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

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Presentation on theme: "What is a Number?. What is a number? Names and symbols are arbitrary."— Presentation transcript:

1 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.

5

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7 Numbers that are not numbers…. 0

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

9 What is a number? Names and symbols are arbitrary. Measurement: “Rules for assigning numbers to objects (or concepts) to represent quantities of attributes.”

10 What is a number? Names and symbols are arbitrary. Measurement:

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12 What is a number? Names and symbols are arbitrary. But to be a true number scale the symbols must follow some logical and systematic arrangement.

13 What is a number? Names and symbols are arbitrary. Measurement: “Standardized process of assigning symbols to objects according to certain prespeciified and nondegenerating rules.”

14 Is it possible to have an IQ of 160? But what does it mean? 160

15 What is a number? Names and symbols are arbitrary. Measurement:

16 What is a number? Names and symbols are arbitrary. Measurement: “An object is never measured… only the object’s attributes.”

17 What is a number? Object characteristics.

18 What is a number? Scales: “A scale is the continuum upon which measurements are located.”

19 Zero degrees centigrade….

20 So then what is this…..

21 What is a number? Scales: Likert Scale Ice cream is good for breakfast. 1. Strongly disagree 2. Disagree 3. Neither agree nor disagree 4. Agree 5. Strongly agree

22 What is a number? Scales: Likert Scale

23 What is a number? Scales: Likert Scale

24 What is a number? Scales: Likert

25 What is a number? Scales:

26 What is a number? Scales:

27 What is a number? Semantic scales:

28 What is a number? Scales:

29 What is a number? Scales:

30 What is a number? But complex concepts in business may not be easily measured.

31 What is a number? But complex concepts in business may not be easily measured. Harvard professor S.S. Stevens created scales to measure difficult concepts.

32 Stevens’ Scales

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

34 Steven’s Scales: Ratio

35 Steven’s Scales: 1. Nominal Scales

36 Steven’s Scales: 1. Nominal Scales a. Name

37 Steven’s Scales: 1. Nominal Scales a. Name b. Classify

38 Steven’s Scales: 1. Nominal Scales a. Name b. Classify c. Categorize

39 Steven’s Scales: 1. Nominal Scales a. Name b. Classify c. Categorize

40 Steven’s Scales: 1. Nominal Scales 2. Ordinal Scales

41 Steven’s Scales: 1. Nominal Scales 2. Ordinal Scales Does everything a nominal scales does. Ranks objects or concepts by some characteristic.

42 Steven’s Scales: 1. Nominal Scales 2. Ordinal Scales 3. Interval scales

43 Steven’s Scales: 1. Nominal Scales 2. Ordinal Scales 3. Interval scales Does everything an ordinal scale does. Interval is now meaningful.

44 Steven’s Scales: 1. Nominal Scales 2. Ordinal Scales 3. Interval scales 4. Ratio scales

45 Steven’s Scales: 1. Nominal Scales 2. Ordinal Scales 3. Interval scales 4. Ratio scales Has all the characteristics of all other scales, but it also has meaningful ratios. It has a true zero.

46 Good source:

47 Steven’s Scales: 1. Nominal Scales 2. Ordinal Scales X = f(x) 3. Interval scalesX = kx + c 4. Ratio scalesX = kx

48 Which scale to use? 1. Amount of information needed

49 Which scale to use? 1. Amount of information needed Each higher scale carries more information than the one before it.

50 Which scale to use? 1. Amount of information needed 2. Characteristics of stimulus or concept

51 Which scale to use? 1. Amount of information needed 2. Characteristics of stimulus or concept 3. Application context

52 Which scale to use? 1. Amount of information needed 2. Characteristics of stimulus or concept 3. Application context 4. Capacity of scale

53 Which scale to use? 1. Amount of information needed 2. Characteristics of stimulus or concept 3. Application context 4. Capacity of scale 5. Post-measurement analysis

54 Which scale to use? 1. Amount of information needed 2. Characteristics of stimulus or concept 3. Application context 4. Capacity of scale 5. Post-measurement analysis Statistics are designed for specific types of scales. Using the wrong scale will give answers that are nonsense.

55 Measurement characteristics:

56 Y = x(true) + x(sy-error) + x(random)

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

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

59 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……

60 Measurement characteristics: This is called a Sampling Error Y = x(true) + x(sy-error) + x(random) + x(sampling error)

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

62 WHY?

63 Measurement characteristics: Validity

64 Measurement characteristics: Validity 1. Face

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66 Measurement characteristics: Validity 1. Face 2. Content

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68 Measurement characteristics: Validity 1. Face 2. Content 3. Criteria

69 Measurement characteristics: Validity 1. Face 2. Content 3. Criteria a. Concurrent b. Predictive

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71 Measurement characteristics: Validity 1. Face 2. Content 3. Criteria a. Concurrent b. Predictive 4. Construct

72 Measurement characteristics: Validity 1. Face 2. Content 3. Criteria a. Concurrent b. Predictive 4. Construct

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74 Measurement characteristics: Validity 1. Face 2. Content 3. Criteria a. Concurrent b. Predictive 4. Construct a. Convergent

75 Measurement characteristics: Validity 1. Face 2. Content 3. Criteria a. Concurrent b. Predictive 4. Construct a. Convergent b. Divergent

76 Measurement characteristics: Validity 1. Face 2. Content 3. Criteria a. Concurrent b. Predictive 4. Construct a. Convergent b. Divergent c. Discriminant

77 Measurement characteristics: Validity 1. Face 2. Content 3. Criteria a. Concurrent b. Predictive 4. Construct a. Convergent b. Divergent c. Discriminant d. Nomological

78 Measurement characteristics: Reliability

79 Measurement characteristics: Reliability 1. Stability

80 Measurement characteristics: Reliability 1. Stability a.Test-retest b. Equivalent forms

81 Measurement characteristics: Reliability 1. Stability a.Test-retest b. Equivalent forms 2. Equivalence

82 Measurement characteristics: Reliability 1. Stability a.Ttest-retest b. Equivalent forms 2. Equivalence a. Kuder-Richardson b. Cronbach’s Alpha

83 Measurement characteristics: Reliability 1. Stability a.Test-retest b. Equivalent forms 2. Equivalence a. Kuder-Richardson b. Cronbach’s Alpha Lee Cronbach

84 Measurement characteristics: Reliability 1. Stability a.Test-retest b. Equivalent forms 2. Equivalence a. Kuder-Richardson b. Cronbach’s Alpha Learn, Effective, & Like the instructor

85 Measurement characteristics: Reliability 1. Stability a.Test-retest b. Equivalent forms 2. Equivalence a. Kuder-Richardson b. Cronbach’s Alpha 3. Inter-rater Consistency a. Krippendorff’s Alpha


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