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Chapter 3

Chapter 3. Introduction to Scaling. LEVELS OF MEASUREMENT Stevens (1946) NOIR. Variables are measured at one of these four levels Qualities of one level are characteristic of the next level up The more precise (higher) the level of measurement, the more accurate is the measurement process.

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Chapter 3

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  1. Chapter3 Introduction to Scaling

  2. LEVELS OF MEASUREMENTStevens (1946) NOIR • Variables are measured at one of these four levels • Qualities of one level are characteristic of the next level up • The more precise (higher) the level of measurement, the more accurate is the measurement process

  3. Qualities Example What You Can Say What You Can’t Say Assignment of labels Gender— (male or female) Preference— (like or dislike) Voting record— (for or against) Each observation belongs in its own category An observation represents “more” or “less” than another observation NOMINAL SCALE DATA

  4. Qualities Example What You Can Say What You Can’t Say Assignment of values along some underlying dimension (order) Rank in college Order of finishing a race One observation is ranked above or below another. The amount that one variable is more or less than another ORDINAL SCALE DATA

  5. Qualities Example What You Can Say What You Can’t Say Equal distances between points Arbitrary or artificial zero Number of words spelled correctly Intelligence test scores Temperature One score differs from another on some measure that has equally appearing intervals The amount of difference is an exact representation of differences of the variable being studied INTERVAL SCALE DATA

  6. Qualities Example What You Can Say What You Can’t Say Meaningful and non-arbitrary or absolute zero Age Weight Time One value is twice as much as another or no quantity of that variable can exist Not much! RATIO SCALE DATA

  7. Ascending Order Numbers are said to be in ascending order when they are arranged from the smallest to the largest number. E.g. 5, 9, 13, 17 and 21 are arranged in ascending order.Descending OrderNumbers are said to be in descending order when they are arranged from the largest to the smallest number.E.g. 25, 21, 17, 13 and 9 are arranged in descending order.

  8. *Transformation of Data:is about a relationship between a set of data.X and Y are a set of data. Types of Transformation: • Nominal Data---Isomorphic Transformation • Ordinal Data ---Monotonic Transformation • Interval Data---Linear Transformation • Regression or Linear FormulaY= bX+ab=2 a=1 Y=2X+1 • Ratio Data---linear Transformation • Y= bX+a • b=2 a= 0 always • Y=bX or Y=cX

  9. Isomorphic Transformation • Any set of numbers (DATA) • The numbers are usually isolated, no relation between the numbers, and use nominal scale (data). Ex. 6, 87, 49, 105, 21, 0, 1008, 631

  10. Monotonic Transformation They are rank ordered numbers (DATA), and use ordinal scale(data) examples; 1, 2, 3, 4, or 2, 4, 6, 8, 10 • Spearman Correlation can be used to measure the degree of MONOTONIC RELATIONSHIP between two variables.

  11. MONOTONIC RELATIONSHIP • AMONOTONIC RELATIONSHIP is a relationship that does one of the following: (1) as the value of one variable increases, so does the value of the other variable; or (2) as the value of one variable increases, the other variable value decreases.(Ex. + or – correlations)

  12. Linear Transformation • We use linear formula for straight line Y=bX+a, if b=2 and a=1 then Y=2X+1 This formula Y=2X+1 is used for Interval DATA/Scale. Ex. If X=3 the Y=7

  13. Linear Transformation • We use linear formula for straight line Y=bX+a • If a=0 then; • The formula for ratio scale (data) is Y=bX • if b=2, X=3 and a=0 then Y=6 • Ex. if X=7 then Y=14 • Exercise 1 p.64 next slide

  14. Ranking • Score Rank position Final Rank • 3 1 1.5 • 3 2 1.5 • 5 3 3 • 6 4 5 • 6 5 5 • 6 6 5 • 12 7 7

  15. *Exercise 1 p.64 • 1. Identify the type of transformation that follows and the type of data (scales of measurement) to which such transformations may be legitimately applied. • A.X Y 37 75 26 53 54 109 28 57 3265

  16. Exercise 1 p.64 cont.. • B. X Y 125 154 183 210 242 154

  17. Exercise 1 p.64 cont.. C. X Y 2287 25102 1919 6 5

  18. Exercise 1 p.64 cont.. C. X Y 225 2519 19102 6 87

  19. Exercise 1 p.64 Cont • A.X Y 18 36 16 32 55 110 22 44 3978

  20. *Scaling Approaches in Test Development by W.S.Torgerson(1958) • 1. Subject-Centered Methods • 2. Stimulus-Centered Methods • 3. Response-Centered Methods

  21. 1- Subject-Centered Methods • We are interested in the subject’s score. • Find the location of an individual’s score on a quantitative continuum with respect to a particular psychological construct i.e., Depression, Anxiety, Stress, IQ, etc. • 0______________________________100 • Usually uses an interval scale e.g., from 0 to ???

  22. 2- Stimulus-Centered Methods The concentration is on stimuli • What is stimuli? Usually the items on an inventory or instrument, but it may be a physical stimuli. • SAD

  23. Light Therapy Research • 3 groups of SAD patients • Group 1--- 200 W light Group 2 ---300 W light Group 3-----400 W light

  24. 200 W 300 W 400W

  25. 2- Stimulus-Centered Methods • JND: In psychophysics a Just Noticeable Difference, is the smallest detectable difference between a starting (primary) and secondary level of a particular sensory stimulus. It is also known as the Difference Limen or the Differential Threshold. This rule was first discovered by Ernst Heinrich Weber • It is called the Weber’s Law • Weber’s Law is based on JND

  26. 2- Stimulus-Centered Methods • Weber’s Law is based on JND An equal stimulus (300 W light bulb) Produces an equal magnitude in the participants sensory response (feeling good).

