Bell Curves
The results of intelligence tests follow the bell curve, a graph in the general shape of a bell. When the bell curve is used in psychological testing, the graph demonstrates a normal distribution of a trait, in this case, intelligence, in the human population. Many human traits naturally follow the bell curve. For example, if you lined up all your female schoolmates according to height, it is likely that a large cluster of them would be the average height for an American woman: 5’4”–5’6”. This cluster would fall in the center of the bell curve, representing the average height for American women (Figure 2). There would be fewer women who stand closer to 4’11”. The same would be true for women of above-average height: those who stand closer to 5’11”.
The trick to finding a bell curve in nature is to use a large sample size. Without a large sample size, it is less likely that the bell curve will represent the wider population.
representative sample
A representative sample is a subset of the population that accurately represents the general population.
If, for example, you measured the height of the women in your classroom only, you might not actually have a representative sample. Perhaps the women’s basketball team wanted to take this course together, and they are all in your class. Because basketball players tend to be taller than average, the women in your class may not be a good representative sample of the population of American women. But if your sample included all the women at your school, it is likely that their heights would form a natural bell curve.
The same principles apply to intelligence tests scores. Individuals earn a score called an intelligence quotient (IQ). Over the years, different types of IQ tests have evolved, but the way scores are interpreted remains the same. The average IQ score on an IQ test is 100. The bell curve uses the standard deviation to show how all scores are dispersed from the average score (Figure 3).
standard deviation
Standard deviation is is a measure of the amount of variation or dispersion in a set of data values from its average (mean) value. Standard deviations describe how data are dispersed in a population and give context to large data sets.
In modern IQ testing, one standard deviation is 15 points. So a score of 85 would be described as “one standard deviation below the mean.” How would you describe a score of 115 and a score of 70? Any IQ score that falls within one standard deviation above and below the mean (between 85 and 115) is considered average, and 82% of the population has IQ scores in this range. An IQ score of 130 or above is considered a superior level.
Only 2.2% of the population has an IQ score below 70 (American Psychological Association [APA], 2013). A score of 70 or below indicates significant cognitive delays, major deficits in adaptive functioning, and difficulty meeting “community standards of personal independence and social responsibility” when compared to same-aged peers (APA, 2013, p. 37). An individual in this IQ range would be considered to have an intellectual development disorder (intellectual disability) and exhibit deficits in intellectual functioning and adaptive behavior (American Association on Intellectual and Developmental Disabilities, 2013). Formerly known as mental retardation, the accepted term now is intellectual development disorder, and it has four subtypes: mild, moderate, severe, and profound. The Diagnostic and Statistical Manual of Psychological Disorders lists criteria for each subgroup (APA, 2013).
| Intellectual Development Disorder Subtype | Percentage of Intellectually Disabled Population | Description |
|---|---|---|
| Mild | 85% | 3rd- to 6th-grade skill level in reading, writing, and math; may be employed and live independently |
| Moderate | 10% | Basic reading and writing skills; functional self-care skills; requires some oversight |
| Severe | 5% | Functional self-care skills; requires oversight of daily environment and activities |
| Profound | <1% | May be able to communicate verbally or nonverbally; requires intensive oversight |
On the other end of the intelligence spectrum are those individuals whose IQs fall into the highest ranges. Consistent with the bell curve, about 2% of the population falls into this category. People are considered gifted if they have an IQ score of 130 or higher, or superior intelligence in a particular area. Long ago, popular belief suggested that people of high intelligence were maladjusted. This idea was disproven through a groundbreaking study of gifted children. In 1921, Lewis Terman began a longitudinal study of over 1500 children with IQs over 135 (Terman, 1925). His findings showed that these children became well-educated, successful adults who were, in fact, well-adjusted (Terman & Oden, 1947). Additionally, Terman’s study showed that the subjects were above average in physical build and attractiveness, dispelling an earlier popular notion that highly intelligent people were “weaklings.” Some people with very high IQs elect to join Mensa, an organization dedicated to identifying, researching, and fostering intelligence. Members must have an IQ score in the top 2% of the population, and they may be required to pass other exams in their application to join the group.
What Do You Think?: Intellectually Disabled Criminals and Capital Punishment
The case of Atkins v. Virginia was a landmark case in the United States Supreme Court. On August 16, 1996, two men, Daryl Atkins and William Jones, robbed, kidnapped, and then shot and killed Eric Nesbitt, a local airman from the U.S. Air Force. A clinical psychologist evaluated Atkins and testified at the trial that Atkins had an IQ of 59. The mean IQ score is 100. The psychologist concluded that Atkins had an intellectual disability (formerly known as mental retardation). The jury found Atkins guilty, and he was sentenced to death. Atkins and his attorneys appealed to the Supreme Court. In June 2002, the Supreme Court reversed a previous decision and ruled that executions of criminals with intellectual disability are ‘cruel and unusual punishments’ prohibited by the Eighth Amendment. The court wrote in its decision:
Clinical definitions of [intellectual disability] require not only subaverage intellectual functioning, but also significant limitations in adaptive skills. [Persons with intellectual disability] frequently know the difference between right and wrong and are competent to stand trial. Because of their impairments, however, by definition they have diminished capacities to understand and process information, to communicate, to abstract from mistakes and learn from experience, to engage in logical reasoning, to control impulses, and to understand others’ reactions. Their deficiencies do not warrant an exemption from criminal sanctions, but diminish their personal culpability (Atkins v. Virginia, 2002, par. 5).
The court also decided that there was a state legislature consensus against the execution of people with intellectual disability and that this consensus should stand for all of the states. The Supreme Court ruling left it up to the states to determine their own definitions of intellectual disability. The definitions vary among states as to who can be executed. In the Atkins case, a jury decided that because he had many contacts with his lawyers and thus was provided with intellectual stimulation, his IQ had reportedly increased, and he was now smart enough to be executed. He was given an execution date and then received a stay of execution after it was revealed that lawyers for co-defendant, William Jones, coached Jones to “produce a testimony against Mr. Atkins that did match the evidence” (Liptak, 2008). After the revelation of this misconduct, Atkins was re-sentenced to life imprisonment.
Atkins v. Virginia (2002) highlights several issues regarding society’s beliefs around intelligence. In the Atkins case, the Supreme Court decided that intellectual disability does affect decision-making and therefore should affect the nature of the punishment such criminals receive. Where, however, should the lines of intellectual disability be drawn? In May 2014, the Supreme Court ruled in a related case (Hall v. Florida) that IQ scores cannot be used as a final determination of a prisoner’s eligibility for the death penalty (Roberts, 2014).