Descriptive Statistics Chapter 4
Four Scales of Measurement <ul><li>Nominal </li></ul><ul><ul><li>A scale in which the variable values are banes that have ...
Four Scales of Measurement <ul><li>Ratio </li></ul><ul><ul><li>Scale on which the magnitude of the difference between any ...
Distributions <ul><li>Distributions of scores may be graphed to represent visually the relationships among the scores in t...
Normal Distribution
Histogram <ul><li>Graph showing frequency of scores </li></ul>
Frequency Polygon <ul><li>Graph showing distribution of scores </li></ul>
Basic Notation <ul><li>Symbols </li></ul><ul><ul><li>Add the following </li></ul></ul><ul><ul><li>Denotes any score </li><...
Measures of Central Tendency <ul><li>Mean </li></ul><ul><ul><li>Arithmetic average of the scores in a distribution </li></...
Measures of Central Tendency
Measures of Central Tendency <ul><li>Relationships among mode, median, and mean for symmetrical and skewed distributions <...
Measures of Dispersion <ul><li>Range </li></ul><ul><ul><li>Distance between the extremes of a distribution  </li></ul></ul...
Standard Deviation
Mean
Measures of Dispersion
Correlation <ul><li>Definition </li></ul><ul><ul><li>Quantify relationship between variables </li></ul></ul><ul><li>Correl...
Quantification of  Test Performance Chapter 5
Norm Referenced Assessment  <ul><li>Developmental scores </li></ul><ul><ul><li>Raw scores that have been transformed into ...
Criterion-Referenced Assessment <ul><li>Single skill scores </li></ul><ul><li>Multiple skill scores </li></ul><ul><li>Glob...
Norms Chapter 6
Representativeness <ul><li>General characteristics and experience; dependent on construct being measured </li></ul><ul><ul...
Technical Considerations <ul><li>Finding people </li></ul><ul><ul><li>Cluster sampling (schools) </li></ul></ul><ul><li>Pr...
Using Norms Correctly <ul><li>Tester must select tables based on </li></ul><ul><ul><li>Age </li></ul></ul><ul><ul><li>grad...
Reliability Chapter 7
Reliability <ul><li>Definition: generalizing what we see today under one set of conditions to other occasions and conditio...
Reliability <ul><li>Determining which reliability method to use </li></ul><ul><ul><li>Type of generalization we wish to ma...
Reliability <ul><li>Difference scores </li></ul><ul><ul><li>We might be interested in differences between two scores: read...
Validity Chapter 8
Validity <ul><li>Definition: appropriateness, meaningfulness, and usefulness of the specific inference that can be made on...
Validity <ul><li>Factors affecting generalizability </li></ul><ul><li>Reliability: upper limits of a test’s validity </li>...
Responsibility for Valid Assessment <ul><li>Valid use of assessment procedures is the responsibility of: </li></ul><ul><ul...
Adapting Tests to Accommodate Student with Disabilities Chapter 9
Concerns about Testing Adaptations <ul><li>Changes in student population </li></ul><ul><li>Changes in educational standard...
Factors affecting Accurate Assessment <ul><li>Ability to understand the assessment </li></ul><ul><li>Ability to respond to...
Testing Accommodations <ul><li>Current practice </li></ul><ul><ul><li>Extended time </li></ul></ul><ul><ul><li>Braille </l...
Making Entitlement Decisions Chapter 16
Rationale for Entitlement <ul><li>Lack of academic success </li></ul><ul><li>No-fault failure </li></ul><ul><li>Political ...
Entitlements <ul><li>Special services </li></ul><ul><li>Different outcome expectancies </li></ul><ul><li>Procedural safegu...
Determining Eligibility  for Services <ul><ul><li>Official exceptionalities </li></ul></ul><ul><ul><ul><li>Autism </li></u...
Determining Eligibility  for Services <ul><li>Establishing educational need </li></ul><ul><li>Establishing exceptionality ...
Assessment of Intelligence: Overview Chapter 17
Intelligence Tests as  Samples of Behavior <ul><li>Assess a student’s capacity to profit from instruction </li></ul><ul><l...
