MEASUREMENT - University of Idaho of...LEVEL OF MEASUREMENT NOMINAL ORDINAL INTERVAL RATIO EXAMPLES Names of activities, locations, gender Ranks, preferences Attitude scales, Length

MEASUREMENT

Nominal, Ordinal, Interval and Ratio variables and the concepts

of Reliability and Validity

This lecture is brought to you by:

The letter

Can you say Research?

http://video.pbs.org:8080/ramgen/mr_rogers/Homepage/intromovie.rm

What is a variable?

• Any characteristic that can take on more than one form or value. Something that can, and does, vary.

• Variables are what are measured.

• They represent the properties of an object that we are interested in measuring.

• What is measurement?

• Conceptualization or conceptual definition. • Assigning numbers to represent the (often

hidden) values or properties of a variable.

• Linking a concept (idea) to a measure (technique) to make it empirically observable.

What is measurement?

There are two systems for numbering:

• The abstract set

• Variable specific characteristics

The abstract set

• Has formal rules and procedures.

• Forms the subject of mathematics.

Variable specific set

• Represents the properties of the variable being measured.

• Specifically it represents the differences in value that a variable can take:

• A,B,C,D and F represent the values of a grading system and the relationships between values:

• Outstanding work ; Very good to excellentwork; Adequate work ;Passing work that is minimally adequate, Failing work that is clearly inadequate and unworthy of credit.

The challenge is

• To merge the rules that govern the abstract set with those that govern the variable specific set, without violating the principles of either.

• If A=4; B=3; C=2; D=1; and F=0is an A four times as good as a D?

Abstract numbers have properties

• Identity– each number has particular meaning, and the

categories are discrete.

• Magnitude (order)– there is an inherent order from large to small

• Interval– the difference between 7 and 8 is the same

increment as between 194 and 195

• A true zero– There is a true (real) absence of the property.

Not all numbers are equal!!

• Stevens (1946) classified variables into four levels.

• These are referred to as level of measurement, or levels of data.

• Nominal

• Ordinal

• Interval

• Ratio

Nominal variables

• The least like “real” numbers.

• The only property they have is identity or name (nominal=name).

• Numbers if used are simply codes for the real names of the properties.

Nominal

Which recreational activities do you participate in?

(Please circle the number of all that apply)

1 HIKING

2 FISHING

3 PICNICKING

4 BOATING

5 SWIMMING

Nominal

Which recreational activities do you participate in? (Please list the activities in the spaces below)

1__Baking brownies_________

2__Underwater Ping-pong_____

3__Cow tipping_____________

4__Reading Statistics books____

Four people ran in the race

• We know their names!

Earl Greg Mike Matt

Ordinal variables

• Have identity

• Have magnitude (order). A>B>C>D.

• We know relative order.

• We DO NOT know how much better A was relative to B.

• Consider two races in which we know the order of finish (ranks).

Ordinal variables

Brad=1

Aaron=2

Tyler=3

Mitch=4

Delcie=1

Steffany=2

Brita=3

Beth=4

Can we say who was fastest overall?

Was Beth, who was slowest in her race, faster

or slower than Aaron, who was second in his

race?

Ordinal variables

Brad=4.2 minutes

Aaron=4.22

Tyler=5.01

Mitch=5.9

Delcie=3.97

Steffany=4.0

Brita=4.12

Beth=4.21

Can we say who was fastest overall?

Was Beth, who was slowest in her race, faster

or slower than Aaron, who was second in his

race?


Brad Aaron Tyler Mitch

1

2

3

4

We know the order they finished in

Ordinal

Which recreational activities are most important to you? (In the spaces below please write in the names of the three most important activities selected form the list below)

MOST IMPORTANT ACTIVITY ____________

2nd MOST IMPORTANT ACTIVITY _____________

3rd MOST IMPORTANT ACTIVITY __________

Ordinal

The interval, or distance between numbers is unequal and unknown:

Idaho MN OH RANKSkiing AxeThrow Opera 1

Rugby Skiing Rugby 2

Opera Opera Skiing 3

AxeThrow Rugby AxeThrow 4

What is most popular overall?

