The Bell Curve: Intelligence and Class Structure in American Life

by Richard J. Herrnstein

  The standard independent variables, described in Appendix 2, are zAFQT89, the 1989 scoring of the AFQT; zSES, the socioeconomic background of the NLSY subjects; and zAge, based on the age of the NLSY subjects as of December 31, 1990. All are expressed as standard scores with a mean of 0 and a standard deviation of 1.

  All dependent variables are binary. The coefficients are parameter estimates when the dependent variable = “yes.” The linear logistic model has the form

  logit(p) = log(p/(1−p)) = α + ß′x

  where α is the intercept parameter and ß is the vector of slope parameters for a vector of independent variables x. Take as an example the first set of results presented subsequently, involving poverty. Suppose you want to know the probability that a person is under the poverty line in 1989 (Poverty = “Yes”), stipulating that the person in question has an IQ (zAFQT) 1.5 standard deviations below the mean, socioeconomic background (zSES) .3 standard deviation above the mean, and is exactly of mean age. Using the parameters in the basic analysis for poverty rounded to four decimal places, and a computationally convenient re-expression of p, the probability is computed as follows:

  The probability we set out to compute is 18.37 percent.

  “The High School Sample” consists of those who received a high school diploma through the normal route (not a GED) and reported exactly twelve years of education as of the 1990 interview.

  “The College Sample” consists of those who completed a bachelor’s degree and reported exactly sixteen years of education as of the 1990 interview.

  The software used for the analyses is JMP Version 3, by SAS Institute Inc. JMP treats nominal independent variables differently from other major software packages such as SAS and SPSS. In those packages, a parameter for a nominal variable represents the difference between that level of the nominal variable and an omitted level serving as a reference group. In JMP, a parameter represents the difference of a given level from the average over all levels of the nominal variable. The implied parameter for the remaining level is the negative sum of the other levels (i.e., the parameters sum to zero over all the effect levels). For example, suppose Race were being used as a nominal variable, with categories of Black, Latino, and White. In the JMP printout, the coefficients would appear as

  Race[Black-White] x1

  Race [Latino-White] x2

  The order is determined by the alphabetical order of the categories. In this case, the coefficient x1 applies to blacks, x2 to Latinos. The implied White coefficient is −1 × (x1 + x2). In the case of a binary independent variable such as Sex, the printout would show a single line

  Sex [Female-Male] x1

  which applies to females. The coefficient for Male equals −x1.

  CHAPTER 5: POVERTY

  DEPENDENT VARIABLE: Under the official poverty line in 1989.

  SAMPLE RESTRICTIONS: Excludes those who reported they were out of the labor force because they were in school in either the 1989 or 1990 interviews.

  Basic Analysis:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prot>ChiSq

  Model 3 90.94009 181.8802 0.000000

  Error 3363 784.40179

  C Total 3366 875.34188

  RSquare (U) 0.1039

  Observations 3367

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −2.6487288 0.0768803 1187 0.0000

  zAFQT89 −0.8376338 0.0935061 80.25 0.0000

  zSES −0.3300720 0.0900996 13.42 0.0002

  zAge −0.0238375 0.0723735 0.11 0.7419

  The High School Sample:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 22.01811 44.03622 0.000000

  Error 1232 325.26939

  C Total 1235 347.28750

  RSquare (U) 0.0634

  Observations 1236

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −2.7237775 0.1290286 445.63 0.0000

  zAFQT89 −0.8267293 0.1627358 25.81 0.0000

  zSES −0.3619703 0.1499855 5.82 0.0158

  zAge +0.1049227 0.1094603 0.92 0.3378

  The College Sampk: Omitted. Only six persons in the cross-sectional College Sample were in poverty.

  For Mothers Married as of the 1989 Interview:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 17.14553 34.29106 0.000000

  Error 786 179.84999

  C Total 789 196.99552

  RSquare (U) 0.0870

  Observations 790

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −2.7732817 0.1646023 283.87 0.0000

  zAFQT89 −0.6437797 0.2140132 9.05 0.0026

  zSES −0.3910629 0.2020317 3.75 0.0529

  zAge −0.3338674 0.1587605 4.42 0.0355

  For MothersWho Were Separated, Divorced, or Never Married as of the1989 Interview:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 8.07114 16.14228 0.001060

  Error 211 135.77658

  C Total 214 143.84772

  RSquare (U) 0.0561

  Observations 215

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −0.7449132 0.1713794 18.89 0.0000

  zAFQT89 −0.6722121 0.2277019 8.72 0.0032

  zSES −0.1597461 0.1952709 0.67 0.4133

  zAge −0.1524315 0.1530986 0.99 0.3194

  CHAPTER 6: SCHOOLING

  DEPENDENT VARIABLE: Permanently dropped out of high school.

