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Psychological Test

A standardized process or device that yields quantifiable information about a sample of behavior or cognitive processes.

Standardized Procedure

Uniform rules and procedures for administration and scoring that ensure consistency across examinees and testing sessions.

Behavior Sample

A representative collection of observed responses or performances used to infer broader traits or capabilities.

Quantification

Assigning numerical values to test performance to allow statistical comparison and trait measurement.

MAPIN Classification

A functional taxonomy categorizing tests into Mental ability, Achievement, Personality, Interests, and Neuropsychological measures.

Maximum Performance vs. Typical Performance

Maximum performance measures evaluate optimal capabilities under best effort, whereas typical performance measures assess routine habits, traits, or attitudes.

Paper-and-Pencil vs. Performance Tests

Paper-and-pencil tests utilize written booklets or answer sheets, whereas performance tests require physical manipulation of objects or apparatuses.

Speed vs. Power Tests

Speed tests use simple items under strict time limits to assess response rate, whereas power tests feature items of increasing difficulty under generous limits to evaluate mastery.

Individual vs. Group Tests

Individual tests are administered one-on-one by a trained examiner, whereas group tests are administered simultaneously to multiple examinees by a single proctor.

Norm-Referenced vs. Criterion-Referenced Interpretation

Norm-referenced interpretation compares scores against a reference norm group, whereas criterion-referenced interpretation evaluates performance against a predefined content standard.

Differential Perspective

A foundational orientation in testing focusing on quantifying individual differences rather than establishing universal laws of human behavior.

Four Assumptions of Testing

The premises that humans possess recognizable traits, these traits can be quantified, they remain reasonably stable over time, and quantified measures relate to real-world behavior.

Six Major Forces in Testing

The primary historical drivers shaping testing: scientific impulse, concern for the individual, practical applications, statistical methodology, rise of clinical psychology, and computers.

Remote Background (Up to 1840)

An early historical period focused on universal human philosophy, with ancient Chinese civil service exams serving as an early precursor to testing.

Setting the Stage (1840-1880)

A 40-year period marked by mental health reform, adoption of written school exams, Darwinian focus on variation, and Wundt's founding of experimental psychology in 1879.

The Roots (1880-1915)

The 35-year foundational era of modern testing featuring Galton's work on individual differences, Cattell coining 'mental test' in 1890, Binet's 1905 scale, and Spearman's factor theory.

Flowering (1915-1940)

A 25-year period of rapid test expansion initiated by Terman's 1916 Stanford-Binet, WWI Army Alpha/Beta group tests, achievement batteries, projective inkblots, and interest inventories.

Consolidation (1940-1965)

A 25-year period of professional maturity following WWII, marked by Gulliksen's CTT text, technical testing standards, and seminal textbooks by Cronbach and Anastasi.

Just Yesterday (1965-2000)

A 35-year transformative era characterized by the emergence of Item Response Theory, public/legal scrutiny of testing, and mainframes/desktop computerization.

And Now (2000-Present)

The contemporary era defined by test proliferation, managed care demands for brief instruments, evidence-based practice, and computer-adaptive/online testing.

Francis Galton

A pioneer of individual differences and statistical methods who developed bivariate distribution charts and introduced evolutionary theory into psychology.

James McKeen Cattell

An American psychologist who studied under Wundt and Galton, established early sensory-motor battery testing, and coined the term 'mental test' in 1890.

Alfred Binet & Theodore Simon

The developers of the 1905 Binet-Simon Scale, which focused on higher mental processes to identify children needing special educational support.

Charles Spearman

An English theorist who proposed the two-factor theory of intelligence in 1904 and developed tetrad differences, the precursor to factor analysis.

Arthur Otis

A student of Terman who developed the Army Alpha and Army Beta tests during WWI, pioneering group mental ability testing.

Lewis Terman

The Stanford psychologist who revised the Binet scale in 1916 to create the Stanford-Binet Intelligence Scale and introduced the intelligence quotient concept to the US.

Raw Score

The immediate, unadjusted numerical score obtained directly from an examinee's test responses, such as total correct items.

Normed Score (Derived Score)

A raw score transformed into a relative metric to indicate an examinee's standing relative to a standardized norm group.

Nominal Scale

A level of measurement that uses numbers strictly as qualitative labels or category identifiers with no quantitative or ordinal meaning.

