Digits Backward and the Mercer-Kamin Law

An Empirical Response to Mercer’s Treatment of Internal Validity of IQ Tests
  • Robert A. Gordon
Part of the Perspectives on Individual Differences book series (PIDF)


Jensen (e.g., 1980a) has grouped the various criteria for detecting bias in ability tests under two broad headings: internal and external. Studies under the first heading concern themselves with relations among the components of a test; those under the second are concerned with predictive relations between the test as a whole and outside variables. Mercer organized her chapter in this book to parallel Jensen’s distinction, and my chapter parallels hers, but, because of space limitations, only the half of her chapter concerned with internal validity.


Digit Span Passing Rate Item Difficulty Interval Scale Unit Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Achinstein, P. Law and explanation: An essay in the philosophy of science. London: Oxford University Press, 1971.Google Scholar
  2. Angoff, W. H. A technique for the investigation of cultural differences. Paper presented at the annual meeting of the American Psychological Association, Honolulu, September 1972. (ERIC Document Reproduction Service No. ED 069686.)Google Scholar
  3. Angoff, W. H. Use of difficulty and discrimination indices for detecting item bias. In R. A. Berk (Ed.), Handbook of methods for detecting test bias. Baltimore: Johns Hopkins University Press, 1982.Google Scholar
  4. Angoff, W. H., & Ford, S. F. Item-race interaction on a test of scholastic aptitude. Journal of Educational Measurement, 1973, 10, 95–105.CrossRefGoogle Scholar
  5. Baughman, E. E., & Dahlstrom, W. G. Negro and white children: A psychological study in the rural South. New York: Academic Press, 1968.Google Scholar
  6. Baumeister, A. A. Serial memory span thresholds of normal and mentally retarded children. Journal of Educational Psychology, 1974, 66, 889–894.PubMedCrossRefGoogle Scholar
  7. Bayley, N. Consistency and variability in the growth of intelligence from birth to eighteen years. Journal of Genetic Psychology, 1949, 75, 165–196.PubMedGoogle Scholar
  8. Beals, R. Acculturation. In A. L. Kroeber (Ed.), Anthropology today. Chicago: University of Chicago Press, 1953.Google Scholar
  9. Belmont, J. M., & Butterfield, E. C. What the development of short-term memory is. Human Development, 1971, 14, 236–248.PubMedCrossRefGoogle Scholar
  10. Benbow, C. P., & Stanley, J. C. Consequences in high school and college of sex differences in mathematical reasoning ability: A longitudinal perspective. American Educational Research Journal, 1982, 19, 598–622.Google Scholar
  11. Berk, R. A. (Ed.). Handbook of methods for detecting test bias. Baltimore: Johns Hopkins University Press, 1982.Google Scholar
  12. Bond, H. M. The education of the Negro in the American social order. New York: Octagon Books, 1966. (Originally published, 1934.)Google Scholar
  13. Box, G. E. P. Non-normality and tests on variances. Biometrika, 1953, 40, 318–335.Google Scholar
  14. Brotemarkle, R. A. Some memory span test problems: An analytical study at the college-adult level. Psychological Clinic, 1924, 15, 229–258.Google Scholar
  15. Case, R. Validation of a neo-Piagetian mental capacity construct. Journal of Experimental Child Psychology, 1972, 14, 287–302.CrossRefGoogle Scholar
  16. Case, R., & Globerson, T. Field independence and central computing space. Child Development, 1974, 45, 772–778.CrossRefGoogle Scholar
  17. Chase, C. I., & Pugh, R. C. Social class and performance on an intelligence test. Journal of Educational Measurement, 1971, 8, 197–202.CrossRefGoogle Scholar
  18. Chiang, A., & Atkinson, R. C. Individual differences and interrelationships among a select set of cognitive skills. Memory and Cognition, 1976, 4, 661–672.CrossRefGoogle Scholar