Effect of Pupil Characteristics on Assessment of Intelligence <ul><li>Acculturation is the most important characteristics ...
Behaviors Sampled by Intelligence Tests <ul><li>Discrimination </li></ul><ul><li>Generalization </li></ul><ul><li>Motor be...
Dilemmas in Current Practice <ul><li>Currently marked by controversy </li></ul><ul><li>Understanding what that test assess...
Assessment  Of Intelligence: Individual Tests <ul><li>Chapter 18 </li></ul>
Why do We give Individual Intelligence Tests? <ul><li>General intelligence tests </li></ul><ul><ul><li>Stanford-Binet  (SB...
Non-Verbal Intelligence Tests <ul><li>Comprehensive Tests of Nonverbal Intelligence </li></ul><ul><li>Leiter International...
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EEX 501 Assess Ch4,5,6,7,All

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EEX 501 Assess Ch4,5,6,7,All

  1. 1. Descriptive Statistics Chapter 4
  2. 2. Four Scales of Measurement <ul><li>Nominal </li></ul><ul><ul><li>A scale in which the variable values are banes that have no inherent relationship (numbers on a football jersey) </li></ul></ul><ul><li>Ordinal </li></ul><ul><ul><li>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) </li></ul></ul><ul><ul><li>Age equivalent, grade equivalent, percentiles </li></ul></ul>
  3. 3. Four Scales of Measurement <ul><li>Ratio </li></ul><ul><ul><li>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 </li></ul></ul><ul><ul><li>All mathematical operations can be performed: add scores, square scores, create ratios (height & weight) </li></ul></ul><ul><li>Equal-Interval </li></ul><ul><ul><li>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 </li></ul></ul>
  4. 4. Distributions <ul><li>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 </li></ul>
  5. 5. Normal Distribution
  6. 6. Histogram <ul><li>Graph showing frequency of scores </li></ul>
  7. 7. Frequency Polygon <ul><li>Graph showing distribution of scores </li></ul>
  8. 8. Basic Notation <ul><li>Symbols </li></ul><ul><ul><li>Add the following </li></ul></ul><ul><ul><li>Denotes any score </li></ul></ul><ul><ul><li>Scores in a distribution </li></ul></ul><ul><ul><li>Frequency of an occurrence </li></ul></ul><ul><ul><li>Mean of a distribution </li></ul></ul><ul><ul><li>Variance of a distribution </li></ul></ul><ul><ul><li>Standard deviation </li></ul></ul>
  9. 9. Measures of Central Tendency <ul><li>Mean </li></ul><ul><ul><li>Arithmetic average of the scores in a distribution </li></ul></ul><ul><li>Median </li></ul><ul><ul><li>Score that divides the top 50 percent of the scores from the bottom 50 percent </li></ul></ul><ul><li>Mode </li></ul><ul><ul><li>Score most frequently obtained </li></ul></ul>
  10. 10. Measures of Central Tendency
  11. 11. Measures of Central Tendency <ul><li>Relationships among mode, median, and mean for symmetrical and skewed distributions </li></ul>
  12. 12. Measures of Dispersion <ul><li>Range </li></ul><ul><ul><li>Distance between the extremes of a distribution </li></ul></ul><ul><li>Variance (S2) </li></ul><ul><ul><li>Average squared distance of the scores from the mean </li></ul></ul><ul><li>Standard Deviation (positive square root of the variance) </li></ul><ul><ul><li>A unit of measure </li></ul></ul><ul><ul><li>Can be measured as a standard deviation unit from the mean </li></ul></ul>
  13. 13. Standard Deviation
  14. 14. Mean
  15. 15. Measures of Dispersion
  16. 16. Correlation <ul><li>Definition </li></ul><ul><ul><li>Quantify relationship between variables </li></ul></ul><ul><li>Correlation coefficient </li></ul><ul><ul><li>Tell what extent any two variables go together, the extent to which changes in one variable are reflected by changes in the second variable </li></ul></ul><ul><li>Pearson-product moment correlation coefficient </li></ul><ul><ul><li>Most common coefficient </li></ul></ul><ul><li>Zero correlation </li></ul><ul><ul><li>No relationship </li></ul></ul><ul><li>Causality </li></ul><ul><ul><li>Refers to one thing causing another; the presence of correlation does not imply causality </li></ul></ul>