Ordinal

The interval, or distance between numbers is unequal and unknown:

“AVERAGE Rank” “overall” RANK

Skiing 2.0 1

Opera 2.33 2

Rugby 2.66 3

AxeThrow 3.0 4

Interval variables

• Have identity and magnitude.

• Also have known distance between values.

• Form a true scale, but without a zero point.

• Temperature:

– Is August 31, at 100F twice as hot as September 18 at 50F?

– There is a true zero, isn’t there??



3:15pm

3:21pm

3:22pm

4:19pm

We know how far apart they finished,

but when did they START?



3:15pm

3:21pm

3:22pm

4:19pm

We know how far apart they finished,

but when did they START?

Brad is 1:04 faster than Mitch

Interval

What is your current age? (Please check the letter that best matches your age)

A. 11-15

B. 16-20

C. 21-25

D. 26-30

C. 31-35 . . . . . . .etc.

Interval

How important are each of the following activities to you?

How important is each activity to you?ACTIVITY (Please circle one response for each activity)

1. HIKING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY

IMPORTANT IMPORTANT IMPORTANT IMPORTANT IMPORTANT

2. FISHING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY


3. PICNICKING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY


4. BOATING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY


5. SWIMMING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERYIMPORTANT IMPORTANT IMPORTANT IMPORTANT IMPORTANT

Wondering where /what is the interval here?

• Pause to talk about the Bass et al. handout on magnitude estimation …..

• Bass, B. M., Cascio, W. F. & O'Connor, E. J. (1974). Magnitude estimations of expressions of frequency and amount. Journal of Applied Psychology, 59(3), 310-320.

• The Neon Green/Lime sheet

Interval

How important are each of the following activities to you?

How important is each activity to you?ACTIVITY (Please circle one response for each activity)

1. HIKING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY


2. FISHING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY


3. PICNICKING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY


4. BOATING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY


5. SWIMMING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERYIMPORTANT IMPORTANT IMPORTANT IMPORTANT IMPORTANT

From Table 2: ~48 ~36 ~24 ~12 ~0

Interval = 12 “semantic units” (units of meaning)

Ratio Variables

• Have identity, magnitude and interval.

• And since they have a true zero, they can be expressed as ratios of each other.

• They are true numbers.

• All mathematical properties apply.

• The represent score data.



1:45

1:51

1:52

2:49

The race started at 1:30 P.M.



1:45

1:51

1:52

2:49

The race started at 1:30 P.M.

Brad is 58.23% faster than Mitch

Ratio

How much time did you spend participating in each of these activities? (Please write in the number of hours for each activity in the spaces below)

I SPENT ______ HOURS HIKINGI SPENT ______ HOURS FISHINGI SPENT ______ HOURS PICNICKINGI SPENT ______ HOURS BOATINGI SPENT ______ HOURS SWIMMING

LEVEL OF MEASUREMENT

NOMINAL ORDINAL INTERVAL RATIO

EXAMPLES Names of activities, locations,

gender

Ranks, preferences

Attitude scales, Length of stay, income, age

PROPERTIES Identity (equivalence)

Identity, magnitude (relativity)

Identity, magnitude,

equal intervals

Identity, magnitude,

equal intervals, true zero

MATHEMATICAL OPERATIONS

Count (frequency)

Rank order Rank order, add, subtract,

average

Rank order, add, subtract,

average, multiply, divide

TYPE OF DATA Nominal Ranks Scale Scores

TYPES OF COMPARISONS

A is not equal/equal to

B

A is less than/greater

than

A is three units more/less than

B

A is twice as large/small as B

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MEASUREMENT - University of Idaho of...LEVEL OF MEASUREMENT NOMINAL ORDINAL INTERVAL RATIO EXAMPLES Names of activities, locations, gender Ranks, preferences Attitude scales, Length