Basic Statistical Terminology

Understanding psychometrics requires familiarity with key statistical concepts. This page explains essential terminology used in IQ testing and cognitive assessment.

Measures of Central Tendency

Mean (Average)

The sum of all values divided by the number of values. In IQ testing, the mean is standardized to 100.

Mean = Σx / n // Sum of all scores divided by number of scores

Median

The middle value when data is ordered from lowest to highest. Less affected by extreme scores than the mean.

Mode

The most frequently occurring value in a dataset. Less commonly used in psychometrics.

Measures of Variability

Standard Deviation (SD)

A measure of how spread out scores are from the mean. In IQ testing, one standard deviation equals 15 points.

SD = √(Σ(x - mean)² / n) // Square root of variance

IQ Score Distribution

Range	IQ Scores	Percentage of Population
Mean ± 1 SD	85-115	68.27%
Mean ± 2 SD	70-130	95.45%
Mean ± 3 SD	55-145	99.73%

Variance

The average of squared differences from the mean. Standard deviation squared.

Variance = SD²

Range

The difference between the highest and lowest scores. Simple but affected by outliers.

Standardization Concepts

Z-Score

Number of standard deviations a score is from the mean. Used to compare scores across different tests.

Z = (X - Mean) / SD // Converts any score to standard units

Percentile Rank

The percentage of scores that fall below a particular score. An IQ of 100 is at the 50th percentile.

Common IQ Percentiles

IQ Score	Percentile	Rarity
130	98th	1 in 50
145	99.9th	1 in 1,000
160	99.997th	1 in 31,500

Normal Distribution

A bell-shaped curve where most scores cluster around the mean. IQ scores follow this distribution by design.

Reliability

Test-Retest Reliability

Consistency of scores when the same test is given twice. Good IQ tests have reliabilities above 0.90.

Internal Consistency

How well different parts of a test measure the same construct. Measured by Cronbach's alpha.

α = (k/(k-1)) × (1 - Σσ²ᵢ/σ²ₜ) // k = number of items, σ² = variance

Standard Error of Measurement (SEM)

The amount of error expected in an individual's score. Used to create confidence intervals.

SEM = SD × √(1 - reliability) // Lower SEM = more precise measurement

Validity

Construct Validity

Whether a test actually measures what it claims to measure (e.g., does an IQ test measure intelligence?).

Predictive Validity

How well test scores predict future outcomes. IQ scores predict academic and job performance.

Concurrent Validity

How well a test correlates with other established measures of the same construct.

Correlation and Regression

Correlation Coefficient (r)

Measures the strength and direction of relationship between two variables. Ranges from -1 to +1.

Interpreting Correlations

r = 0.90 to 1.00: Very strong positive
r = 0.70 to 0.89: Strong positive
r = 0.40 to 0.69: Moderate positive
r = 0.20 to 0.39: Weak positive
r = -0.20 to 0.20: No relationship

Coefficient of Determination (r²)

The proportion of variance in one variable explained by another. If r = 0.50, then r² = 0.25 (25% of variance explained).

Regression to the Mean

The tendency for extreme scores to be less extreme upon retesting. Important for understanding score changes.

Psychometric-Specific Terms

g-loading

The correlation between a test or subtest and general intelligence (g). Higher g-loading means the test better measures general cognitive ability.

Flynn Effect

The observation that IQ scores have increased over generations, requiring periodic re-norming of tests.

Ceiling Effect

When a test cannot accurately measure very high abilities because it lacks difficult enough items.

Floor Effect

When a test cannot accurately measure very low abilities because it lacks easy enough items.

Key Takeaway

These statistical concepts form the foundation of psychometric testing. Understanding them helps interpret test scores accurately and appreciate both the strengths and limitations of cognitive assessment.