  27. The Weber’s Law • Weber’s law, also called Weber–Fechner law, historically important psychological law quantifying the perception of change in a given stimulus. The law states that the change in a stimulus that will be just noticeable is a constant ratio of the original stimulus (see the ratio on the next slide). • KEY TERMS • Threshold: the point at which a physiological or psychological effect begins to be produced. • Intensity: The magnetite of a quantity such as energy per unit, or the degree of strength.

  28. The Weber Law

  29. 2- Stimulus-Centered Methods • Louis L.Thurston (1929)Law of Comparative Judgment. Estimates the scale values for each stimulus by using Z-Score. • See p.43 problem #8 next side

  30. 2- Stimulus-Centered MethodsExercise 8 p.43

  31. 3- Response-CenteredMethods • The concentration is on subject/participant response • Thegoal is to locate the stimuli and the individual.Ex. (where do you stand on an issue). • Louis Guttman (1950)Scalogram • Analysis, see next slide • Coefficient of Reproducibility=C • C=1- [Total #of errors/total number • of responses] • See Exercise 2 p. 64

  32. StatementsStrikes by Public Employees (Issue) • A.Clerical personnel in public employment should have the right to strike. • B. Public school teachers should have the right to strike. • C.Nurses in state and city hospitals should have the right to strike. • D. City firefighters should have the right to strike.

  33. Key, orAllowable Response Patterns to the Guttman Scale of Four Attitude Items on Strikes by Public Employees Statements Allowable PatternsA B C D • + + + + • + + + - • + + - - • + - - - • - - - -

  34. *P2 p64: Consider the following responses of 10 subjects to the four items on strikes by public employees (see allowable response patterns). Subject Items or Statements A B C D • + + + + • + - + + • + + - - • + - - - • + + - - • - - - - • + - + - • - + + - • + - - - • - + - -

  35. *P2 p64: Consider the following responses of 10 subjects to the four items on strikes by public employees (see allowable response patterns). Subject Items or Statements A B C D • + + + + • + - + + • + + - - • + - - - • + + - - • - - - - • + - + - • - + + - • + - - - • - + - -

  36. Ex.2 p64: Consider the following responses of 10 subjects to the four items on strikes by public employees (see allowable response patterns).

  37. THERE IS AN ORDERED SCALE

  38. 3- Response-CenteredMethods • The goal is to locate the stimuli and the individual scale (I scale)on the Joint Scale (J scale) • C. H. Coombs(1950) Unfolding Technique J scale and I scale • See p. 56-59

  39. Response-Centered Methods • Subject (J scale) Location Response Patterns (I scales) • Region 1 ABCD • Region 2 BACD • Region 3 BCAD • Region 4 BCDA • Region 5 CBDA • Region 6 CDBA • Region 7 DCBA

  40. Chapter 4*Process of Test Construction 1-Identifying purposes of test scores use • 2-Identifying behaviors to represent the construct • 3- Preparing test specification • 4- Item construction • 5- Item Review • 6- Preliminary item tryouts • 7- Field test • 8- Statistical Analysis • 9- Reliability and Validity • 10- Guidelines

  41. 1-Identifying Purpose(s) of Test Scores Use • For variety of reasons e.g., use depression tests to assist us with diagnosis Use SAT or GRE---College Admission

  42. 2-Identifying Behavior(s) to Represent a Construct • Behavior(s)=Symptoms or characteristics of a disorder or a construct • Ex. If the construct is depression, then behaviors are; hypersomnia, or hyposomnia, lack of energy, social withdrawal, poor concentration, loss of appetiteetc.

  43. 2-Identifying Behavior(s) to Represent a Construct • *6 Different Activities for Test Developers Test developers should engage in one or more of these activities • 1-Content Analysis • 2-Review of Research • 3-Clinical Incidents • 4-Direct Observations • 5-Expert Judgment • 6-Instruction Objectives

  44. *6 Different Activities for Test Developers • 1-Content Analysis It is about what goes in the test. • Ex. If you are creating a self-esteem test for children, you need to know which items should select to measure the children’ self-esteem p.68 i.e., children describing themselves.

  45. *6 Different Activities for Test Developers • 2-Review of Research Review different related research and use different statistical procedures (Meta Analysis, Item Analysis, and Factor Analysis) to learn about a behavior which has been frequently studied.

  46. *6 Different Activities for Test Developers • 3-Clinical Incidents Are a list of “critical behaviors” for rating a behavior or a job performance e.g., in job evaluation, # of days absent, being on time etc. • 4-Direct Observations Identifying a behavior by direct observation.

  47. *6 Different Activities for Test Developers 5-Expert Judgment Receiving input from individuals who have first hand experience with the construct of interest. Ex. If you want to evaluate the staff nurses in a hospital then, you need to talk to their supervisors to identify the type of performance that should be included in your evaluation.

  48. *6 Different Activities for Test Developers • 6-Instruction Objectives Develop a set of instructional objectives for your test (inventory). What are the objectives of your test? Find them and follow them. The test developer should focus on the specific content and the tasks that examinees should be able to perform. e.g. know the basic stats to calculate reliability and validity in test construction exam.

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