1. M e a s u r e m e n t

2. Hard: concrete concepts Soft : abstract concepts (construct)
What is Measurement?
DATA:
Hard: concrete concepts
Soft : abstract concepts (construct)

3. Alternative definition
Measurement is the process of linking abstract concepts to empirical indicants.
Zellar & Carmines

4. Concepts Indicants Weight Distance Depression Test anxiety
Marital satisfaction
Pounds/grams/tons
meters, kilometers
?????

5. Some Definitions
Variable

6. Some Definitions
Variable
Attribute

7. Some Definitions
Variable
Gender
Attribute

8. Some Definitions
Variable
Gender
Attribute
Female
Male

9. Qualities of Variables
exhaustive - should include all possible answerable responses
mutually exclusive - no respondent should be able to have two attributes simultaneously (e.g., employed vs. unemployed - it is possible to be both if looking for a second job while employed)

10. Levels of Measurement

11. The Levels of Measurement
Nominal
Ordinal
Interval
Ratio

12. Nominal Measurement
the values just “name” the attribute uniquely

13. Nominal Measurement the values just “name” the attribute uniquely
does not imply any ordering of the cases

14. Nominal Measurement the values just “name” the attribute uniquely
does not imply any ordering of the cases
for example, jersey numbers in football

15. Nominal Measurement the values just “name” the attribute uniquely
does not imply any ordering of the cases
for example, jersey numbers in football
even though player 10 has higher number than player 5, you can’t say from the data that he’s greater than or more than the other

16. Ordinal Measurement when attributes can be rank-ordered
distances between attributes do not have any meaning
for example, code Educational Attainment as
0=less than H.S.
1=H.S. degree
3=M.S. degree
4=Phd degree
is distance from 0 to 1 same as 3 to 4?

17. Interval Measurement
when distance between attributes has meaning

18. Interval Measurement when distance between attributes has meaning
for example, temperature (in Fahrenheit) - distance from is same as distance from 70-80

19. Interval Measurement when distance between attributes has meaning
for example, temperature (in Fahrenheit) - distance from is same as distance from 70-80
but note that ratios don’t make any sense - 80 degrees is not twice as hot as 40 degrees (although the attribute values are)

20. Ratio Measurement
has an absolute zero that is meaningful

21. Ratio Measurement has an absolute zero that is meaningful
can construct a meaningful ratio (fraction)

22. Ratio Measurement has an absolute zero that is meaningful
can construct a meaningful ratio (fraction)
for example,number of clients in past six months

23. Ratio Measurement has an absolute zero that is meaningful
can construct a meaningful ratio (fraction)
for example,number of clients in past six months
it is meaningful to say that “...we had twice as many clients in this period as we did in the previous six months

24. Why is Level of Measurement Important?
helps you decide what statistical analysis is appropriate on the values that were assigned
helps you decide how to interpet the data from that variable

25. The Hierarchy of Levels
Nominal

26. The Hierarchy of Levels
Nominal
Attributes are only named; weakest

27. The Hierarchy of Levels
Ordinal
Nominal
Attributes are only named; weakest

28. The Hierarchy of Levels
Ordinal
Attributes can be ordered
Nominal
Attributes are only named; weakest

29. The Hierarchy of Levels
Interval
Ordinal
Attributes can be ordered
Nominal
Attributes are only named; weakest

30. The Hierarchy of Levels
Interval
Distance is meaningful
Ordinal
Attributes can be ordered
Nominal
Attributes are only named; weakest

31. The Hierarchy of Levels
Ratio
Interval
Distance is meaningful
Ordinal
Attributes can be ordered
Nominal
Attributes are only named; weakest

32. The Hierarchy of Levels
Ratio
Absolute zero
Interval
Distance is meaningful
Ordinal
Attributes can be ordered
Nominal
Attributes are only named; weakest

33. Scales and Scaling

34. General Issues in Scaling

35. What is a scale?
the assignment...

36. What is a scale? the assignment... ...of objects...
Are you willing to permit immigrants to live in your country?
Are you willing to permit immigrants to live in your neighborhood?
Would you let your child marry an immigrant?