  17. 17. Quantification of Test Performance Chapter 5
  18. 18. Norm Referenced Assessment <ul><li>Developmental scores </li></ul><ul><ul><li>Raw scores that have been transformed into age equivalents, grade equivalents or developmental quotients </li></ul></ul><ul><li>Scores of relative standing </li></ul><ul><ul><li>Percentile rank </li></ul></ul><ul><ul><li>Standard score </li></ul></ul><ul><ul><ul><li>Z score </li></ul></ul></ul><ul><ul><ul><li>T score </li></ul></ul></ul><ul><ul><ul><li>Stanines </li></ul></ul></ul>
  19. 19. Criterion-Referenced Assessment <ul><li>Single skill scores </li></ul><ul><li>Multiple skill scores </li></ul><ul><li>Global ratings </li></ul>
  20. 20. Norms Chapter 6
  21. 21. Representativeness <ul><li>General characteristics and experience; dependent on construct being measured </li></ul><ul><ul><li>Age </li></ul></ul><ul><ul><li>Grade in school </li></ul></ul><ul><ul><li>Gender </li></ul></ul><ul><ul><li>Acculturation of parents </li></ul></ul><ul><ul><li>Geography </li></ul></ul><ul><ul><li>Race & culture </li></ul></ul><ul><ul><li>intelligence </li></ul></ul><ul><li>Relevant special characteristics: some characteristics of the sample and population are important only for particular types of tests </li></ul>
  22. 22. Technical Considerations <ul><li>Finding people </li></ul><ul><ul><li>Cluster sampling (schools) </li></ul></ul><ul><li>Proportional representation </li></ul><ul><ul><li>Various kinds of people should be included in the same proportion in the sample as they occur in the general population </li></ul></ul><ul><li>Number of subjects </li></ul><ul><ul><li># should be large enough to guarantee stability </li></ul></ul><ul><li>Smoothing norms </li></ul><ul><ul><li>Remove unwanted fluctuations in the shapes of the age or grade distributions by adjusting the relationship between standard scores and percentiles </li></ul></ul><ul><li>Age of norms </li></ul><ul><ul><li>Represent population: skills & levels change </li></ul></ul><ul><li>Relevance of norms; relevant for what the is supposed to measure </li></ul>
  23. 23. Using Norms Correctly <ul><li>Tester must select tables based on </li></ul><ul><ul><li>Age </li></ul></ul><ul><ul><li>grade </li></ul></ul>
  24. 24. Reliability Chapter 7
  25. 25. Reliability <ul><li>Definition: generalizing what we see today under one set of conditions to other occasions and conditions (reliability coefficient) </li></ul><ul><ul><li>Generalizing to different time: stability </li></ul></ul><ul><ul><li>Generalizing to different item samples </li></ul></ul><ul><ul><ul><li>Internal consistency </li></ul></ul></ul><ul><li>Factors affecting reliability </li></ul><ul><ul><li>Test length: more items greater reliability </li></ul></ul><ul><ul><li>Test-retest interval:interval between tests </li></ul></ul><ul><ul><li>Constriction or extension: range of ability </li></ul></ul><ul><ul><li>Guessing: responding randomly to items </li></ul></ul><ul><ul><li>Variation within the testing situation: error introduced into the results of testing: headaches, sick, misunderstand directions </li></ul></ul>
  26. 26. Reliability <ul><li>Determining which reliability method to use </li></ul><ul><ul><li>Type of generalization we wish to make </li></ul></ul><ul><ul><li>Considerations </li></ul></ul><ul><ul><ul><li>Stability: retest after two weeks </li></ul></ul></ul><ul><ul><ul><li>Alternate form reliability: different form of test </li></ul></ul></ul><ul><ul><ul><li>Correlation coefficient </li></ul></ul></ul><ul><li>Standard error of measurement </li></ul><ul><ul><li>Estimate the amount of each type of error associated with true scores </li></ul></ul><ul><li>Estimated true scores </li></ul><ul><ul><li>We never know a subject’s true score </li></ul></ul><ul><ul><li>Confidence intervals </li></ul></ul><ul><ul><ul><li>The likelihood that a person’s true score might be found within a specified range </li></ul></ul></ul><ul><ul><ul><li>Establishing confidence intervals </li></ul></ul></ul>
