Is the Data Scaled, Ordinal, or Nominal Proportional?

This presentation will assist you in determining if the data associated with the problem you are working on

This presentation will assist you in determining if the data associated with the problem you are working on

Participant Score

A 10

B 11

C 12

D 12

E 12

F 13

G 14

This presentation will assist you in determining if the data associated with the problem you are working on is:


Scaled


Scaled

Ordinal


Scaled

Ordinal

Nominal Proportional

First, a little background

With inferential statistics you will use either parametric or nonparametric methods.

What is a parametric method?

Parametric methods use story telling tools like center (what is the average height?), spread (how big is the difference between the shortest and tallest person?), or association (what is the relationship between height and weight?) in a sample to generalize to a population.

Parametric methods use story telling tools like center (what is the relationship between height and weight?) in a sample to generalize to a population.

Parametric methods use story telling tools like center (e.g., what is the average height?), spread (how big is the difference between the shortest and tallest person?), or association (what is the relationship between height and weight?) in a sample to generalize to a population.

Parametric methods use story telling tools like center (what is the average height?), spread (e.g., how big is the difference between the shortest and tallest person?), or association (what is the relationship between height and weight?) in a sample to generalize to a population.

Parametric methods use story telling tools like center (what is the average height?), spread (how big is the difference between the shortest and tallest person?), or association (e.g., what is the relationship between height and weight?). in a sample to generalize to a population.

Parametric methods use story telling tools like center (what is the average height?), spread (how big is the difference between the shortest and tallest person?), or association (e.g., what is the relationship between height and weight?) in a sample to generalize to a population.

Parametric methods use these story telling tools (center, spread, association) in a sample

Parametric methods use these story telling tools (center, spread, association) in a sample

SAMPLE

Parametric methods use these story telling tools (center, spread, association) in a sampleto generalize to

SAMPLE

Parametric methods use these story telling tools (center, spread, association) in a sample to generalize to

SAMPLEgeneralize to

Parametric methods use these story telling tools (center, spread, association) in a sample to generalize to a population.

SAMPLEgeneralize to

Parametric methods use these story telling tools (center, spread, association) in a sample to generalize to a population.

SAMPLEgeneralize to

POPULATION

We ask . . .

We ask . . .

what is the probability that what's happening in a sample,

We ask . . .

what is the probability that what's happening in a sample,

SAMPLE:center, spread,

association

We ask . . .

what is the probability that what's happening in a sample, is happening in


association

We ask . . .

what is the probability that what's happening in a sample, is happening in a population.


association

We ask . . .

what is the probability that what's happening in a sample, is happening in a population.


association

POPULATION: center, spread, association

To make that kind of leap (from sample to population) requires that certain conditions are met.

To make that kind of leap (from sample to population) requires that certain conditions are met.

Conditions or assumptions that must be met

These are called parametric CONDITIONS or ASSUMPTIONS

The first condition is that the data be scaled

What is scaled data?


Note – scaled data has two subcategories (1) interval data (no zero point but equal

intervals) and (2) ratio data (a zero point and equal

intervals)


For the purposes of this presentation we will not discuss these further but just focus on both as scaled data.


Participant Score

A 10

B 11

C 12

D 12

E 12

F 13

G 14

Scaled data is data that has a couple of attributes.

We will describe those attributes with illustrations from a scaled variable:

We will describe those attributes with illustrations from a scaled variable: Temperature.

Attribute #1 – scaled data assume a quantity.

Meaning that 2 is more than 3 and 4 is more than 3 and 20 is less than 30, etc.

For example: 40 degrees is more than 30 degrees. 110 degrees isless than 120 degrees.


Meaning that 3 is more than 2 and 4 is more than

3 and 20 is less than 30, etc.





100 degrees is more than 40 degrees




60 degrees is less than 80 degrees




60 degrees is less than 80 degrees

If the data represents varying amounts then this is the first requirement for data to be

considered - scaled.

Attribute #2

Attribute #2 – scaled data has equal intervals or each unit has the same value.


Meaning the distance between 1 and 2 is the same as

the distance between 14 and 15 or 1,123 and

1,124.


Meaning the distance between 1 and 2 is the same as

the distance between 14 and 15 or 1,123 and

1,124. They all have a unit value of 1 between them.

In our temperature example:

40o - 41o

100o - 101o

70o – 71o

Each set of readings are the same distance

apart: 1o

40o - 41o

100o - 101o

70o – 71o


apart: 1o

The point here is that each unit value is the same across the

entire scale of numbers

40o - 41o

100o - 101o

70o – 71o


apart: 1o

Note, this is not the case with ordinal numbers where 1st place in a marathon might be 2:03 hours, 2nd place 2:05 and 3rd place 2:43.

