Measuring Intelligence: Scales, Methodology, and Psychometric Properties

Overview of Measuring Intelligence

• Most intelligence measures are grounded in an analytic view of intelligence, focusing on what can be quantified through cognitive testing.

• The primary goal of modern and historical intelligence testing has been to establish a systematic measurement of the child's (or adult's) intellectual powers.

The Binet-Simon Scale (1905)

• Initial Purpose: Developed by Alfred Binet and Theodore Simon to differentiate between "normal" and "retarded" children (using the terminology of the early 20th century). The objective was to identify individuals with abnormally low intelligence scores who might require specialized educational attention.

• Methodology:

  • Standardization: Binet and Simon wrote test items specific to different age groups and standardized the results across those groups.

  • Progressive Testing: Children would take tests starting at their age level and move progressively to higher "age" tests until they reached a level they could no longer pass.

  • Concept of Mental Age: A child was assigned a "mental age" based on the highest age-normed items they could successfully complete.

  • Implications: A child with low intelligence would possess a "mental age" lower than their actual chronological age. This established the first formal conceptualization of intelligence testing.

The Stanford-Binet Scale and the IQ Formula

• Lewis Terman's Contribution: Terman adapted the Binet-Simon scale to create the Stanford-Binet scale (1916).

• The Intelligence Quotient (IQ): Terman introduced the concept of IQ as a mathematical ratio.

• Original IQ Formula:     $IQ = \frac{\text{Mental Age}}{\text{Chronological Age}} \times 100$

• Calculation Examples:

  • If a 7-year-old child passes all age 7 items: $\frac{7}{7} \times 100 = 100$ (Average Intelligence).

  • If a 7-year-old child passes age 8 items: The IQ will be above $100$ (Above Average Intelligence).

  • If a 7-year-old child fails to pass age 6 items: The IQ will be below $100$ (Below Average Intelligence).

• The Problem with Ratio IQ:

  • The highest items for measuring mental age were capped at age 16 items.

  • Because the chronological age (the denominator) continues to rise while the mental age (the numerator) levels off, IQ scores would mathematically decrease simply by getting older.

  • Example: A 17-year-old could only achieve a maximum mental age of 16, resulting in an IQ of $\frac{16}{17} \times 100 \approx 94$, even if their actual cognitive ability had not declined.

Modern IQ Calculation and Distribution

• Deviation Score: Nowadays, IQ is calculated based on a deviation score relative to the whole population rather than a simple mental age/chronological age ratio.

• The Normal Distribution: Results are plotted on a bell-shaped curve.

  • Mean ($\mu$): The average IQ is set at $100$.

  • Standard Deviation ($\sigma$): The standard deviation is set at $15$.

  • This statistical framework provides bounds to classify performance as intellectual disability, average, or gifted.

Stanford-Binet: Fifth Edition (SB5)

• The test has been updated multiple times; the current version utilizes 10 core subtests yielding 5 factors of IQ:

  1. Fluid Reasoning (Fluid Intelligence): The capacity to solve novel problems, such as matrix reasoning.

  2. Knowledge (Crystallized Intelligence): Acquired knowledge, often measured via vocabulary.

  3. Quantitative Reasoning: Numerical ability and mathematical problem-solving.

  4. Visual-Spatial Reasoning: The ability to detect and analyze patterns in visual stimuli.

  5. Working Memory: The capacity to store and manipulate information in short-term memory.

Wechsler Intelligence Scales

• Developed by David Wechsler, these scales are among the most widely used intelligence measurements.

Versions of the Test

• WAIS-IV (2008): Wechsler Adult Intelligence Scale, for ages 16 and older.

• WISC-V (2014): Wechsler Intelligence Scale for Children, specifically for ages 7 to 16.

• WPPSI: Wechsler Preschool and Primary Scale of Intelligence, for children under the age of 7.

WAIS-IV Structure (Full-Scale IQ - FSIQ)

• Verbal Comprehension Index (VCI):

  • Similarities: Identifying commonalities (e.g., "In what ways are apples and pears alike?").

  • Vocabulary: Defining words (e.g., "What is a guitar?").

  • Information: General knowledge questions (e.g., "What is the capital of France?").

  • Comprehension (Supplementary): Social and practical reasoning (e.g., "Why are we tried by a jury of our peers?").

• Working Memory Index (WMI):

  • Digit Span: Repeating strings of numbers back to the examiner.

  • Arithmetic: Mental math calculations without paper or pencil (e.g., "If you buy six postcards for 45\text{\textcent} each, how much change from $\$5$?").

  • Letter-Number Sequencing (Supplementary): Reordering a mixed sequence (e.g., Repeating "Q-1-B-3-J-2" as "1-2-3-B-J-Q").

• Perceptual Reasoning Index (PRI):

  • Block Design: Copying patterns using physical blocks.

  • Matrix Reasoning: Finding the pattern that completes a vertical and horizontal rule.

  • Visual Puzzles: Combining geometric parts to match a target shape.

  • Picture Completion (Supplementary): Identifying missing components in pictures (e.g., a car without wheels or a balloon without a string).

  • Figure Weights (Supplementary): Determining weights needed to balance a scale (e.g., knowing 2 stars equal 1 green pentagon and 1 red circle equals 1 blue square and 1 star).

• Processing Speed Index (PSI):

  • Symbol Search: Timed task identifying if specific symbols are present in a group.

  • Coding: Transposing symbols into boxes based on a numerical key, similar to a codebreaker puzzle.

  • Cancellation (Supplementary): Quickly crossing out specific target shapes (e.g., red squares and yellow triangles) among distractors.

Raven’s Progressive Matrices

• An alternative measure of intelligence consisting of matrices in order of increasing difficulty.

• Format: Participants identify the missing element to complete a pattern based on vertical and horizontal rules.

• Key Characteristics:

  • Non-verbal: Does not require spoken or written language.

  • Measure of reasoning: Assesses Spearman’s $g$ (general intelligence).

  • Skill-independent: Independent of language, reading, and writing skills.

  • Application: Frequently used for job selection as it is considered a relatively unbiased test of intelligence.

Psychometric Properties: Reliability and Validity

• Reliability: The consistency of a measure over time.

  • Assessed via test-retest correlations (correlation between scores from the same person on two different occasions).

  • IQ tests generally exhibit high reliability, around $0.85$ (where $1.0$ is perfect reliability).

• Validity: The extent to which a test measures what it claims to measure.

  • Assessed by correlating test scores with theoretically related criteria, such as success in school.

  • Correlation between IQ and school success typically ranges from $0.40$ to $0.75$.

Arguments For and Against Intelligence Testing

Arguments For

• Practical Decision Making: Helps determine if a person has a learning disability or identifying the impact of brain damage to tailor treatment and education.

• Objectivity: These tests are more objective and less biased than subjective evaluative methods.

• Predictive Power: They are effective at predicting academic and occupational outcomes:

  • IQ & school grades: $0.4 \text{ to } 0.6$

  • IQ & number of years of schooling: $0.6 \text{ to } 0.8$

  • IQ & occupational attainment: $0.4 \text{ to } 0.5$

  • IQ & job performance: < 0.3 \text{ to } > 0.5

Arguments Against

• Validity Concerns: Critics argue they measure acquired learning (achievement) rather than innate learning ability.

• Cultural Bias: Potential bias toward Western cultures and dominant social groups with rich academic backgrounds.

• Labeling and Self-Fulfilling Prophecies: Negative labels can lead to reduced effort or lowered expectations, resulting in lower performance (the label causes the outcome).

• Narrow Scope: They often fail to capture other forms of intelligence, such as emotional intelligence.