  27. 27. Reliability <ul><li>Difference scores </li></ul><ul><ul><li>We might be interested in differences between two scores: reading achievement commensurate with her intellectual ability </li></ul></ul><ul><li>Desirable standards </li></ul><ul><ul><li>Important for test authors to present sufficient information in test manuals for the user to interpret test results accurately </li></ul></ul><ul><ul><li>Provide sufficient reliability data to allow user to evaluate reliability of the test scores that are to be interpreted </li></ul></ul><ul><ul><ul><li>.60 group data </li></ul></ul></ul><ul><ul><ul><li>.90 individual data </li></ul></ul></ul><ul><ul><ul><li>.80 screening </li></ul></ul></ul>
  28. 28. Validity Chapter 8
  29. 29. Validity <ul><li>Definition: appropriateness, meaningfulness, and usefulness of the specific inference that can be made on the basis of observation </li></ul><ul><li>Methods of validating test inferences </li></ul><ul><ul><li>Content validity: test’s items actually represent the domain it measures </li></ul></ul><ul><ul><li>Criterion related validity:extent to which a person’s performance can be estimated from the performance on the assessment </li></ul></ul><ul><ul><li>Construct validity: extent to which a test measures a theoretical trait (IQ) </li></ul></ul>
  30. 30. Validity <ul><li>Factors affecting generalizability </li></ul><ul><li>Reliability: upper limits of a test’s validity </li></ul><ul><ul><li>All valid tests are reliable </li></ul></ul><ul><ul><li>Unreliable tests are not valid </li></ul></ul><ul><ul><li>Reliable tests may or may not be valid </li></ul></ul><ul><ul><li>Valid procedures measure the traits they are designed to measure </li></ul></ul><ul><li>Systematic bias </li></ul><ul><ul><li>Method used to measure a skill or trait is often believed to affect what score a child will receive </li></ul></ul><ul><ul><li>A true score can be considered a composite of trait variance and method of measurement variance </li></ul></ul>
  31. 31. Responsibility for Valid Assessment <ul><li>Valid use of assessment procedures is the responsibility of: </li></ul><ul><ul><li>The author </li></ul></ul><ul><ul><li>The user of the assessment process </li></ul></ul><ul><li>Validity is the only technical characteristic of a assessment in which we are interested </li></ul><ul><ul><li>We must know whether inferences drawn from an assessment are accurate </li></ul></ul>
  32. 32. Adapting Tests to Accommodate Student with Disabilities Chapter 9
  33. 33. Concerns about Testing Adaptations <ul><li>Changes in student population </li></ul><ul><li>Changes in educational standards </li></ul><ul><li>Need for accurate measurement </li></ul><ul><li>Participation </li></ul><ul><ul><li>Standards apply to all students </li></ul></ul><ul><li>Accommodation </li></ul><ul><ul><li>Adapting or modifying assessment measures </li></ul></ul>
  34. 34. Factors affecting Accurate Assessment <ul><li>Ability to understand the assessment </li></ul><ul><li>Ability to respond to assessment stimuli </li></ul><ul><li>Nature of the norm group </li></ul><ul><li>Exposure to curriculum being tested </li></ul><ul><li>Legal considerations </li></ul><ul><li>Current practice decisions </li></ul><ul><li>Recommendations for participation </li></ul>
