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What is a Number?

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What is a number? Names and symbols are arbitrary.

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

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What is a number? Names and symbols are arbitrary.

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Numbers that are not numbers…. 0 http://en.wikipedia.org/wiki/0_%28number%29

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

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

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

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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.

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

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

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

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

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What is a number? Object characteristics.

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

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Zero degrees centigrade….

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So then what is this…..

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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

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What is a number? Scales: Likert Scale

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What is a number? Scales: Likert Scale

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What is a number? Scales: Likert

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What is a number? Scales:

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What is a number? Scales:

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What is a number? Semantic scales:

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What is a number? Scales:

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What is a number? Scales:

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

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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.

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Stevens’ Scales

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

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Steven’s Scales: Ratio

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Steven’s Scales: 1. Nominal Scales

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

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

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

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

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

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Steven’s Scales: 1. Nominal Scales 2. Ordinal Scales Does everything a nominal scales does. Ranks objects or concepts by some characteristic. http://www.usatoday.com/sports/sagarin/fbt09.htm

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

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

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

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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.

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http://www.fao.org/docrep/W3241E/w3241e04.htm Good source:

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

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Which scale to use? 1. Amount of information needed

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

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

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

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

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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

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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.

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Measurement characteristics:

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

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

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

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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……

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

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

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WHY?

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Measurement characteristics: Validity

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Measurement characteristics: Validity 1. Face

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Measurement characteristics: Validity 1. Face 2. Content

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

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

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

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

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

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

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

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

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Measurement characteristics: Reliability

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Measurement characteristics: Reliability 1. Stability

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

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

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

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

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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

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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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