.894) *
4840.897 (0.900) *
4860.903 (0.906) *
4870.912 (0.919) **
4910.922 (0.925) *
4930.928 (0.931) *
5090.934 (0.938) *
5100.941 (0.944) *
5120.947 (0.950) *
5150.956 (0.963) **
5520.966 (0.969) *
5550.972 (0.975) *
5690.978 (0.981) *
5780.984 (0.988) *
5830.991 (0.994) *
6300.997 (1.000) *

n = 160

Tests used