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

Adjustment of the protonorms to norms conversion (males)

© April 2018 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.

Prot.Prop.# scores (* = 1 score)
250.0008 (0.0016) **
950.0020 (0.0024) *
970.0028 (0.0032) *
1070.0036 (0.0040) *
1140.0044 (0.0049) *
1270.0053 (0.0057) *
1310.0061 (0.0065) *
1350.0069 (0.0073) *
1490.0093 (0.0113) *****
1500.0117 (0.0121) *
1520.0125 (0.0129) *
1540.0133 (0.0137) *
1580.0141 (0.0146) *
1650.0150 (0.0154) *
1760.0158 (0.0162) *
1830.0166 (0.0170) *
1900.0174 (0.0178) *
1910.0182 (0.0186) *
2000.0198 (0.0210) ***
2060.0214 (0.0218) *
2080.0222 (0.0226) *
2140.0234 (0.0243) **
2200.0247 (0.0251) *
2210.0255 (0.0259) *
2270.0263 (0.0267) *
2310.0271 (0.0275) *
2490.0279 (0.0283) *
2500.0291 (0.0299) **
2530.0319 (0.0340) *****
2550.0352 (0.0364) ***
2570.0368 (0.0372) *
2600.0376 (0.0380) *
2610.0388 (0.0396) **
2630.0400 (0.0404) *
2670.0412 (0.0420) **
2690.0424 (0.0428) *
2700.0437 (0.0445) **
2710.0453 (0.0461) **
2750.0485 (0.0509) ******
2760.0513 (0.0517) *
2780.0521 (0.0525) *
2790.0534 (0.0542) **
2800.0546 (0.0550) *
2810.0554 (0.0558) *
2820.0570 (0.0582) ***
2830.0594 (0.0606) ***
2840.0610 (0.0614) *
2860.0627 (0.0639) ***
2870.0643 (0.0647) *
2880.0659 (0.0671) ***
2900.0675 (0.0679) *
2920.0687 (0.0695) **
2930.0703 (0.0711) **
2960.0719 (0.0728) **
2970.0732 (0.0736) *
3000.0760 (0.0784) ******
3020.0788 (0.0792) *
3050.0800 (0.0808) **
3060.0821 (0.0833) ***
3080.0837 (0.0841) *
3110.0845 (0.0849) *
3120.0861 (0.0873) ***
3130.0881 (0.0889) **
3150.0893 (0.0897) *
3170.0909 (0.0922) ***
3180.0938 (0.0954) ****
3200.0978 (0.1002) ******
3220.1006 (0.1011) *
3230.1027 (0.1043) ****
3240.1051 (0.1059) **
3270.1095 (0.1132) *********
3290.1152 (0.1172) *****
3300.1180 (0.1188) **
3310.1209 (0.1229) *****
3320.1233 (0.1237) *
3330.1245 (0.1253) **
3340.1265 (0.1277) ***
3350.1289 (0.1302) ***
3370.1306 (0.1310) *
3390.1322 (0.1334) ***
3400.1451 (0.1568) *****************************
3410.1605 (0.1641) *********
3420.1665 (0.1690) ******
3440.1694 (0.1698) *
3450.1734 (0.1770) *********
3470.1791 (0.1811) *****
3480.1815 (0.1819) *
3490.1835 (0.1851) ****
3500.1859 (0.1867) **
3510.1880 (0.1892) ***
3520.1904 (0.1916) ***
3530.1968 (0.2021) *************
3540.2025 (0.2029) *
3550.2057 (0.2086) *******
3560.2090 (0.2094) *
3570.2106 (0.2118) ***
3580.2122 (0.2126) *
3590.2134 (0.2142) **
3600.2175 (0.2207) ********
3610.2219 (0.2231) ***
3620.2255 (0.2280) ******
3630.2284 (0.2288) *
3640.2308 (0.2328) *****
3650.2357 (0.2385) *******
3660.2405 (0.2425) *****
3670.2510 (0.2595) *********************
3680.2643 (0.2692) ************
3690.2724 (0.2757) ********
3700.2781 (0.2805) ******
3710.2825 (0.2846) *****
3720.2866 (0.2886) *****
3740.2906 (0.2926) *****
3750.2947 (0.2967) *****
3760.2971 (0.2975) *
3770.3023 (0.3072) ************
3790.3137 (0.3201) ****************
3800.3310 (0.3420) ***************************
3810.3472 (0.3525) *************
3820.3549 (0.3573) ******
3830.3589 (0.3605) ****
3840.3618 (0.3630) ***
3850.3650 (0.3670) *****
3860.3694 (0.3719) ******
3870.3832 (0.3945) ****************************
3880.3973 (0.4002) *******
3890.4022 (0.4042) *****
3900.4107 (0.4171) ****************
3910.4232 (0.4293) ***************
3920.4309 (0.4325) ****
3930.4382 (0.4438) **************
3940.4450 (0.4462) ***
3950.4487 (0.4511) ******
3960.4515 (0.4519) *
3970.4531 (0.4543) ***
3980.4559 (0.4576) ****
3990.4608 (0.4640) ********
4000.4665 (0.4689) ******
4010.4701 (0.4713) ***
4020.4753 (0.4794) **********
4030.4834 (0.4875) **********
4040.4903 (0.4931) *******
4050.4960 (0.4988) *******
4060.5000 (0.5012) ***
4070.5036 (0.5061) ******
4080.5073 (0.5085) ***
4090.5117 (0.5150) ********
4100.5166 (0.5182) ****
4110.5194 (0.5206) ***
