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Descriptive Statistics

Chapter 4

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Four Scales of Measurement Nominal

A scale in which the variable values are banes that have no inherent relationship (numbers on a football jersey)

Ordinal A scale that orders or ranks information on some

kind of continuum (best to worse) but does not have equal difference between the ranks (class standing)

Age equivalent, grade equivalent, percentiles

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Four Scales of Measurement Ratio

Scale on which the magnitude of the difference between any two adjacent points on the scale is the same and has an absolute and logical zero that allows the construction of ratios

All mathematical operations can be performed: add scores, square scores, create ratios (height & weight)

Equal-Interval A ratio scale without an absolute zero: this means that a score

of 50 is not twice as much as a score of 25: many scores used in education and psychology are equal interval

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Distributions

Distributions of scores may be graphed to represent visually the relationships among the scores in the group. Horizontal axis is is continuum on which individual is measured, vertical axis is frequency

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Normal Distribution

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Histogram Graph showing frequency of scores

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Frequency Polygon

Graph showing distribution of scores

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Basic Notation

Symbols Add the following Denotes any score Scores in a distribution Frequency of an occurrence Mean of a distribution Variance of a distribution Standard deviation

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Measures of Central Tendency

Mean Arithmetic average of the scores in a

distribution Median

Score that divides the top 50 percent of the scores from the bottom 50 percent

Mode Score most frequently obtained

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Measures of Central Tendency

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Measures of Central Tendency Relationships among mode, median, and mean

for symmetrical and skewed distributions

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Measures of Dispersion Range

Distance between the extremes of a distribution Variance (S2)

Average squared distance of the scores from the mean

Standard Deviation (positive square root of the variance) A unit of measure Can be measured as a standard deviation unit from

the mean

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Standard Deviation

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Mean

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Measures of Dispersion

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Correlation Definition

Quantify relationship between variables Correlation coefficient

Tell what extent any two variables go together, the extent to which changes in one variable are reflected by changes in the second variable

Pearson-product moment correlation coefficient Most common coefficient

Zero correlation No relationship

Causality Refers to one thing causing another; the presence of correlation does

not imply causality

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Quantification of Test Performance

Chapter 5

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Norm Referenced Assessment Developmental scores

Raw scores that have been transformed into age equivalents, grade equivalents or developmental quotients

Scores of relative standing Percentile rank Standard score

• Z score• T score• Stanines

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Criterion-Referenced Assessment

Single skill scores Multiple skill scores Global ratings

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Norms

Chapter 6

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Representativeness General characteristics and experience;

dependent on construct being measured Age Grade in school Gender Acculturation of parents Geography Race & culture intelligence

Relevant special characteristics: some characteristics of the sample and population are important only for particular types of tests

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Technical Considerations Finding people

Cluster sampling (schools) Proportional representation

Various kinds of people should be included in the same proportion in the sample as they occur in the general population

Number of subjects # should be large enough to guarantee stability

Smoothing norms Remove unwanted fluctuations in the shapes of the age or grade

distributions by adjusting the relationship between standard scores and percentiles

Age of norms Represent population: skills & levels change

Relevance of norms; relevant for what the is supposed to measure

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Using Norms Correctly Tester must select tables based on

Age grade

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Reliability

Chapter 7

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Reliability Definition: generalizing what we see today

under one set of conditions to other occasions and conditions (reliability coefficient) Generalizing to different time: stability Generalizing to different item samples

• Internal consistency Factors affecting reliability

Test length: more items greater reliability Test-retest interval:interval between tests Constriction or extension: range of ability Guessing: responding randomly to items Variation within the testing situation: error introduced into the results of testing:

headaches, sick, misunderstand directions

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Reliability Determining which reliability method to use

Type of generalization we wish to make Considerations

• Stability: retest after two weeks• Alternate form reliability: different form of test• Correlation coefficient

Standard error of measurement Estimate the amount of each type of error associated with true scores

Estimated true scores We never know a subject’s true score Confidence intervals

• The likelihood that a person’s true score might be found within a specified range• Establishing confidence intervals