  SAMPLE RESTRICTIONS: Excludes those who obtained a GED.

  Basic Analysis:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 393.8978 787.7956 0.000000

  Error 3568 779.9904

  C Total 3571 1173.8882

  RSquare (U) 0.3355

  Observations 3572

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −2.85322606 0.0939659 922.00 0.0000

  zAFQT89 −1.72295934 0.1028145 280.83 0.0000

  zSES −0.64776232 0.0896658 52.19 0.0000

  zAge +0.05695640 0.0688286 0.68 0.4079

  Basic Analysis, Adding an Interaction Term for zAFQT and zSES:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 4 399.9876 799.9751 0.000000

  Error 3567 773.9006

  C Total 3571 1173.8882

  RSquare (U) 0.3407

  Observations 3572

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −2.9143231 0.1029462 801.41 0.0000

  zAFQT89 −1.8937642 0.1188518 253.89 0.0000

  zSES −0.9402389 0.1250634 56.52 0.0000

  zAge +0.0522667 0.0682755 0.59 0.4440

  zAFQT89*zSES −0.4133224 0.1187879 12.11 0.0005

  DEPENDENT VARIABLE: Received a GED instead of a high school diploma.

  SAMPLE RESTRICTIONS: Excludes those who obtained neither a high school diploma nor a GED.

  Basic Analysis:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 72.06475 144.1295 0.000000

  Error 3490 915.28145

  C Total 3493 987.34620

  RSquare (U) 0.0730

  Observations 3494

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −2.3548461 0.0653867 1297 0.0000

  zAFQT89 −0.4325254 0.0851185 25.82 0.0000

  zSES −0.6082151 0.0837515 52.74 0.0000

  zAge− 0.0416441 0.0662445 0.40 0.5296

  DEPENDENT VARIABLE: Received a ba
chelor’s degree.

  SAMPLE RESTRICTIONS: Excludes those who had less than a bachelor’s degree and were in postsecondary education in either the 1989 or 1990 interview.

  Basic Analysis:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 807.9072 1615.814 0.000000

  Error 3817 1364.3417

  C Total 3820 2172.2489

  RSquare (U) 0.3719

  Observations 3821

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −2.41992250 0.0786991 945.50 0.0000

  zAFQT89 +1.80771403 0.0795537 516.34 0.0000

  zSES +1.04818417 0.0690372 230.52 0.0000

  zAge −0.29777760 0.0516373 33.25 0.0000

  CHAPTER 7: UNEMPLOYMENT, IDLENESS, AND INJURY

  DEPENDENT VARIABLE: Out of the labor force for four weeks or more in 1989.

  SAMPLE RESTRICTIONS: Civilian males who did not respond “unable to work” or “in school” to the question on labor force participation in the 1989 or 1990 interview.

  Basic Analysis:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 9.44293 18.88586 0.000289

  Error 1682 548.25144

  C Total 1685 557.69437

  RSquare (U) 0.0169

  Observations 1686

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −2.20264085 0.0868001 643.94 0.0000

  zAFQT89 −0.36246881 0.0992802 13.33 0.0003

  zSES +0.21788340 0.1075722 4.10 0.0428

  zAge −0.12815393 0.0864018 2.20 0.1380

  The High School Sample:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 4.45831 8.916625 0.030420

  Error 617 156.98046

  C Total 620 161.43878

  RSquare (U) 0.0276

  Observations 621

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −2.69780012 0.1767563 232.95 0.0000

  zAFQT89 −0.42151253 0.2264362 3.47 0.0627

  zSES +0.56489480 0.230053 6.03 0.0141

  zAge −0.14556950 0.1672623 0.76 0.3841

  The College Sample:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 6.794337 13.58867 0.003522

  Error 264 56.536860

  C Total 267 63.331196

  RSquare (U) 0.1073

  Observation 268

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>Sq

  Intercept −3.12957075 0.6081769 26.48 0.0000

  zAFQT89 −0.84324247 0.4526768 3.47 0.0625

  zSES +0.94514750 0.3875388 5.95 0.0147

  zAge −0.46061574 0.299044 2.37 0.1235

  DEPENDENT VARIABLE: Unemployed for four weeks or more in 1989.

  SAMPLE RESTRICTIONS: Civilian males who did not respond “unable to work” or “in school” to the question on labor force participation in the 1989 or 1990 interview and were in the labor force throughout 1989.

