Chapter 2 1 measurement 2018 PDF

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Measurement

Measurement 

numbers to



attributes of people,

Attributes: Age Height Intelligence

People

 Measurement is the process of assigning:

events or objects…

 following a rule.

Measurem ents 36.3 / 39.0 median (2016) 63.7 / 69.2 mean (2014) ??? IQ points.

https://factfinder.census.gov/

 The numbers become data

Events

Attributes: Attendance Cost Earnings

 The “meaning” of the number is given by the

measurement process.

https://www.cdc.gov/

Measurements 1.2 billion tickets (2016) $ 8.84

(2018)

$ 38 billion

(2016)

https://www.statista.com/topics/964/film/

Objects

Attributes: Size Population Wealth

Measurem ents 52,419 sq miles 4,874,747 (2017) $ 44,758 median (2016) 17.1% at poverty level

PSYC2130-A.A.Lazarte 2.1 Measurement

1

Measurement

Measurement Scales

 A measurement has to be valid and reliable: 

Validity :

https://www.census.gov/quickfacts/al 2

PSYC2130-A.A.Lazarte 2.1 Measurement



Numbers have

A measure is valid if it is relevant or

4 > 2



their own properties:

6 – 4 = 3 – 1

6 = 2´3

appropriate as representation of the attribute. 

Skull size IS NOT a valid measure of intelligence.



Grade obtained in a written essay IS a valid measure of



Attributes also

English mastery



is reliable if repeated

 The match between the numbers and

measurements of the same attribute give the same

attributes properties defines a measurement

value.

scale.

Distances measured with a rubber yardstick may NOT be reliable.



All

normal individuals have cognitive abilities, etc.

Reliability : A measure



have their own properties:

 We perceive people taller than other people.

 Relations among “numbers” (e.g. 4/2 = 2) do not

always have meaningful translation into the attribute

Scores in SAT tends to be reliable.

that is being measured.

3

PSYC2130-A.A.Lazarte 2.1 Measurement

Properties of Measurement Scale

Properties of Measurement Scale 

MAGNI TUDE: of the attribute that allows us to

differences in the amount of the attribute being measured.

establish , or = relations.

Distances betw een mile mar kers

1 m il e

PSYC2130-A.A.Lazarte 2.1 Measurement

>

2 m il es Mile 67

... taller than ...

72 Inches

E xi t

35 M il e

M il e

34

75

Distances betw een exit ma rk er s

1 m ile

60 Inches 5

PSYC2130-A.A.Lazarte 2.1 Measurement

Exit 91

amount

the elements along a dimension, i.e. we can

Exit 9 0

order

76

there is an

EQUAL I NTERVALS: equal differences between numbers represent equal

E xi t



4

Mile 68

PSYC2130-A.A.Lazarte 2.1 Measurement

5 m iles 6

Properties of Measurement Scale 

Examples of Measurement Scales

ABSOLUTE ( UNI QUE) ZERO:



 There is a value, usually represented with 0, that

Favorit e Color (1= Red, 2=Blue, 3=Green, 4=Yellow)

represents absence of the attribute. This value is fixed, unique, absolute or non-arbitrary.  

Income: 0 dollars, i.e. no income at all.

Numbers:

Distance: 0 inches, i.e. two objects are at the same

3

>

1

OK

location 

Years of working experience: 0 years, i.e. no working

Attribute:

experience.

John

> Mary

likes

likes

green

red

Is green more than red? 

(Magnitude)

No!

NOMINAL SCALE PSYC2130-A.A.Lazarte 2.1 Measurement

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PSYC2130-A.A.Lazarte 2.1 Measurement

Examples of Measurement Scales 

Soprano Talent :

Numbers: Attribute:

10

8

>

Susan > Tracy

6

Yes

10 – 8

8 -

=

OK

> Mary

(Magnitude) Numbers: Attribute:

>

Does Susan sing better than Tracy?

Susan-Tracy = Tracy-Mary

(Equal Intervals)

I ntelligence:

120 > 110 > 100

Attribute:

Peter > John > George

(Magnitude) Numbers:

Is the difference in singing the same?

No

Attribute:

 9

Numbers:

120 / 100 = 1.2 or

´ 100 ´ George

(continuation)

Peter = 1.2

(Absolute Zero)

No

Is Peter 1.2 times as intelligent as George?  20 40

120

INTERVAL SCALE

PSYC2130-A.A.Lazarte 2.1 Measurement

Is the difference in intelligence the same? OK

Peter - John =

10

Reading Speed:

msec/word

40/ 20= 2

Numbers:

200 < 350 < 500

Attribute:

Beth < Scott < Steve

(Magnitude)

Yes

Is Beth faster than Scott? OK

500 - 350 = 350 – 200

Attribute:

Steve - Scott =

(Equal Intervals) Yes

New “0”

OK

Numbers:

Scott - Beth

0

OK

OK

100

120/ 100= 1.2

120 - 110 = 110 - 100

Examples of Measurement Scales 

120 = 1.2 Attribute:

Yes

PSYC2130-A.A.Lazarte 2.1 Measurement

Examples of Measurement Scales IQ Scores

Is Peter more intelligent than John? OK

John - George

ORDINAL SCALE

I ntelligence:

OK

(Equal Intervals) Yes

PSYC2130-A.A.Lazarte 2.1 Measurement



IQ Scores

Numbers:

OK

OK

6

Examples of Measurement Scales 

from 1 to 10

8

OK Is the difference in speed the same? OK

(Old 80) 11

PSYC2130-A.A.Lazarte 2.1 Measurement

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Examples of Measurement Scales 

Reading Speed:

Numbers:

msec/words

Attribute:

Steve = 2.5

´ 200 ´ Beth

(Absolute Zero) Yes

 Mutually exclusive and exhaustive classes of

(continuation)

elements are represented by numerals. We use the numbers as simple labels.

500 /200 = 2.5 or 500 = 2.5

Nominal Scales

OK

 Examples:

Gender (0 = female 1 = male), SSN,

area code, players numbers.

Is Steve 2.5 times slower than Beth? OK

 Properties:  NO magnitude,  NO equal intervals,  NO absolute zero.

RATIO SCALE

PSYC2130-A.A.Lazarte 2.1 Measurement

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PSYC2130-A.A.Lazarte 2.1 Measurement

Ordinal Scales  Elements are assigned

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Interval Scales  Equal scale intervals reflect equal amounts of

to equivalence classes

the attribute. The difference between two

that are rank ordered with respect to each

numbers makes sense, but their ratio doesn’t.

other. Numbers as ranks.

 Example: temperature, Test scores (at best).

 Example: Preferences, SES, Number-grades

 Properties:

 Properties

 Magnitude

 Magnitude

 Equal Intervals

 NO equal intervals

 NO absolute zero

 NO absolute zero

PSYC2130-A.A.Lazarte 2.1 Measurement

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PSYC2130-A.A.Lazarte 2.1 Measurement

Scale Identification

Ratio Scales  The scale has an absolute zero.

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(1) Are numbers used only as labels?

The ratio

Ratio

between two numbers have a meaning.

NO

 Examples: length, weight, times, in general

YES Nominal Scale

physical measures.

Interva l

 Properties:

(2) Do equal numerical intervals represent equal amounts of the attribute?

 Magnitude  Equal Intervals

NO

Ordinal

 Absolute Zero

Ordinal Scale

YES

(3) Is 0 a fixed, absolute or no-arbitrary value?

Nom inal

PSYC2130-A.A.Lazarte 2.1 Measurement

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NO

YES

Interval Scale

Ratio Scale

PSYC2130-A.A.Lazarte 2.1 Measurement

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