  19. Cleary, T. A., & Hilton, T. L. An investigation of item bias. Educational and Psychological Measurement, 1968, 28, 61–75.CrossRefGoogle Scholar
  20. College Entrance Examination Board. Profiles, college-bound seniors, 1981. New York: Author, 1982.Google Scholar
  21. Crannell, C. W., & Parrish, J. M. A comparison of immediate memory span for digits, letters, and words. Journal of Psychology, 1957, 44, 319–327.CrossRefGoogle Scholar
  22. Darlington, R. B., & Boyce, C. M. The validity of Jensen’s statistical methods. Behavioral and Brain Sciences, 1982, 5, 323–324.CrossRefGoogle Scholar
  23. Dawley, D. A nation of lords: The autobiography of the Vice Lords. Garden City, New York: Anchor Books, 1973.Google Scholar
  24. Dempster, F. N. Memory span and short-term memory capacity: A developmental study. Journal of Experimental Child Psychology, 1978, 26, 419–431.CrossRefGoogle Scholar
  25. Dempster, F. N. Memory span: Sources of individual and developmental differences. Psychological Bulletin, 1981, 89, 63–100.CrossRefGoogle Scholar
  26. Dempster, F. N., & Cooney, J. B. Individual differences in digit span, susceptibility to proactive interference, and aptitude/achievement test scores. Intelligence, 1982, 6, 399–416.CrossRefGoogle Scholar
  27. Dempster, F. N., & Zinkgraf, S. A. Individual differences in digit span and chunking. Intelligence, 1982, 6, 201–213.CrossRefGoogle Scholar
  28. Dorfman, D. D. The Cyril Burt question: New findings. Science, 1978, 201, 1177–1186.PubMedCrossRefGoogle Scholar
  29. “Dunbar Report”(untitled). Baltimore: Baltimore City Public Schools, 1982.Google Scholar
  30. Durning, K. P. Preliminary assessment of the Navy Memory for Numbers Test. Unpublished master’s thesis, San Diego State College, 1968.Google Scholar
  31. Globerson, T. Mental capacity and cognitive functioning: Developmental and social class differences. Developmental Psychology, 1983, 19, 225–230.CrossRefGoogle Scholar
  32. Gordon, R. A. Examining labelling theory: The case of mental retardation. In W. R. Gove (Ed.), The labelling of deviance (2nd ed.). Beverly Hills, Calif.: Sage Publications, 1980. (Originally published, 1975.)Google Scholar
  33. Gordon, R. A. Labelling theory, mental retardation, and public policy: Larry P. and other developments since 1974. In W. R. Gove (Ed.), The labelling of deviance (2nd ed.). Beverly Hills, Calif.: Sage Publications, 1980.Google Scholar
  34. Gordon, R. A., & Rudert, E. E. Bad news concerning IQ tests. Sociology of Education, 1979, 52, 174–190.CrossRefGoogle Scholar
  35. Gutkin, T. B., & Reynolds, C. R. Factorial similarity of the WISC-R for Anglos and Chicanos referred for psychological services. Journal of School Psychology, 1980, 18, 34–39. (a)CrossRefGoogle Scholar
  36. Gutkin, T. B., & Reynolds, C. R. WISC-R factor equivalence across race: Examining the standardization sample. Paper presented at the annual meeting of the American Psychological Association, Montreal, September 1980. (b)Google Scholar
  37. Guttman, L. Introduction to facet design and analysis. Proceedings of the Fifteenth International Congress of Psychology, Brussels, 1957. Amsterdam: North-Holland Publishing, 1959.Google Scholar
  38. Guttman, L. The nonmetric breakthrough for the behavioral sciences. Proceedings of the Second National Conference on Data Processing. Rehovot: Information Processing Association of Israel, 1966.Google Scholar
  39. Halligan, P. D. Personal communication, January 19, 1982.Google Scholar
  40. Harris, A. J., & Lovinger, R. J. Longitudinal measures of the intelligence of disadvantaged Negro adolescents. School Review, 1968, 76, 60–66.CrossRefGoogle Scholar
