Measurement with Numbers Scaling: 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…. http://en.wikipedia.org/wiki/0_%28number%29

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

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.”

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

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

Zero degrees centigrade….

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

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

Scales: Likert Scale

Scales:

Scales: Likert-like

Scales: Likert Scale

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

Scales:

Semantic scales:

Semantic scales:

Hybrid Scales:

But complex concepts in business may not be easily measured.

Harvard professor S.S. Stevens created numerical scales to measure difficult concepts. S. S. Stevens 1906 - 1973

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

Steven’s Scales: 1. Nominal Scales

Steven’s Scales: Nominal Scales a. Name

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

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

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

Why is this 380? Why is this 235?

Steven’s Scales: Nominal Scales Ordinal Scales

Steven’s Scales: Nominal Scales Ordinal Scales Does everything a nominal scales does. Ranks objects or concepts by some characteristic. http://www.usatoday.com/sports/ncaab/sagarin/ http://sportspolls.usatoday.com/ncaa/football/polls/coaches-poll/

Steven’s Scales: Nominal Scales Ordinal Scales Interval scales

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

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

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.

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

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

Which scale to use? Amount of information needed

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

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

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

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

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

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.

Measurement Characteristics: Lecture 7B Measurement Characteristics:

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) If you take a sample… you will create a 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 need to be taken in order to be confident that the student actually 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 Stability

Measurement characteristics: Reliability Stability Test-retest Equivalent forms

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

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

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

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

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 -

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 Face validity

Measurement characteristics: Validity Face Content

Measurement characteristics: Validity Face Content Criteria

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

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

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

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

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

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

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.