Understanding IQ Scores: do Intelligent People have Higher or Lower Scores?
It is a common misconception that intelligent individuals have higher IQ scores compared to the general population. However, this idea does not align with how IQ scores are structured and calculated. IQ scores are standardized to ensure they accurately reflect a person's relative intelligence relative to their peers. Let's delve deeper into how IQ scores are determined and why the concept of 'smart' and IQ scores may not always align perfectly.
How IQ Scores are Arrived At
Unlike school tests where scores depend on the number of correct answers, IQ scores are standardized. Most IQ tests have a set number of questions, and the average score is arbitrarily designated as 100, regardless of the test's difficulty level. For instance, if an IQ test has 100 questions, many people might score around 40, which is then assigned a score of 100. This is simply the average score for that specific test.
An important concept to understand is that the number 100 in IQ tests does not imply that those who scored 100 have an average level of intelligence. Rather, it is the median score of the test-takers, which changes depending on the test's design. In tests with a higher top score, the average might be 80, and in tests with a lower top score, the average might be 120. The key is that the average score is usually 100, but it is not aligned with the difficulty of the test.
The Standard Deviation and Reliability of IQ Scores
IQ test scores also have a standard deviation, typically around 15 points. This means that when someone takes the test multiple times, their scores can vary significantly and still be considered the same level of intelligence. For example, if a person scores 100 on an IQ test the first time, they might score 90 or 115 on subsequent tests. These fluctuations are normal and do not indicate a change in intelligence.
It is important to note that IQ tests are not meant to reflect a person's true level of intelligence over time but rather to provide a snapshot of their cognitive abilities at a given moment. A single score can be influenced by a variety of factors, including preparation, stress, and test anxiety, all of which can impact performance.
Understanding the Gaussian Distribution and Norming Groups
IQ tests are designed to produce a Gaussian distribution, also known as a normal distribution. In this distribution, half of the scores fall below the mean (100) and half above, creating a bell curve. This distribution is achieved by including or excluding test items of varying difficulty levels until the test matches the desired distribution for the norming group.
The norming group consists of a selected subset of people who represent the general population. For example, the Wechsler Adult Intelligence Scale (WAIS) has different norming groups for the US and Canadian versions. However, the norming process is expensive, and the group sizes are typically small, often in the thousands. The Woodcock-Johnson, a well-known IQ test, has one of the largest norming groups of 8,000 participants.
An interesting aspect of the norming process is that it deliberately excludes individuals with organic retardation, who have genetic defects that significantly impact their intelligence. These individuals are real and their inclusion in large-scale IQ tests can skew the distribution to the lower end of the spectrum. This means that the percentage of people with subaverage IQ scores is likely higher than it would be if organic retardation were not factored in.
Skewness in IQ Scores
The figure below illustrates how skew can develop when too many easy test items are used. This is similar to the effect when organic retardation is included in a full population estimate.
Moreover, item difficulties alone can affect the skewness of the distribution. If an average item difficulty is higher than 0.5, the distribution becomes positively skewed, meaning more people score higher. Conversely, if the average item difficulty is lower than 0.5, the distribution becomes negatively skewed, meaning more people score lower.
For a more in-depth understanding, refer to the work by Arthur R. Jensen, 'Bias in Mental Testing' (1980), which provides a comprehensive analysis of these concepts.
In conclusion, while it is tempting to equate intelligence with high IQ scores, the reality is more nuanced. IQ scores are standardized and can fluctuate based on various factors. Skewed distributions, which can include organic retardation, further complicate the relationship between intelligence and IQ scores. Understanding these concepts helps to demystify the realm of intelligence testing and encourages a more accurate and inclusive approach to assessing cognitive abilities.