  41. Herskovits, M. J. The myth of the Negro past. New York: Harper and Brothers, 1941.Google Scholar
  42. Herskovits, M. J. Problem, method and theory in Afroamerican studies. Afroamerica, 1945, 1, 5–24. (a)Google Scholar
  43. Herskovits, M. J. The processes of cultural change. In R. Linton (Ed.), The science of man in the world crisis. New York: Columbia University Press, 1945. (b)Google Scholar
  44. Herskovits, M. J. Man and his works: The science of cultural anthropology. New York: Knopf, 1951.Google Scholar
  45. Herskovits, M. L. Acculturation: The study of culture contact. Gloucester, Mass.: Peter Smith, 1958. (Originally published, 1938.)Google Scholar
  46. Hills, J. R., & Stanley, J. C. Prediction of freshman grades from SAT and from level 4 of SCAT in three predominantly Negro state colleges. Proceedings of the 76th Annual Convention of the American Psychological Association, 1968, 3, 241–242.Google Scholar
  47. Hills, J. R., & Stanley, J. C. Easier test improves prediction of black students’ college grades. Journal of Negro Education, 1970, 39, 320–324.CrossRefGoogle Scholar
  48. Honzik, M. P., Macfarlane, J. W., & Allen, L. The stability of mental test performance between two and eighteen years. Journal of Experimental Education, 1948, 17, 309–324.Google Scholar
  49. Hsia, J. Cognitive assessment of Asian Americans. Paper presented at Symposium on bilingual research, sponsored by NIE-NCBR, Los Alamitos, Calif., September 3–5, 1980.Google Scholar
  50. Hunt, J. McV. Has compensatory education failed? Has it been attempted? Harvard Educational Review, 1969, 39, 278–300.Google Scholar
  51. Ironson, G. H. Use of chi-square and latent trait approaches for detecting item bias. In R. A. Berk (Ed.), Handbook of methods for detecting test bias. Baltimore: Johns Hopkins University Press, 1982.Google Scholar
  52. Jacobs, J. Experiments on “prehension.” Mind, 1887, 12, 75–79.CrossRefGoogle Scholar
  53. Jennrich, R. I. An asymptotic x 2 test for the equality of two correlation matrices. Journal of the American Statistical Association, 1970, 65, 904–912.Google Scholar
  54. Jensen, A. R. How much can we boost IQ and scholastic achievement? Harvard Educational Review, 1969, 39, 1–123. (a)Google Scholar
  55. Jensen, A. R. Reducing the heredity-environment uncertainty: A reply. Harvard Educational Review, 1969, 39, 449–483. (b)Google Scholar
  56. Jensen, A. R. Educability and group differences. New York: Harper & Row, 1973.Google Scholar
  57. Jensen, A. R. Cumulative deficit: A testable hypothesis? Developmental Psychology, 1974, 10, 996–1019. (a)CrossRefGoogle Scholar
  58. Jensen, A. R. How biased are culture-loaded tests? Genetic Psychology Monographs, 1974, 90, 185–244. (b)Google Scholar
  59. Jensen, A. R. Cumulative deficit in IQ of blacks in the rural South. Developmental Psychology, 1977, 13, 184–191. (a)CrossRefGoogle Scholar
  60. Jensen, A. R. An examination of culture bias in the Wonderlic Personnel Test. Intelligence, 1977, 1, 51–64. (b)CrossRefGoogle Scholar
  61. Jensen, A. R. Bias in mental testing. New York: Free Press, 1980. (a)Google Scholar
  62. Jensen, A. R. Correcting the bias against mental testing: A preponderance of peer agreement. Behavioral and Brain Sciences, 1980, 3, 359–368. (b)CrossRefGoogle Scholar
  63. Jensen, A. R. Uses of sibling data in educational and psychological research. American Educational Research Journal, 1980, 17, 153–170. (c)Google Scholar
  64. Jensen, A. R., & Figueroa, R. A. Forward and backward digit span interaction with race and IQ: Predictions from Jensen’s theory. Journal of Educational Psychology, 1975, 67, 882–893.PubMedCrossRefGoogle Scholar
  65. Jensen, A. R., & Osborne, R. T. Forward and backward digit span interaction with race and IQ: A longitudinal developmental comparison. Indian Journal of Psychology, 1979, 54, 75–87.Google Scholar