Ordinal Scale

A level of measurement that ranks observations in order of magnitude without equal intervals between ranks.

Interval Scale

A measurement level featuring equal distances between score points but lacking an absolute, non-arbitrary zero point.

Ratio Scale

The highest level of measurement, characterized by equal score intervals and a true zero point representing total absence of the measured trait.

Mean (M)

The arithmetic average of a score distribution, calculated by dividing the sum of all scores by the total sample size.

Median (Mdn)

The middlemost score in an ordered distribution that divides the total number of cases into two equal halves.

Mode

The most frequently occurring raw score value in a distribution.

Standard Deviation (SD)

A descriptive statistic quantifying the average dispersion or spread of individual scores around the distribution mean.

Variance (SD^2)

The average squared deviation of scores from the mean, representing total score variability.

Interquartile Range

A measure of variability representing the score distance between the 25th percentile (Q1) and the 75th percentile (Q3).

z-Score

The fundamental standard score expressing how many standard deviation units a raw score lies above or below a mean of 0 (SD=1).

z-Score Formula

z=(X-M)/SD, where X is the raw score, M is the sample mean, and SD is the standard deviation.

Percentile Rank (PR)

The percentage of examinees in a normative group who score at or below a given raw score.

Percentile (%ile)

A specific point on a score distribution below which a designated percentage of cases falls.

Standard Score System

A family of derived scores converted linearly or nonlinearly from z-scores into a distribution with an arbitrarily chosen mean and standard deviation.

Standard Score Transformation Formula

SS = (SD_s / SD_r)(X-M_r)+M_s, where SD_s and M_s are target scale parameters and SD_r and M_r are raw parameters.

Linear vs. Nonlinear Transformation

Linear transformations preserve exact relative distance between raw scores; nonlinear transformations alter raw score spacing to fit a target shape such as a normal curve.

T-Score (McCall's T)

A widely used standard score system set to a mean of 50 and a standard deviation of 10.

Deviation IQ

A standard score intelligence metric with a mean of 100 and a standard deviation typically set to 15 (or 16).

Ratio IQ

An obsolete historical intelligence metric calculated as (Mental Age / Chronological Age) * 100

Ratio IQ Formula

Ratio IQ=(MA/CA)100, where MA is mental age and CA is chronological age.

Stanine

A nine-point standard score scale (mean = 5, SD = 2) that divides a normal distribution into equal-interval units covering specified percentages.

Normal Curve Equivalent (NCE)

A normalized standard score system (mean=50, SD=21.06) designed to match percentile ranks exactly at 1, 50, and 99.

Theta Score (theta)

The ability continuum score in Item Response Theory representing an examinee's trait level, typically spanning -4.0 to +4.0.

Correction for Guessing Formula

Corrected Score = R - [W/(K-1)], where R is correct answers, W is wrong answers, and K is options per item.

National Norms

Normative distributions derived from large standardization samples carefully selected to represent the general national population.

International Norms

Norms compiled from multi-country population samples participating in standardized cross-national assessment programs.

Convenience Norm Groups

Norms based on easily accessible ad hoc groups, requiring caution due to limited representativeness.

User Norms

Normative distributions derived from examinees who actually completed a test and were processed by a test publisher over a specific period.

Subgroup Norms

Separate normative distributions established for specific demographic or functional subdivisions of a population, such as by age or gender.

Local Norms

Norms constructed from the score distributions of examinees within a single local school, district, or institutional setting.

Institutional Norms

Normative distributions derived using institutional averages (e.g., school mean scores) rather than individual examinee scores.

Age Equivalent (AE) / Mental Age (MA)

A developmental norm expressing an examinee's performance as the chronological age for which that raw score is median.

Grade Equivalent (GE)

A developmental norm describing performance in terms of the grade level and month of the school year for which a raw score is typical.

Reliability

The consistency, replicability, and dependability of test scores across administrations, raters, or equivalent item sets.

Classical Test Theory (CTT)

A foundational psychometric model postulating that an observed score consists of a true score plus random measurement error.

Observed Score (O)

An examinee's actual obtained raw or scale score on a testing procedure.

True Score (T)

The hypothetical error-free mean score an examinee would obtain across infinite replications of a test procedure.

Error Score (E)

The unsystematic difference between observed score and true score (E=O-T).

