What is a Number?

What is a number? Names and symbols are arbitrary.

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

What is a number? Names and symbols are arbitrary.

Numbers that are not numbers…. 0

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

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

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

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.

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

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

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

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

Object characteristics. are measured, not objects,

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

Zero degrees centigrade….

So then what is this…..

What is a number? Scales: Likert Scale Is a statement (not a question) followed by five categories of agreement.

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

What is a number? Scales: Likert Scale

What is a number? Scales: Likert Scale

What is a number? Scales: Likert

What is a number? Scales:

What is a number? Scales: Semantic scales: Typically: Opposite adjectives separated by 7 selection points.

What is a number? Scales:

Semantic scales:

Semantic scales:

Hybrid Scales:

But complex concepts in business may not be easily measured.

What is a number? So….. Harvard professor S.S. Stevens created numerical scales to measure difficult concepts.

S. S. Stevens

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

Steven’s Scales: Ratio

Steven’s Scales: 1. Nominal Scales

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

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

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

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

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

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

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

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

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

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.

Good source:

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

Which scale to use? 1. Amount of information needed

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

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

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

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

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

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.

Measurement characteristics:

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

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

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

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……

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

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

WHY?

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 needs to be taken to be confident that the student knows what the grades indicate that they know?

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.

Measurement characteristics: Reliability

Measurement characteristics: Reliability 1. Stability

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

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

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

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

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

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 Klaus Krippendorff

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

Measurement characteristics: Validity 1. Face validity

Measurement characteristics: Validity 1. Face 2. Content

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

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

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

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

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

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

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

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

Measurement characteristics: Validity 1. Face 2. Content 3. Criteria a. Concurrent b. Predictive 4. Construct 5. Utilitarian (?) A measurement may satisfy a utilitarian goal independently of any validity of the actual measurement.