  66. Jensen, A. R., & Reynolds, C. R. Race, social class and ability patterns on the WISC-R. Personality and Individual Differences, 1982, 3, 423–438.CrossRefGoogle Scholar
  67. Kamin, L. J. Expert witness testimony. Larry P. et al. v. Wilson Riles et al. Reporters’ daily transcript, United States District Court, Northern District of California, 1977.Google Scholar
  68. Kamin, L. J. Expert witness testimony. Parents in Action on Special Education (P.A.S.E.) et al. v. Joseph P. Hannon et al. Reporters’ daily transcript, United States District Court, Northern District of Illinois, 1980.Google Scholar
  69. Kaufman, A. S. WISC-R research: Implications for interpretation. School Psychology Digest, 1979, 8, 5–27.Google Scholar
  70. Kaufman, A. S., & Doppelt, J. E. Analysis of WISC-R standardization data in terms of the stratification variables. Child Development, 1976, 47, 165–171.CrossRefGoogle Scholar
  71. Keiser, R. L. The Vice Lords: Warriors of the streets. New York: Holt, Rinehart and Winston, 1969.Google Scholar
  72. Kempthorne, O., & Wolins, L. Testing reveals a big social problem. Behavioral and Brain Sciences, 1982, 5, 327–336.CrossRefGoogle Scholar
  73. Kennedy, W. A. A follow-up normative study of Negro intelligence and achievement. Monographs of the Society for Research in Child Development, 1969, 34(2, Serial No. 126).Google Scholar
  74. Kennedy, W. A., Van de Reit, V., & White, J. C., Jr. A normative sample of intelligence and achievement of Negro elementary school children in the Southeastern United States. Monographs of the Society for Research in Child Development, 1963, 28(6, Serial No. 90).Google Scholar
  75. Labovitz, S. The assignment of numbers to rank order categories. American Sociological Review, 1970, 35, 515–524.CrossRefGoogle Scholar
  76. Linton, R. The study of man: An introduction. New York: Appleton-Century, 1936.Google Scholar
  77. Lynn, R. The intelligence of the Japanese. Bulletin of the British Psychology Society, 1977, 30, 69–72.Google Scholar
  78. Lynn, R. IQ in Japan and the United States shows a growing disparity. Nature, 1982, 297, 222–223.CrossRefGoogle Scholar
  79. Lynn, R., & Dziobon, J. On the intelligence of the Japanese and other Mongoloid peoples. Personality and Individual Differences, 1980, 1, 95–96.CrossRefGoogle Scholar
  80. McGurk, F. C. J. Race differences—Twenty years later. Homo, 1975, 26, 219–239.Google Scholar
  81. McNemar, Q. The revision of the Stanford-Binet Scale: An analysis of the standardization data. Boston: Houghton Mifflin, 1942.Google Scholar
  82. Medley, D. M., & Quirk, T. J. The application of a factorial design to the study of cultural bias in general culture items on the National Teacher Examination. Journal of Educational Measurement, 1974, 11, 235–245.CrossRefGoogle Scholar
  83. Mefferd, R. B., Jr., Wieland, B. A., & James, W. E. Repetitive psychometric measures: Digit span. Psychological Reports, 1966, 18, 3–10.PubMedCrossRefGoogle Scholar
  84. Mercer, J. R. Expert witness testimony. Larry P. et al. v. Wilson Riles et al. Reporters’ daily transcript, United States District Court, Northern District of California, 1977.Google Scholar
  85. Mercer, J. R. Test “validity,” “bias,” and “fairness”: An analysis from the perspective of the sociology of knowledge. Interchange, 1978-1979, 9, 1–16.CrossRefGoogle Scholar
  86. Mercer, J. R. In defense of racially and culturally non-discriminatory assessment. School Psychology Digest, 1979, 8, 89–115. (a)Google Scholar
  87. Mercer, J. R. SOMPA technical manual. New York: Psychological Corporation, 1979. (b)Google Scholar
  88. Miele, F. Cultural bias in the WISC. Intelligence, 1979, 3, 149–164.CrossRefGoogle Scholar