  Basic Analysis:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 11.30841 22.61682 0.000049

  Error 1393 348.71511

  C Total 1396 360.02353

  RSquare(U) 0.0314

  Observations 1397

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −2.53577016 0.1076083 555.30 0.0000

  zAFQT89 −0.49486463 0.1298967 14.51 0.0001

  zSES −0.02534849 0.1383889 0.03 0.8547

  zAge −0.02181428 0.1108396 0.04 0.8440

  The High School Sample:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 1.86533 3.730657 0.292056

  Error 533 140.49123

  C Total 536 142.35656

  RSquare(U) 0.0131

  Observations 537

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −2.59878187 0.1766146 216.51 0.0000

  zAFQT89 −039353140 0.2368752 2.76 0.0966

  zSES +0.13951940 0.2353179 0.35 0.5532

  zAge −0.10510566 0.1762471 0.36 0.5509

  The College Sample:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 3.570096 7.140193 0.067561

  Error 224 40.506133

  C Total 227 44.076230

  RSquare (U) 0.0810

  Observations 228

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept −3.1686886 0.7276735 18.96 0.0000

  zAFQT89 −0.9196886 0.5641635 2.66 0.1031

  zSES +1.0039255 0.5015717 4.01 0.0453

  zAge +0.2941965 0.3311174 0.79 0.3743

  CHAPTER 8: FAMILY MATTERS

  DEPENDENT VARIABLE: Ever married before the age of 30.

  SAMPLE RESTRICTIONS: Persons who turned thirty by the 1990 interview.

  Basic Analysis:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 6.43345 12.8669 0.004933

  Error 1630 839.76747

  C Total 1633 846.20092

  RSquare (U) 0.0076

  Observations 1634

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept +1.19841361 0.128902 86.44 0.0000

  zAFQT89 −0.0473587 0.0757854 0.39 0.5320

  zSES −0.1905526 0.0786307 5.87 0.0154

  zAge +0.20403379 0.1290545 2.50 0.1139

  The High School Sample:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 6.92871 13.857 0.003106

  Error 601 259.40296

  C Total 604 266.33168

  RSquare (U) 0.0260

  Observations 605

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept +1.41494853 0.2342703 36.48 0.0000

  zAFQT89 +0.51424443 0.1598383 10.35 0.0013

  zSES −0.1128845 0.1582799 .51 0.4757

  zAge +0.36827169 0.2422543 2.31 0.1285

  The College Sample:

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 3 0.17181 0.343616 0.951627

  Error 233 145.35748

  C Total 236 145.52929

  RSquare (U) 0.0012

  Observations 237

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept +0.71372375 0.3946174 3.27 0.0705

  zAFQT89 +0.05013859 0.2237528 0.05 0.8227

  zSES +0.0968295 0.1833680 0.28 0.5975

  zAge −0.0177807 0.2950863 0.00 0.9520

  DEPENDENT VARIABLE: Divorced within the first five years of marriage.

  SAMPLE RESTRICTIONS: Persons married prior to January 1, 1986.

  Basic Analysis, Adding Date of First Marriage (MarDate 1):

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 4 21.8881 43.77626 0.000000

  Error 2026 991.3719

  C Total 2030 1013.2600

  RSquare (U) 0.0216

  Observations 2031

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept +5.70860970 1.9858067 8.26 0.0040

  zAFQT89 −0.35734009 0.0781258 20.92 0.0000

  zSES +0.22195410 0.0787612 7.94 0.0048

  zAge −0.17766944 0.0741478 5.74 0.0166

  MarDatel −0.08677335 0.0243113 12.74 0.0004
<
br />   The High School Sample, Adding Date of First Marriage (MarDate 1):

  Whole-Model Test

  Source DF −LogLikihood ChiSquare Prob>ChiSq

  Model 4 3.54304 7.086073 0.131409

  Error 870 428.70643

  C Total 874 432.24947

  RSquare (U) 0.0082

  Observations 875

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept +5.4451395 3.1286887 3.03 0.0818

  zAFQT89 −0.0379171 0.1348129 1.08 0.7785

  zSES +0.2206925 0.1288222 2.93 0.0867

  zAge −0.1078057 0.1146773 0.88 0.3472

  MarDatel −0.0839950 0.0383236 4.80 0.0284

  The College Sample, Adding Date of First Marriage (MarDate 1):

  Whole-Model Test

  Source DF -LogLikelihood ChiSquare Prob>ChiSq

  Model 4 5.548154 11.09631 0.025503

  Error 204 48.414468

  C Total 208 53.962623

  RSquare (U) 0.1028

  Observations 209

  Parameter Estimates

  Term Estimate Std Error ChiSquare Prob>ChiSq

  Intercept +32.392875 13.508886 5.75 0.0165

  zAFQT89 −0.75619367 0.4502182 2.82 0.0930

  zAge −0.55875424 0.4046911 1.91 0.1674

  MarDatel −0.41113710 0.1629791 6.36 0.0116

  Basic analysis, Adding Parental Living Arrangements at Age 14 (Adultl4):