1. Measurement with Numbers Scaling: What is a Number?

2. What is a number?
Names and symbols are arbitrary.

3. What is a number?
Names and symbols are arbitrary.
Four…. IV …. 4….

4. What is a number?
Names and symbols are arbitrary.

7. Numbers that are not numbers….

8. Numbers that are not numbers… Some make the world go around.

9. Measurement: So then? “Rules for assigning numbers to objects
What is a…..
Measurement:
“Rules for assigning numbers to objects
(or concepts) to represent quantities of attributes.”

10. Measurement But to be a true number scale the symbols
must follow some logical
and
systematic arrangement.

11. Numbers can be assigned using… Scales:
“A scale is the continuum upon which
measurements are located.”

12. Zero degrees
centigrade….

13. Scales: Likert Scale is a common example.
It is a statement (not a question) followed by five categories of
agreement.

14. Scales: Likert Scale Ice cream is good for breakfast.
1. Strongly disagree
2. Disagree
3. Neither agree nor disagree
4. Agree
5. Strongly agree

15. Scales:
Likert Scale

16. Scales:

17. Scales: Likert-like

18. Scales:
Likert Scale

19. Typically: Opposite adjectives
Scales:
Semantic scales:
Typically: Opposite adjectives
separated by 7 selection points.

20. Scales:

21. Semantic
scales:

23. Semantic
scales:

24. Hybrid
Scales:

25. But complex concepts in business may not be easily measured.

26. Harvard professor S.S. Stevens
created numerical scales to measure
difficult concepts.
S. S. Stevens

27. Steven’s original paper in Science, 103(2684), June 7, 1946.

29. Steven’s Scales:
1. Nominal Scales

30. Steven’s Scales:
Nominal Scales
a. Name

31. Steven’s Scales:
Nominal Scales
a. Name
b. Classify

32. Steven’s Scales:
Nominal Scales
a. Name
b. Classify
c. Categorize

33. Steven’s Scales:
Nominal Scales
a. Name
b. Classify
c. Categorize

35. Why is this 380?
Why is this 235?

36. Steven’s Scales:
Nominal Scales
Ordinal Scales

37. Steven’s Scales: Nominal Scales Ordinal Scales
Does everything a nominal scales does.
Ranks objects or concepts by some
characteristic.

38. Steven’s Scales:
Nominal Scales
Ordinal Scales
Interval scales

39. Steven’s Scales: Nominal Scales Ordinal Scales Interval scales
Does everything an
ordinal scale does.
The Interval is
now meaningful.

40. Steven’s Scales: Nominal Scales Ordinal Scales Interval scales
Ratio scales

41. Steven’s Scales: Nominal Scales Ordinal Scales Interval scales
Ratio scales
Has all the characteristics of all other scales,
but it also has meaningful ratios. It has a true
zero.

42. Good source:

43. Steven’s Scales: Nominal Scales Ordinal Scales X = f(x)
Interval scales X = kx + c
Ratio scales X = kx

44. Which scale to use?
Amount of information needed

45. Which scale to use? Amount of information needed
Each higher scale carries more information
than the one before it.

46. Which scale to use? Amount of information needed
Characteristics of stimulus or concept

47. Which scale to use? Amount of information needed
Characteristics of stimulus or concept
Application context

48. Which scale to use? Amount of information needed
Characteristics of stimulus or concept
Application context
Capacity of scale

49. Which scale to use? Amount of information needed
Characteristics of stimulus or concept
Application context
Capacity of scale
Post-measurement analysis

50. Which scale to use? Amount of information needed
Characteristics of stimulus or concept
Application context
Capacity of scale
Post-measurement analysis
Statistics are designed for specific types
of scales. Using the wrong scale will give
answers that are nonsense.

51. Measurement Characteristics:
Lecture 7B
Measurement Characteristics:

52. Measurement characteristics:
Y = x(true) + x(sy-error) + x(random)

53. Measurement characteristics:
Y = x(true) + x(sy-error) + x(random)
Systematic error can be eliminated.

54. Measurement characteristics:
Y = x(true) + x(sy-error) + x(random)
Random error cannot be eliminated.

55. Measurement characteristics:
Y = x(true) + x(sy-error) + x(random)
If a sample is taken to estimate an answer:
another form of error is added……

56. Measurement characteristics:
This is called a Sampling Error
Y = x(true) + x(sy-error) + x(random) + x(sampling error)
If you take a sample… you will create a sampling error!

57. You and a friend (in the same class) take the
same exam at the same time and
get different grades.

58. WHY?

59. Take a piece of paper…
write down five different reasons
why these two friends taking the same class
would get different grades...
What then did the grade actually measure?
Write down a definition of a “grade.”
If you suggested that a “grade” is a measurement
of what a student knows, how many “grades” would
you suggest need to be taken in order to be confident that
the student actually knows what the grades indicate
that they know?

60. Measurement characteristics:
Validity
Before validity can be established, it is necessary to
show that measurements have reliability.
A measurement can be reliable without being
valid, but it cannot be judged to be valid without
reliability.

61. Measurement characteristics:
Reliability

62. Measurement characteristics:
Reliability
Stability

63. Measurement characteristics:
Reliability
Stability
Test-retest
Equivalent forms

64. Measurement characteristics:
Reliability
Stability
Test-retest
Equivalent forms
2. Equivalence

65. Measurement characteristics:
Reliability
Stability
Test-retest
Equivalent forms
2. Equivalence
a. Kuder-Richardson
b. Cronbach’s Alpha

66. Measurement characteristics:
Reliability
Stability
Test-retest
Equivalent forms
2. Equivalence
a. Kuder-Richardson
b. Cronbach’s Alpha
Lee Cronbach

67. Measurement characteristics:
Reliability
Stability
Test-retest
Equivalent forms
2. Equivalence
a. Kuder-Richardson
b. Cronbach’s Alpha
Learn, Effective, & Like the instructor

68. Measurement characteristics:
Reliability
Stability
Test-retest
Equivalent forms
2. Equivalence
a. Kuder-Richardson
b. Cronbach’s Alpha
3. Inter-rater Consistency
a. Krippendorff’s Alpha
Klaus Krippendorff
1932 -

69. Measurement characteristics:
If a measurement is reliable, it
may be valid:
But there are many ways that
a measurement could be valid or invalid.

71. Measurement characteristics:
Validity
Face validity

73. Measurement characteristics:
Validity
Face
Content

75. Measurement characteristics:
Validity
Face
Content
Criteria

76. Measurement characteristics:
Validity
Face
Content
Criteria
a. Concurrent
b. Predictive

78. Measurement characteristics:
Validity
Face
Content
Criteria
a. Concurrent
b. Predictive
4. Construct

80. Measurement characteristics:
Validity
Face
Content
Criteria
a. Concurrent
b. Predictive
4. Construct
a. Convergent

81. Measurement characteristics:
Validity
Face
Content
Criteria
a. Concurrent
b. Predictive
4. Construct
a. Convergent
b. Divergent

82. Measurement characteristics:
Validity
Face
Content
Criteria
a. Concurrent
b. Predictive
4. Construct
a. Convergent
b. Divergent
c. Discriminant

83. Measurement characteristics:
Validity
Face
Content
Criteria
a. Concurrent
b. Predictive
4. Construct
a. Convergent
b. Divergent
c. Discriminant
d. Nomological

84. Measurement characteristics:
Validity
Face
Content
Criteria
a. Concurrent
b. Predictive
4. Construct
5. Utilitarian (?)
A measurement may satisfy a utilitarian goal
independently of any validity of the actual measurement.