  89. Mintz, S. W., & Price, R. An anthropological approach to the Afro-American past: A Caribbean perspective. Philadelphia: Institute for the Study of Human Issues, 1976.Google Scholar
  90. Mood, A. M., Graybill, F. A., & Boes, D. C. Introduction to the theory of statistics (3rd ed.). New York: McGraw-Hill, 1974.Google Scholar
  91. Nichols, P. L. The effects of heredity and environment on intelligence test performance in 4 and 7 year old white and Negro sibling pairs. Doctoral dissertation, University of Minnesota, 1970. (University Microfilms No. 71-18, 874.)Google Scholar
  92. Osborne, R. T. Racial differences in mental growth and school achievement: A longitudinal study. Psychological Reports, 1960, 7, 233–239.Google Scholar
  93. Osborne, R. T. Twins: Black and white. Athens, Ga: Foundation for Human Understanding, 1980.Google Scholar
  94. Reschly, D. J. WISC-R factor structures among Anglos, blacks, Chicanos, and native-American Papagos. Journal of Consulting and Clinical Psychology, 1978, 46, 417–422.CrossRefGoogle Scholar
  95. Reynolds, C. R. The invariance of the factorial validity of the Metropolitan Readiness Tests for blacks, whites, males, and females. Educational and Psychological Measurement, 1979, 39, 1047–1052.CrossRefGoogle Scholar
  96. Reynolds, C. R. Differential construct validity of a preschool battery for blacks, whites, males, and females. Journal of School Psychology, 1980, 18, 112–125.CrossRefGoogle Scholar
  97. Reynolds, C. R. The problem of bias in psychological assessment. In C. R. Reynolds & T. B. Gutkin (Eds.), The handbook of school psychology. New York: Wiley, 1982.Google Scholar
  98. Rock, D. A., & Werts, C. E. Construct validity of the SAT across populations—An empirical confirmatory study (RDR 78-79, No. 5). Princeton, N.J.: Educational Testing Service, 1979.Google Scholar
  99. Rogers, E. M. Diffusion of innovations. New York: Free Press, 1962.Google Scholar
  100. Rucci, A. J., & Tweney, R. D. Analysis of variance and the “second discipline” of scientific psychology: A historical account. Psychological Bulletin, 1980, 87, 166–184.CrossRefGoogle Scholar
  101. Salmon, W. C. Confirmation and relevance. In G. Maxwell & R. M. Anderson, Jr. (Eds.), Induction, probability, and confirmation. Minnesota Studies in the Philosophy of Science (Vol. 6). Minneapolis: University of Minnesota Press, 1975.Google Scholar
  102. Sandoval, J. The WISC-R and internal evidence of test bias with minority groups. Journal of Consulting and Clinical Psychology, 1979, 47, 919–927.CrossRefGoogle Scholar
  103. Sandoval, J., & Mülle, M. P. W. Accuracy of judgments of WISC-R item difficulty for minority groups. Journal of Consulting and Clinical Psychology, 1980, 48, 249–253.CrossRefGoogle Scholar
  104. Scarr, S. The effects of family background: A study of cognitive differences among black and white twins. In S. Scarr (Ed.), Race, social class, and individual differences in I.Q. Hillsdale, N.J.: Erlbaum, 1981.Google Scholar
  105. Schapera, I. The contributions of Western civilization to modern Kxatla culture. Transactions of the Royal Society of South Africa, 1936, 24, 221–252.CrossRefGoogle Scholar
  106. Scriven, M. The key property of physical laws—inaccuracy. In H. Feigl & G. Maxwell (Eds.), Current issues in the philosophy of science. New York: Holt, Rinehart & Winston, 1961.Google Scholar
  107. Shuey, A. M. The testing of Negro intelligence (2nd ed.). New York: Social Science Press, 1966.Google Scholar
  108. Siegel, S. Nonparametric statistics for the behavioral sciences. New York: McGraw-Hill, 1956.Google Scholar
  109. Stanley, J. C. Plotting ANOVA interactions for ease of visual interpretation. Educational and Psychological Measurement, 1969, 29, 793–797.CrossRefGoogle Scholar
