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

What is a Number?

What is a number?Names and symbols are arbitrary.


Four…. IV …. 4….

Numbers that are not numbers….

0

http://en.wikipedia.org/wiki/0_%28number%29

http://en.wikipedia.org/wiki/0_%28number%29

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

e


Measurement:

“Rules for assigning numbers to objects (or concepts) to represent quantities of attributes.”


Measurement:


But to be a true number scale the symbolsmust follow some logical

and systematic arrangement.


Measurement:

“Standardized process of assigning symbols to objects according to certain prespeciified and

nondegenerating rules.”

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

160


Measurement:


Measurement:

“An object is never measured… only theobject’s attributes.”

What is a number? Object characteristics.

What is a number?

Scales:

“A scale is the continuum upon which measurements are located.”

Zero degreescentigrade….

So then what is this…..

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

What is a number?

Scales:

What is a number?

Semanticscales:

What is a number?

Scales:

What is a number?

But complex concepts in businessmay not be easily measured.

What is a number?

But complex concepts in businessmay not be easily measured.

Harvard professor S.S. Stevenscreated scales to measure difficult

concepts.

Stevens’ Scales

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

Steven’s Scales:

Ratio

Steven’s Scales: 1. Nominal Scales


a. Name


a. Nameb. Classify


a. Nameb. Classify

c. Categorize

Steven’s Scales: 1. Nominal Scales2. Ordinal Scales

Steven’s Scales: 1. Nominal Scales2. Ordinal Scales

Does everything a nominal scales does.Ranks objects or concepts by some

characteristic.

http://www.usatoday.com/sports/sagarin/fbt09.htm

http://www.usatoday.com/sports/sagarin/fbt09.htm

Steven’s Scales: 1. Nominal Scales2. Ordinal Scales 3. Interval scales

Steven’s Scales: 1. Nominal Scales2. Ordinal Scales 3. Interval scales

Does everything an ordinal scale does.

Interval is now meaningful.

Steven’s Scales: 1. Nominal Scales2. Ordinal Scales 3. Interval scales4. Ratio scales

Steven’s Scales: 1. Nominal Scales2. Ordinal Scales 3. Interval scales4. Ratio scales

Has all the characteristics of all other scales, but it also has meaningful ratios. It has a true zero.

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

Good source:

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

Steven’s Scales: 1. Nominal Scales2. Ordinal Scales X = f(x)3. Interval scales X = kx + c4. Ratio scales X = 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 needed2. Characteristics of stimulus or concept

Which scale to use?1. Amount of information needed2. Characteristics of stimulus or concept3. Application context

Which scale to use?1. Amount of information needed2. Characteristics of stimulus or concept3. Application context4. Capacity of scale

Which scale to use?1. Amount of information needed2. Characteristics of stimulus or concept3. Application context4. Capacity of scale5. Post-measurement analysis

Which scale to use?1. Amount of information needed2. Characteristics of stimulus or concept3. Application context4. Capacity of scale5. Post-measurement analysis

Statistics are designed for specific typesof scales. Using the wrong scale will giveanswers that are nonsense.

Measurement characteristics:


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



Systematic error can be eliminated.



Random error cannot be eliminated.



If a sample is taken to estimate an answer:another form of error is added……


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 thesame exam at the same time and

get different grades.

Measurement characteristics:Validity

Measurement characteristics:Validity1. Face

Measurement characteristics:Validity1. Face2. Content

Measurement characteristics:Validity1. Face2. Content3. Criteria


a. Concurrentb. Predictive



4. Construct



4. Constructa. Convergent




b. Divergent




b. Divergentc. Discriminant




b. Divergentc. Discriminant

d. Nomological

Measurement characteristics:Reliability

Measurement characteristics:Reliability1. Stability


a.Test-retestb. Equivalent forms



2. Equivalence


a.Ttest-retestb. Equivalent forms

2. Equivalence a. Kuder-Richardsonb. Cronbach’s Alpha




Lee Cronbach




Learn, Effective, & Like the instructor




3. Inter-rater Consistencya. Krippendorff’s Alpha

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

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