37. What is a scale? the assignment... ...of objects... ...to numbers...
Are you willing to permit immigrants to live in your country?
Are you willing to permit immigrants to live in your neighborhood?
Would you let your child marry an immigrant?

38. What is a scale? the assignment... ...of objects... ...to numbers...
Are you willing to permit immigrants to live in your country?
Are you willing to permit immigrants to live in your neighborhood?
Would you let your child marry an immigrant?
...according to a rule...

39. What is a scale? the assignment... ...of objects... ...to numbers...
Are you willing to permit immigrants to live in your country?
Are you willing to permit immigrants to live in your neighborhood?
Would you let your child marry an immigrant?
cumulative
...according to a rule...

40. Scale versus Response Scale

41. Scale versus Response Scale
results from a process

42. Scale versus Response Scale
is used to collect the response for an item
results from a process

43. Scale versus Response Scale
is used to collect the response for an item
results from a process
each item on scale has a scale value

44. Scale versus Response Scale
is used to collect the response for an item
results from a process
each item on scale has a scale value
item not associated with a scale value

45. Scale versus Response Scale
is used to collect the response for an item
results from a process
each item on scale has a scale value
item not associated with a scale value
refers to a set of items

46. Scale versus Response Scale
is used to collect the response for an item
results from a process
each item on scale has a scale value
item not associated with a scale value
refers to a set of items
used for a single item

47. Purposes of Scaling hypothesis testing
is the construct or concept a single dimensional one?
what dimensions underlie some ratings?
for assigning values to responses
exploration
scoring

48. Dimensionality
One-dimensional Constructs

49. Dimensionality
One-dimensional Constructs
height

50. Dimensionality
One-dimensional Constructs
height
shorter
taller

51. Dimensionality
One-dimensional Constructs
height
shorter
taller
thirst

52. Dimensionality One-dimensional Constructs height thirst shorter taller
less thirsty
more thirsty

53. Dimensionality One-dimensional Constructs height thirst self esteem
shorter
taller
thirst
less thirsty
more thirsty
self esteem

54. Dimensionality One-dimensional Constructs height thirst self esteem
shorter
taller
thirst
less thirsty
more thirsty
self esteem
less
more

55. Dimensionality
Two-dimensional Construct

56. Dimensionality
Two-dimensional Construct
academic ability

57. Dimensionality
Two-dimensional Construct
academic ability
verbal

58. Dimensionality Two-dimensional Construct academic ability verbal worse
better

59. Dimensionality quantitative Two-dimensional Construct academic ability
verbal
worse
better

60. Dimensionality quantitative Two-dimensional Construct academic ability
better
academic ability
verbal
worse
better
worse

61. Dimensionality
Three-dimensional Construct

62. Dimensionality
Three-dimensional Construct

63. Dimensionality semantic differential (meaning)
Three-dimensional Construct

64. Dimensionality semantic differential (meaning)
Three-dimensional Construct
evaluation

65. Dimensionality semantic differential (meaning)
Three-dimensional Construct
evaluation
unfavorable
favorable

66. Dimensionality semantic differential (meaning)
Three-dimensional Construct
potency
evaluation
unfavorable
favorable

67. Dimensionality semantic differential (meaning)
Three-dimensional Construct
potency
powerful
evaluation
powerless
unfavorable
favorable

68. Dimensionality semantic differential (meaning)
Three-dimensional Construct
activity
potency
powerful
evaluation
powerless
unfavorable
favorable

69. Dimensionality semantic differential Three-dimensional Construct
active
activity
potency
powerful
evaluation
passive
powerless
unfavorable
favorable

70. Types of Scales Unidimensional Multidimensional easier to understand
usefule for understanding multidimensional
many concepts may be unidimensional
reflect multiple properties simultaneously
Multidimensional

71. The Major Unidimensional Scale Types
Thurstone
Likert
Guttman