  110. Stanley, J. C, & Porter, A. C. Correlation of scholastic aptitude test score with college grades for Negroes versus whites. Journal of Educational Measurement, 1967, 4, 199–218.CrossRefGoogle Scholar
  111. Stinchcombe, A. L. Environment: The cumulation of effects is yet to be understood. Harvard Educational Review, 1969, 39, 511–522.Google Scholar
  112. Terman, L. M. The measurement of intelligence: An explanation of and a complete guide for the use of the Stanford revision and extension of the Binet-Simon Intelligence Scale. Boston: Houghton Mifflin, 1916.Google Scholar
  113. Terman, L. M. Errors in scoring Binet tests. Psychological Clinic, 1918, 12, 33–39.Google Scholar
  114. Terman, L. M., & Merrill, M. A. Measuring intelligence: A guide to the administration of the new revised Stanford-Binet tests of intelligence. Boston: Houghton Mifflin, 1937.Google Scholar
  115. Terman, L. M., & Merrill, M. A. Stanford-Binet Intelligence Scale: Manual for the Third Revision, Form L-M. Boston: Houghton Mifflin, 1960.Google Scholar
  116. Terman, L. M., Lyman, G., Ordahl, G., Ordahl, L. E., Galbreath, N., & Talbert, W. The Stanford revision and extension of the Binet-Simon scale for measuring intelligence. Baltimore: Warwick & York, 1917.CrossRefGoogle Scholar
  117. Thomas, H. IQ, interval scales, and normal distributions. Psychological Bulletin, 1982, 91, 198–202.CrossRefGoogle Scholar
  118. Tomlinson, H. Differences between pre-school Negro children and their older siblings on the Stanford-Binet scales. Journal of Negro Education, 1944, 13, 474–479.CrossRefGoogle Scholar
  119. Torgerson, W. S. Theory and methods of scaling. New York: Wiley, 1958.Google Scholar
  120. Vernon, P. E. The abilities and achievements of Orientals in North America. New York: Academic Press, 1982.Google Scholar
  121. Vetta, A. Correlation, regression and biased science. Behavioral and Brain Sciences, 1980, 3, 357–358.CrossRefGoogle Scholar
  122. Vetta, A. IQ or intelligence? Behavioral and Brain Sciences, 1982, 5, 336–337.CrossRefGoogle Scholar
  123. Viteles, M. S. The children of a Jewish orphanage. Psychological Clinic, 1919, 12, 248–254.Google Scholar
  124. Wahlsten, D. Race, the heritability of IQ, and the intellectual scale of nature. Behavioral and Brain Sciences, 1980, 3, 358–359.CrossRefGoogle Scholar
  125. Walker, H. M., & Lev, J. Statistical inference. New York: Holt, 1953.CrossRefGoogle Scholar
  126. Wechsler, D. The measurement of adult intelligence. Baltimore: Williams & Wilkins, 1939.CrossRefGoogle Scholar
  127. Wechsler, D. Wechsler Intelligence Scale for Children manual. New York: Psychological Corporation, 1949.Google Scholar
  128. Wechsler, D. Wechsler Intelligence Scale for Children—Revised. New York: Psychological Corporation, 1974.Google Scholar
  129. Weinberg, S. The first three minutes; A modern view of the origin of the universe. New York: Basic Books, 1977.Google Scholar
  130. Wheeler, L. R. A comparative study of the intelligence of East Tennessee mountain children. Journal of Educational Psychology, 1942, 33, 321–334.CrossRefGoogle Scholar
  131. Williams, R. L. The BITCH-100: A culture-specific test. Journal of Afro-American Issues, 1975, 3, 103–116.Google Scholar
  132. Yerkes, R. M. (Ed.). Psychological examining in the United States Army. Memoirs of the National Academy of Sciences (Vol. 15). Washington, D.C.: Government Printing Office, 1921.Google Scholar
  133. Yule, G. U., & Kendall, M. G. An introduction to the theory of statistics (14th ed.). New York: Hafher Publishing, 1950.Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Robert A. Gordon
    • 1
  1. 1.Department of SociologyJohns Hopkins UniversityBaltimoreUSA

Personalised recommendations