CTT Core Equation

O=T+E (Observed Score = True Score + Error Score).

Constant Error vs. Unsystematic Error

Constant error systematically shifts scores in one direction without affecting consistency; unsystematic error introduces random variance that reduces reliability.

Variance Breakdown Formula

Var_O=Var_T+Var_E, indicating observed score variance is the sum of true score variance and error score variance.

Reliability Ratio Formula

r_xx=Var_T/Var_O=Var_T / (Var_T+Var_E), defining reliability as the proportion of observed variance that is true variance.

Correlation Coefficient (r)

A statistic ranging from -1.00 to +1.00 quantifying the direction and magnitude of the linear relationship between two variables.

Factors Affecting Correlation

Factors influencing correlation magnitude: linearity, homoscedasticity, relative positioning, and group heterogeneity (range restriction).

Test-Retest Reliability

A reliability coefficient obtained by administering the same test to the same group on two separate occasions to evaluate temporal stability.

Alternate Form Reliability

A reliability coefficient obtained by administering two parallel or equivalent forms of a test to the same examinees.

Inter-Scorer (Inter-Rater) Reliability

An index measuring score consistency across independent raters scoring the same test performances.

Intraclass Correlation Coefficient (ICC)

An ANOVA-based correlation statistic used to evaluate inter-scorer agreement across multiple raters.

Internal Consistency Reliability

Reliability estimates derived from item interrelationships within a single test administration.

Split-Half Reliability

An internal consistency estimate obtained by splitting a test into equivalent halves (e.g., odd-even) and correlating the subscores.

Spearman-Brown Correction Formula (Half-Length)

r_c = (2r_h)/(1+r_h), used to convert a half-length test correlation into a full-length reliability estimate.

Spearman-Brown Formula (General Length Change)

r_c = (nr_0)/[1+(n-1)r_0], estimating corrected reliability when test length is multiplied by factor n.

Kuder-Richardson Formulas (KR-20/KR-21)

Specialized internal consistency formulas designed specifically for dichotomously scored items (1/0).

Coefficient Alpha (Cronbach's Alpha)

A general internal consistency coefficient reflecting average item intercorrelations across continuous or multi-point items.

Coefficient Alpha Formula

Alpha = [K/(K-1)][1- (Sum(Var_i)/Var_X)], where K is item count, sum(Var_i) is sum of item variances, and Var_X is total test variance.

Standard Error of Measurement (SEM)

The standard deviation of hypothetical observed scores around an individual's true score under repeated testing.

SEM Formula

SEM=SDsqrt(1-r_xx), quantifying measurement error spread using test standard deviation and reliability.

Confidence Band

A score interval constructed around an observed score using SEM (e.g., X+/-1.96SEM for 95% CI) to reflect true score uncertainty.

Standard Error of the Mean Formula

SE_M=SD / sqrt(N), measuring sampling variability of sample means around the population mean.

Standard Error of Estimate Formula

SE_Y'=SD_Y* sqrt(1-r_XY^2), measuring error spread of actual criterion scores around predicted scores.

Reliability of Difference Scores Formula

r_d = (r_avg -r_XY)/(1-r_XY), calculating reliability when interpreting score differences between two correlated tests.

IRT Precision of Measurement SE(theta)

SE(theta) = 1/ sqrt(I(theta)), the IRT standard error calculated specifically for each trait level based on test information.

Generalizability Theory (GT)

An ANOVA framework estimating multiple sources of measurement error simultaneously in a single generalizability study.

Universe Score

The true score equivalent in Generalizability Theory, representing mean performance across all facets of a testing universe.

Validity

The degree to which empirical evidence and theoretical rationales support the adequacy and appropriateness of interpretations made from test scores.

Construct

An underlying theoretical trait, attribute, or process that a test is designed to measure.

Construct Underrepresentation

A validity threat occurring when a test fails to capture important dimensions or aspects of the target construct.

Construct-Irrelevant Variance

A validity threat occurring when test scores are polluted by factors extraneous to the intended construct.

Face Validity

The superficial appearance that a test looks valid to examinees or laypersons, which is not an empirical form of validity.

Content Validity

The degree to which items on a test adequately represent a well-defined domain of knowledge or behavior.

Instructional (Curricular) Validity

A content validity variant evaluating whether test material was actually taught in an educational curriculum.