Measurement

Joseph Stevens, Ph.D.

© 2005

Measurement Process of assigning quantitative or qualitative

descriptions to some attribute Operational Definitions

Assessment Collection of measurement information Interpretation Synthesis Use

Evaluation Value added to assessment information (e.g.

good, poor, “ought”, “needs improvement”)

Assessment Decisions/Purposes Instructional Curricular Treatment/Intervention Placement/Classification Selection/Admission Administration/Policy-making Personal/Individual Personnel Evaluation

Scaling

Process of systematically translating empirical observations into a measurement scale

Origin Units Information Types of scales

Score Interpretation

Direct interpretation Need for analysis, relative

interpretation Normative interpretation Anchoring/Standards

Frames of Reference for Interpretation

Current versus future performance Typical versus maximum or potential Standard of comparison

To self To others To standard

Formative versus summative

Domains Cognitive

Ability/Aptitude Achievement Memory, perception, etc.

Affective Beliefs Attitudes Feelings, interests, preferences,

emotions Behavior

Cognitive Level

Knowledge Comprehension Application Analysis/Synthesis Evaluation

Assessment Tasks Selected Response – MC, T-F, matching Restricted Response – cloze, fill-in,

completion Constructed Response - essay Free Response/Performance Assessments

Products Performances

Rating Ranking Magnitude Estimation

CRT versus NRT

Criterion Referenced Tests (CRT) Comparison to a criterion/standard Items that represent the domain

Relevance Representativeness

Norm Referenced Tests Comparison to a group Items that discriminate one person from

another

Kinds of Scores

Raw Standard scores Developmental Standard Scores Percentile Ranks (PR) Normal Curve Equivalent (NCE) Grade Equivalent (GE)

Scoring Methods

Objective Subjective

Holistic Analytic

Standard

MetDid Not Meet

Pe

rce

nt

100

80

60

40

20

0

Aggregating Scores

Total scores Summated scores Composite scores

Issues Intercorrelation of components Variance Reliability

Theories of Measurement

Classical Test Theory (CTT)X = T + E

Item Response Theory (IRT)http://work.psych.uiuc.edu/irt/tutorial.asp

x

x

1(

eePg

Logistic Reponse Model Item: 2The parameter a is the item discriminating power, the reciprocal (1/a) is the itemdispersion, and the parameter b is an item location parameter.

0

0.2

0.4

0.6

0.8

1.0

-3 -2 -1 0 1 2 3

b

Ability

Pro

bab

ilit

y

Item Characteristic Curve: 2 a = 0.725 b = -1.367

Logistic Reponse Model Item: 3The parameter a is the item discriminating power, the reciprocal (1/a) is the itemdispersion, and the parameter b is an item location parameter.

0

0.2

0.4

0.6

0.8

1.0

-3 -2 -1 0 1 2 3

b

Ability

Pro

bab

ilit

y

Item Characteristic Curve: 3 a = 0.885 b = -0.281

Reliability

Consistency Consistency of Decisions Prerequisite to validity Errors in measurement

Reliability Sources of errors

Variations in physical and mental condition of person measured

Changes in physical or environmental conditions Tasks/Items Administration conditions Time Skill to skill Raters/judges Test forms

Estimating Reliability

Reliability versus standard error of measurement (SEM)

Internal Consistency Cronbach’s alpha Split-half Example

Test-Retest Inter-rater

Estimating Reliability

Correlations, rank order versus exact agreement

Percent Agreement Exact versus close (number of agreements/number of

scores x 100) Problem of chance agreements

Estimating Reliability Kappa Coefficient

Takes chance agreements into account Calculate expected frequencies and subtract Kappa ≥ .70 acceptable Examine pattern of disagreements

Example Percent agreement = 63.8% r = .509 Kappa = .451

Below Meets Exceeds Total

Below 9 3 1 13

Meets 4 8 2 14

Exceeds 2 1 6 9

Total 15 12 9 36

Estimating Reliability

Spearman-Brown prophecy formula More is better

Reliability as error

Systematic error Random error SEM _______

SEM = SDx √ 1 - rxx

Factors affecting reliability

Time limits Test length Item characteristics

Difficulty Discrimination

Heterogeneity of sample Number of raters, quality of

subjective scoring

Validity

Accuracy Unified View (Messick)

Use and Interpretation Evidential basis

Content Criterion Concurrent-Discriminant Construct

Consequential basis

Validity

Internal, structural Multitrait-Multimethod (Campbell &

Fiske) Predictive

Test Development

Construct Representation Content analysis Review of research Direct observation Expert judgment (panels, ratings, Delphi) Instructional objectives

Test Development Blueprint

Content X Process Domain sampling Item frames Matching item type and response format

to purpose Item writing Item Review (grammar, readability,

cueing, sensitivity)

Test Development

Writing instructions Form design (NAEP brown ink) Field and pilot testing Item analysis Review and revision

Equating

Need to link across forms, people, or occasions

Horizontal equating Vertical equating Designs

Common item Common persons

Equating

Equipercentile Linear IRT

Bias and Sensitivity

Sensitivity in item and test development

Differential results versus bias Differential Item Functioning (DIF) Importance of matching, legal versus

psychometric Understanding diversity and individual

differences

Item Analysis

Difficulty, p Means and standard deviations Discrimination, r-point biserial Omits Removing or revising “bad” items Example

Factor Analysis

Method of evaluating structural validity and reliability

Exploratory (EFA) example Confirmatory (CFA) example