4120.5238 (0.5271) ********
4130.5331 (0.5392) ***************
4140.5420 (0.5449) *******
4150.5501 (0.5554) *************
4160.5602 (0.5651) ************
4170.5671 (0.5691) *****
4180.5695 (0.5699) *
4200.5744 (0.5788) ***********
4210.5800 (0.5812) ***
4220.5833 (0.5853) *****
4230.5861 (0.5869) **
4250.5893 (0.5918) ******
4260.5942 (0.5966) ******
4270.5974 (0.5982) **
4280.6059 (0.6136) *******************
4300.6160 (0.6184) ******
4310.6188 (0.6192) *
4320.6221 (0.6249) *******
4330.6334 (0.6419) *********************
4340.6463 (0.6508) ***********
4350.6536 (0.6564) *******
4360.6568 (0.6572) *
4370.6580 (0.6589) **
4380.6601 (0.6613) ***
4390.6621 (0.6629) **
4400.6677 (0.6726) ************
4410.6750 (0.6774) ******
4420.6795 (0.6815) *****
4430.6827 (0.6839) ***
4440.6863 (0.6888) ******
4450.6908 (0.6928) *****
4460.6940 (0.6952) ***
4470.6985 (0.7017) ********
4480.7082 (0.7146) ****************
4490.7167 (0.7187) *****
4500.7191 (0.7195) *
4510.7199 (0.7203) *
4520.7223 (0.7243) *****
4530.7312 (0.7381) *****************
4540.7393 (0.7405) ***
4550.7421 (0.7437) ****
4560.7445 (0.7454) **
4570.7474 (0.7494) *****
4580.7502 (0.7510) **
4590.7522 (0.7534) ***
4600.7555 (0.7575) *****
4610.7599 (0.7623) ******
4620.7648 (0.7672) ******
4630.7688 (0.7704) ****
4650.7736 (0.7769) ********
4670.7793 (0.7817) ******
4680.7829 (0.7842) ***
4730.7858 (0.7874) ****
4740.7878 (0.7882) *
4750.7886 (0.7890) *
4760.7894 (0.7898) *
4770.7906 (0.7914) **
4780.7926 (0.7939) ***
4790.7951 (0.7963) ***
4800.7983 (0.8003) *****
4810.8007 (0.8011) *
4820.8068 (0.8124) **************
4830.8157 (0.8189) ********
4840.8201 (0.8213) ***
4850.8230 (0.8246) ****
4860.8254 (0.8262) **
4870.8302 (0.8343) **********
4880.8347 (0.8351) *
4890.8355 (0.8359) *
4900.8371 (0.8383) ***
4910.8407 (0.8432) ******
4920.8440 (0.8448) **
4930.8460 (0.8472) ***
4940.8476 (0.8480) *
4950.8504 (0.8529) ******
4970.8533 (0.8537) *
4980.8561 (0.8585) ******
5000.8610 (0.8634) ******
5030.8658 (0.8682) ******
5040.8703 (0.8723) *****
5050.8739 (0.8755) ****
5060.8767 (0.8779) ***
5070.8795 (0.8812) ****
5080.8832 (0.8852) *****
5090.8872 (0.8892) *****
5100.8909 (0.8925) ****
5110.8933 (0.8941) **
5170.8945 (0.8949) *
5180.8957 (0.8965) **
5200.8973 (0.8981) **
5210.8989 (0.8998) **
5220.9006 (0.9014) **
5230.9018 (0.9022) *
5250.9026 (0.9030) *
5270.9038 (0.9046) **
5290.9050 (0.9054) *
5320.9062 (0.9070) **
5330.9078 (0.9086) **
5350.9091 (0.9095) *
5360.9099 (0.9103) *
5370.9111 (0.9119) **
5380.9127 (0.9135) **
5400.9159 (0.9184) ******
5410.9188 (0.9192) *
5430.9200 (0.9208) **
5440.9220 (0.9232) ***
5470.9248 (0.9264) ****
5480.9268 (0.9272) *
5490.9276 (0.9281) *
5500.9285 (0.9289) *
5510.9297 (0.9305) **
5520.9309 (0.9313) *
5530.9317 (0.9321) *
5540.9329 (0.9337) **
5550.9349 (0.9361) ***
5570.9365 (0.9369) *
5580.9382 (0.9394) ***
5590.9402 (0.9410) **
5600.9430 (0.9450) *****
5610.9454 (0.9458) *
5620.9462 (0.9466) *
5650.9479 (0.9491) ***
5660.9499 (0.9507) **
5670.9511 (0.9515) *
5690.9519 (0.9523) *
5700.9531 (0.9539) **
5730.9547 (0.9555) **
5740.9559 (0.9563) *
5750.9568 (0.9572) *
5780.9576 (0.9580) *
5800.9588 (0.9596) **
5840.9604 (0.9612) **
5850.9620 (0.9628) **
5870.9636 (0.9644) **
5880.9648 (0.9652) *
5900.9665 (0.9677) ***
5910.9681 (0.9685) *
5940.9689 (0.9693) *
6000.9701 (0.9709) **
6030.9721 (0.9733) ***
6050.9749 (0.9766) ****
6060.9782 (0.9798) ****
6070.9802 (0.9806) *
6080.9810 (0.9814) *
6100.9822 (0.9830) **
6170.9834 (0.9838) *
6180.9842 (0.9846) *
6200.9850 (0.9854) *
6270.9863 (0.9871) **
6300.9875 (0.9879) *
6320.9887 (0.9895) **
6330.9899 (0.9903) *
6500.9907 (0.9911) *
6530.9923 (0.9935) ***
6540.9943 (0.9951) **
6550.9956 (0.9960) *
6720.9964 (0.9968) *
6750.9972 (0.9976) *
6800.9980 (0.9984) *
6810.9988 (0.9992) *
7310.9996 (1.0000) *

n = 1237

Tests used