Psychological Assessment of Intelligence, Psychometrics & Cultural Bias

1. The Evolution of Intelligence Testing & The IQ Metric

A. Alfred Binet & Théodore Simon (1905, 1908, 1911)

The 1905 Scale: Developed 30 items arranged in ascending order of difficulty to identify children requiring special education in France.
The 1908 Revision: Grouped items by age levels (ages 3 to 13) and introduced the revolutionary concept of Mental Age (MA). $\text{Mental Age (MA)} = \text{The chronological age at which an average child successfully passes a given battery of test items.}$

B. William Stern: Formulation of the Ratio IQ (1912)

German psychologist William Stern recognized that subtracting chronological age from mental age was misleading. He proposed the Intelligence Quotient (IQ) as a mathematical ratio:

$\mathbf{Ratio\ IQ} = \left( \frac{\mathbf{Mental\ Age\ (MA)}}{\mathbf{Chronological\ Age\ (CA)}} \right) \times 100$

If $\text{MA} = \text{CA}$ , $\text{IQ} = 100$ (Exactly average performance).
If $\text{MA} > \text{CA}$ , $\text{IQ} > 100$ (Advanced / Above average).
If $\text{MA} < \text{CA}$ , $\text{IQ} < 100$ (Delayed / Below average).

C. Lewis Terman: The Stanford-Binet Intelligence Scale (1916)

Lewis Terman of Stanford University adapted Binet's test for American English, incorporating Stern’s formula and standardizing norms on a large sample.
The Fatal Psychometric Flaw of Ratio IQ for Adults:
- Mental Age growth decelerates during adolescence and levels off completely around ages 16–18.
- In contrast, Chronological Age ( $CA$ ) continues to advance each year.
- Fatal Mathematical Artifact: A 40-year-old performing at a mental age of 16 would have an IQ of: $\text{Ratio IQ} = \left( \frac{16}{40} \right) \times 100 = \mathbf{40}$
- A normal, fully functional 40-year-old would falsely appear to suffer from severe intellectual disability. Ratio IQ is therefore mathematically invalid for adults.

2. David Wechsler & The Deviation IQ Revolution (1939, 1955)

David Wechsler, chief psychologist at Bellevue Psychiatric Hospital, discarded the concept of Mental Age entirely, inventing the Deviation IQ.

Rendering diagram...

The Deviation IQ Formula:

$\mathbf{Deviation\ IQ} = 100 + 15 \times \mathbf{z} = 100 + 15 \left( \frac{\mathbf{X - \mu}}{\mathbf{\sigma}} \right)$

Core Principle: An individual’s score is compared strictly to the statistical distribution of scores obtained by their own age-matched peer cohort.
Standard Distribution: Mean ( $\mu$ ) is fixed at 100, and Standard Deviation ( $\sigma$ ) is fixed at 15 (or 16 on Stanford-Binet).
Normal Distribution Benchmarks:
- $68.26\%$ of the general population scores between $85$ and $115$ ( $\pm 1\ \text{SD}$ ).
- $95.44\%$ of the population scores between $70$ and $130$ ( $\pm 2\ \text{SD}$ ).
- $99.72\%$ of the population scores between $55$ and $145$ ( $\pm 3\ \text{SD}$ ).

Modern Wechsler Test Batteries & WAIS-IV Architecture

WAIS-IV (Wechsler Adult Intelligence Scale): Ages 16 to 90 years.
WISC-V (Wechsler Intelligence Scale for Children): Ages 6 to 16 years, 11 months.
WPPSI-IV (Wechsler Preschool and Primary Scale of Intelligence): Ages 2 years, 6 months to 7 years, 7 months.

WAIS-IV Index Score	Core Cognitive Construct Measured	Exemplar Diagnostic Subtests
1. Verbal Comprehension (VCI)	Verbal concept formation, abstract verbal reasoning, and acquired cultural factual knowledge.	• Similarities: Abstract verbal logic and analogies. • Vocabulary: Defining words. • Information: General cultural and factual recall.
2. Perceptual Reasoning (PRI)	Fluid reasoning, non-verbal spatial processing, and visual-motor integration.	• Block Design: Reproducing 2D/3D patterns with colored cubes. • Matrix Reasoning: Inductive non-verbal pattern completion. • Visual Puzzles: Mentally combining geometric shapes.
3. Working Memory Index (WMI)	Temporary attention, mental manipulation of numerical info, and concentration.	• Digit Span: Repeating digits forward, backward, and ascending order. • Arithmetic: Solving timed mental math problems without paper.
4. Processing Speed Index (PSI)	Rapid visual scanning, perceptual discrimination, decision-making, and psychomotor speed.	• Symbol Search: Rapidly checking if target symbols appear in a line. • Coding: Transcribing digits into corresponding geometric symbols under time limits.

3. Individual vs. Group Intelligence Tests

Parameter	Individual Intelligence Tests (e.g., WAIS-IV, Stanford-Binet 5)	Group Intelligence Tests (e.g., Army Alpha/Beta, OLSAT)
Administration	One trained psychologist to one examinee.	One proctor to hundreds of examinees simultaneously.
Response Format	Oral responses, physical manipulation of blocks, pointing.	Paper-and-pencil or computerized multiple-choice.
Rapport & Observation	Allows rich qualitative observation of anxiety, frustration, hesitation, and problem-solving strategy.	Zero behavioral observation; examiner cannot tell if a low score was due to illness, panic, or low ability.
Scoring Flexibility	Open-ended answers probed dynamically by the examiner.	Strictly objective, standardized key; easily auto-scored.
Cost & Efficiency	Extremely expensive and labor-intensive (60–90 minutes).	Highly economical, rapid mass screening.

Historical Milestone: Army Alpha and Army Beta (WWI, 1917)

Commissioned by the APA and Robert Yerkes to screen 1.7 million American military recruits:

Army Alpha: Written, verbal test for literate English speakers (arithmetic problems, vocabulary, verbal analogies).
Army Beta: Non-verbal, pictorial/performance test for illiterate, non-English-speaking, or foreign-born recruits (maze completion, cube counting, symbol-digit matching).