G Factor

• All standardized tests of academic aptitude or achievement measure this general factor to some degree, but IQ test expressly designed for that purpose--measure it more accurately (Spearman, 1904)
• At the turn of the 20^th century Charles Spearman (1863-1945) used statistical methods such as Correlation and Factor Analysis to define mental abilities as factors.
• When two apparently different abilities are shown to be highly correlated, Spearman took this as an evidence for the existence of a general factor G.

Dispersion between and within individuals

• Thurstone asserted that perceptions have distributions between and within individuals. i.e. Not only different people have different perceptions. The same person may see things differently at different time.
• The same principle applies well to other types of measurement. i.e. By chances you may get a "C" in the mid-term but an "A" in the final.

Mismeasurement of Man

• "Determinists arguments for ranking people according to a single scale of intelligence, no matter how numerically sophisticated, have recorded little more than social prejudice." (Gould, 1981, pp. 27-28)

Multiple Intelligences

• Linguistic (e.g. T. S. Elliot)
• Logical-mathematical (e.g. Stephen Hawking)
• Interpersonal (e.g. Mother Teresa)
• Intrapersonal (e.g. Aristotle)
• Artistic-spatial (e.g. Picaso)
• Musical (e.g. Yo Yo Ma)
• Kinesthetic (e.g. Jackie Chan)
• Naturalist (e.g. Charles Darwin)

Gardner asserted that all eight intelligences are of equal intrinsic value. It is the culture and context in which people live and work that accord capacities a greater social value than others. In addition, scientists from the University of Sheffield, England, provided evidence that numerical reasoning and linguistic ability may be two independent entitles. They examined several patients who suffered severe damage to the language faculty of their brains, and found that their mathematical ability is intact.

Gardner, H. (1983). Frames of mind The theory of multiple intelligence. New York: Basic Books.

Gardner, H. (1996). Leading Minds: An Anatomy of leadership. New York: Basic Books.

Ross, P. (2005 June). Math with words. Scientific American, 292(6), 28-30.

How do people misuse/misinterpret tests?

SAT and Expenditures

• The data published in the Wall Street Journal (June 22, 1995) shows the rank of each state's average SAT score and average expenditure on education. Unfortunately, the data "show" the more a state spends, the worse (on average) their SAT rank is. Does this mean spending less on education will improve SAT rank?
• Problems with this analysis:
  • State level data may not be true within states.
  • Cost of living (and therefore expenditures) varies across the country.
  • Not everyone takes the SAT.
• What happens when we look at data from the National Assessment of Education Progress (NAEP) that a) was designed to measure achievement, and b) is taken by a representative sample? On contrary to the data on the Wall Street Journal, there is a positive relationship between NAEP and expenditures.
• Moral of the story: We cannot afford to be ignorant about how testing is used in our society, even if we do not want to use such tests in our classroom.

GRE and Faculty Psychology

• A human mind is compared to a physical body, which is composed of different faculties (muscles)
• In weight training the motion itself achieves nothing but to make you like Arnold Schwarznegger.
• Some learning materials may be irrelevant and inapplicable, but taking difficult tests like SAT and GRE can make you as smart as Albert Einstein.

IQ Test and Bell Curve Herrnstein and Murray (1994) found that in IQ tests Jews and East Asians, on the average, outperform European Americans, and the mean score of White Americans is higher than Blacks. The asserted that some portion of these differences are genetically (racially) determined. The bell-curve (a spread of ability) exists in spite of intervention (e.g. education, affirmative action...etc)

• Geary, D. C., Salthous, T. A., Chen, G. P., and Fan, L. (1994). Numerical cognition: Are U.S.--East Asian ability differences a recent phenomenon?

• Younger and older adults from the U.S. and China were tested.

• It indicated no consistent ability differences, except the younger Chinese adults substantially outperformed the younger Americans in arithmetic.

• The overall pattern suggests that the advantage of Chinese adults over American adults in arithmetic is a recent phenomenon.

  Philosopher Clark Glymour (1998) gave a philosophical argument against the bell curve theory in "What went wrong? Reflections on science by observation and the bell curve", Philosophy of Science, 65, 1-32. The major argument is that an observed statistical property is not qualified to be a causal inference.

  Reviewing the intelligence debate at its meeting of November 1994, the Board of Scientific Affairs of the American Psychological Association established a Task Force charged with preparing a report (Neisser et al., (1996). "Intelligence: Knows and unknowns". American Psychologist, 51, 77-101) to examine the claims made by Herrnstein and Murray. The summary of the report can be viewed here.

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