  35. 35. Testing Accommodations <ul><li>Current practice </li></ul><ul><ul><li>Extended time </li></ul></ul><ul><ul><li>Braille </li></ul></ul><ul><ul><li>Tape recorder </li></ul></ul><ul><ul><li>Magnifying glass </li></ul></ul><ul><li>Recommendations </li></ul><ul><ul><li>Student’s native language </li></ul></ul><ul><ul><li>Make accommodations so that purpose of testing is not impaired </li></ul></ul><ul><ul><li>Make normative comparisons </li></ul></ul>
  36. 36. Making Entitlement Decisions Chapter 16
  37. 37. Rationale for Entitlement <ul><li>Lack of academic success </li></ul><ul><li>No-fault failure </li></ul><ul><li>Political action </li></ul><ul><li>Problems associated with the criteria </li></ul>
  38. 38. Entitlements <ul><li>Special services </li></ul><ul><li>Different outcome expectancies </li></ul><ul><li>Procedural safeguards </li></ul><ul><li>Special fiscal arrangements </li></ul>
  39. 39. Determining Eligibility for Services <ul><ul><li>Official exceptionalities </li></ul></ul><ul><ul><ul><li>Autism </li></ul></ul></ul><ul><ul><ul><li>Mental retardation </li></ul></ul></ul><ul><ul><ul><li>Specific learning disability </li></ul></ul></ul><ul><ul><ul><li>Emotional disturbance </li></ul></ul></ul><ul><ul><ul><li>Traumatic brain injury </li></ul></ul></ul><ul><ul><ul><li>Speech or language impairment </li></ul></ul></ul><ul><ul><ul><li>Visual impairment </li></ul></ul></ul><ul><ul><ul><li>Deafness and hard of hearing </li></ul></ul></ul><ul><ul><ul><li>Orthopedic impairments </li></ul></ul></ul><ul><ul><ul><li>Other health impaired </li></ul></ul></ul><ul><ul><ul><li>Deaf-blindness </li></ul></ul></ul><ul><ul><ul><li>Multiple disabilities </li></ul></ul></ul><ul><ul><ul><li>Developmental delayed </li></ul></ul></ul>
  40. 40. Determining Eligibility for Services <ul><li>Establishing educational need </li></ul><ul><li>Establishing exceptionality </li></ul><ul><li>Process of determining exceptionality </li></ul>
  41. 41. Assessment of Intelligence: Overview Chapter 17
  42. 42. Intelligence Tests as Samples of Behavior <ul><li>Assess a student’s capacity to profit from instruction </li></ul><ul><li>Samples behavior from a larger domain of behavior </li></ul><ul><li>One can not possibly assess every item in a domain </li></ul>
  43. 43. Effect of Pupil Characteristics on Assessment of Intelligence <ul><li>Acculturation is the most important characteristics to consider in evaluating performance on IQ tests </li></ul><ul><li>Acculturation refers to an individual’s particular set of background experiences and opportunities to learn </li></ul>
  44. 44. Behaviors Sampled by Intelligence Tests <ul><li>Discrimination </li></ul><ul><li>Generalization </li></ul><ul><li>Motor behavior </li></ul><ul><li>General Knowledge </li></ul><ul><li>Vocabulary </li></ul><ul><li>Induction </li></ul><ul><li>Comprehension </li></ul><ul><li>Sequencing </li></ul><ul><li>Detail Recognition </li></ul><ul><li>Analogical Reasoning </li></ul><ul><li>Pattern Completion </li></ul><ul><li>Abstract Reasoning </li></ul><ul><li>Memory </li></ul>
  45. 45. Dilemmas in Current Practice <ul><li>Currently marked by controversy </li></ul><ul><li>Understanding what that test assesses </li></ul>
  46. 46. Assessment Of Intelligence: Individual Tests <ul><li>Chapter 18 </li></ul>
  47. 47. Why do We give Individual Intelligence Tests? <ul><li>General intelligence tests </li></ul><ul><ul><li>Stanford-Binet (SB) 4th edition </li></ul></ul><ul><ul><li>Weschler Scales (WAIS,WISC,WPPSI,WASI) </li></ul></ul><ul><ul><li>Detroit Tests of Learning Aptitude </li></ul></ul><ul><ul><li>Cognitive Assessment System </li></ul></ul>
  48. 48. Non-Verbal Intelligence Tests <ul><li>Comprehensive Tests of Nonverbal Intelligence </li></ul><ul><li>Leiter International </li></ul><ul><li>Test of Non-verbal Intelligence </li></ul><ul><li>Universal Nonverbal </li></ul><ul><li>Naglieri Nonverbal Ability Test </li></ul><ul><li>Peabody Picture Vocabulary Test </li></ul>

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