Measuring intelligence is another area where a principal component analysis is often used. There is not just one test that can be used to accurately measure a person’s intelligence—there are several tests that are known to be related to intelligence. Often intelligence tests can be classified into three groups: spatial reasoning, vocabulary, and memory. PCA is used to combine multiple measurements into an overall measure of intelligence. Psychologists call the first component the general intelligence factor, or g-score.
As Stephen Jay Gould pointed out, intelligence testing and principal component analysis have been used to offer a “scientific” basis for racist, classist, and sexists theories of “intelligence.” 10 There is little doubt that the U.S. Congressional Immigration Act of 1924 was racially motivated, to limit the entrance of several unwanted groups of people into the United States. Kamin states that intelligence tests were used to verify that “83% of the Jews, 80% of the Hungarians, 79% of the Italians, and 87% of the Russians were ‘feeble- minded’. Snyderman and Herrnstein question whether or not psychologists had any influence on the act. They claim that intelligence tests were misused as “evidence” of why some people should not be allowed to emigrate to the United States.
a. The data set Intelligence contains test results for 214 people who have each taken several intelligence tests. Use PCA on the Intelligence data set to find one overall measure of intelligence. How much of the total variability in the several measures of intelligence is explained by this g-score?
b. Intelligence test results are often standardized into an IQ score so that the mean score is 100 with a standard deviation of 15. Transform your data and find the IQ of the 10th person in the Intelligence data set.
c. Explain why intelligence tests (such as vocabulary tests) may have biased results when measuring the intelligence of newly arriving immigrants on Ellis Island.