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Reliability Difference scores

We might be interested in differences between two scores: reading achievement commensurate with her intellectual ability

Desirable standards Important for test authors to present sufficient information in

test manuals for the user to interpret test results accurately Provide sufficient reliability data to allow user to evaluate

reliability of the test scores that are to be interpreted• .60 group data• .90 individual data• .80 screening

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Validity

Chapter 8

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Validity Definition: appropriateness, meaningfulness,

and usefulness of the specific inference that can be made on the basis of observation

Methods of validating test inferences Content validity: test’s items actually represent the

domain it measures Criterion related validity:extent to which a person’s

performance can be estimated from the performance on the assessment

Construct validity: extent to which a test measures a theoretical trait (IQ)

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Validity Factors affecting generalizability Reliability: upper limits of a test’s validity

All valid tests are reliable Unreliable tests are not valid Reliable tests may or may not be valid Valid procedures measure the traits they are designed to

measure Systematic bias

Method used to measure a skill or trait is often believed to affect what score a child will receive

A true score can be considered a composite of trait variance and method of measurement variance

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Responsibility for Valid Assessment Valid use of assessment procedures is the

responsibility of: The author The user of the assessment process

Validity is the only technical characteristic of a assessment in which we are interested We must know whether inferences drawn from an

assessment are accurate

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Adapting Tests to Accommodate Student with

Disabilities

Chapter 9

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Concerns about Testing Adaptations Changes in student population Changes in educational standards Need for accurate measurement Participation

Standards apply to all students Accommodation

Adapting or modifying assessment measures

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Factors affecting Accurate Assessment

Ability to understand the assessment Ability to respond to assessment stimuli Nature of the norm group Exposure to curriculum being tested Legal considerations Current practice decisions Recommendations for participation

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Testing Accommodations Current practice

Extended time Braille Tape recorder Magnifying glass

Recommendations Student’s native language Make accommodations so that purpose of testing is

not impaired Make normative comparisons

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Making Entitlement Decisions

Chapter 16

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Rationale for Entitlement Lack of academic success No-fault failure Political action Problems associated with the criteria

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Entitlements Special services Different outcome expectancies Procedural safeguards Special fiscal arrangements

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Determining Eligibility for Services

Official exceptionalities• Autism• Mental retardation• Specific learning disability• Emotional disturbance• Traumatic brain injury• Speech or language impairment• Visual impairment• Deafness and hard of hearing• Orthopedic impairments• Other health impaired• Deaf-blindness• Multiple disabilities• Developmental delayed

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Determining Eligibility for Services

Establishing educational need Establishing exceptionality Process of determining exceptionality

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Assessment of Intelligence: Overview

Chapter 17

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Intelligence Tests as Samples of Behavior

Assess a student’s capacity to profit from instruction

Samples behavior from a larger domain of behavior

One can not possibly assess every item in a domain

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Effect of Pupil Characteristics on Assessment of Intelligence

Acculturation is the most important characteristics to consider in evaluating performance on IQ tests

Acculturation refers to an individual’s particular set of background experiences and opportunities to learn

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Behaviors Sampled by Intelligence Tests

Discrimination Generalization Motor behavior General Knowledge Vocabulary Induction Comprehension

Sequencing Detail Recognition Analogical Reasoning Pattern Completion Abstract Reasoning Memory

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Dilemmas in Current Practice

Currently marked by controversy Understanding what that test assesses

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Assessment Of Intelligence: Individual Tests

Chapter 18

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Why do We give Individual Intelligence Tests?

General intelligence tests Stanford-Binet (SB) 4th edition Weschler Scales (WAIS,WISC,WPPSI,WASI) Detroit Tests of Learning Aptitude Cognitive Assessment System

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Non-Verbal Intelligence Tests

Comprehensive Tests of Nonverbal Intelligence

Leiter International Test of Non-verbal Intelligence Universal Nonverbal Naglieri Nonverbal Ability Test Peabody Picture Vocabulary Test