They are not equally spaced!

What does a scaled data set look like?

Here are some examples:

Height

HeightPersons HeightCarly 5’ 3”Celeste 5’ 6”Donald 6’ 3”Dunbar 6’ 1”Ernesta 5’ 4”

Height

Attribute #1: We are dealing with amounts

Persons HeightCarly 5’ 3”Celeste 5’ 6”Donald 6’ 3”Dunbar 6’ 1”Ernesta 5’ 4”

HeightPersons HeightCarly 5’ 3”Celeste 5’ 6”Donald 6’ 3”Dunbar 6’ 1”Ernesta 5’ 4”

Attribute #2: There are equal intervals across the scale. One inch is the same value regardless of where you are on the scale.

Intelligence Quotient (IQ)

Intelligence Quotient (IQ)Persons Height IQCarly 5’ 3” 120Celeste 5’ 6” 100Donald 6’ 3” 95Dunbar 6’ 1” 121Ernesta 5’ 4” 103


Attribute #2: Supposedly there are equal intervals across this scale. A little harder to prove but most researchers go with it.

Pole Vaulting Placement

Pole Vaulting PlacementPersons Height IQ PVPCarly 5’ 3” 120 3rd

Celeste 5’ 6” 100 5th

Donald 6’ 3” 95 1st

Dunbar 6’ 1” 121 4th

Ernesta 5’ 4” 103 2nd






Attribute #2: We are NOT dealing with equal intervals. 1st place (16’0”) and 2nd place (15’8”) are not the same distance from one another as 2nd Place and 3rd place (12’2”).

Based on this explanation is your data scaled?

If your data is scaled as shown in these examples, select

If your data is scaled as shown in these examples, select

Scaled

Ordinal


We have now demonstrated scaled data and given you a brief introduction to ordinal data.

Once again, ordinal data is data that is ranked:

In other words,

Ordinal scales use numbers to represent relative amounts of an attribute.


1st Place16’ 3”


1st Place16’ 3”

2nd Place16’ 1”


1st Place16’ 3”

2nd Place16’ 1”

3rd Place15’ 2”


3rd Place15’ 2”

2nd Place16’ 1”

1st Place16’ 3”

Relative Amounts of Bar Height

Example of relative amounts of authority

Corporal2

Sargent3

Lieutenant4

Major5

Colonel6

General7

Private1


Corporal2

Sargent3

Lieutenant4

Major5

Colonel6

General7

Private1

Notice how we are dealing with amounts of authority


Corporal2

Sargent3

Lieutenant4

Major5

Colonel6

General7

Private1

But,


Corporal2

Sargent3

Lieutenant4

Major5

Colonel6

General7

Private1

But, they are not equally spaced.


You can tell if you have an ordinal data set when the data is described as ranks.

You can tell if you have an ordinal data set when the data is described as ranks.

Persons Pole Vault Placement

Carly 3rd

Celeste 5th

Donald 1st

Dunbar 4th

Ernesta 2nd

Or in percentiles

Or in percentiles

Persons ACT Percentile

RankCarly 55%Celeste 23%Donald 97%Dunbar 37%Ernesta 78%

If your data is ranked as shown in these examples, select

If your data is ranked as shown in these examples, select

Scaled

Ordinal


Finally, let’s see what data looks like when it is nominal proportional:

Nominal data is different from scaled or ordinal,

Nominal data is different from scaled or ordinal, because they do not deal with amounts

Nominal data is different from scaled or ordinal, because they do not deal with amounts nor equal intervals.

For example,

Nationality is a variable that does not have amounts nor equal intervals.

1 = Canadian

2 = American

1 = Canadian

2 = American

Being Canadian is not numerically or quantitatively more than being

American

1 = Canadian

2 = American

The numbers 1 and 2 do not represent amounts. They are just a way to distinguish the two groups numerically.

We could have just as easily used 1s for Americans and 2s for Canadians


1 = Canadian

2 = American


1 = American

2 = Canadian

Other examples:

Religious Affiliation

Religious Affiliation1 - Buddhist

2 - Catholic

3 - Jew

4 - Mormon

5 - Muslim

6 - Protestant

Gender

Gender1 - Male

2 - Female

Preference

Preference:

1. People who prefer chocolate ice-cream

Preference:

1. People who prefer chocolate ice-cream

2. People who dislike chocolate ice-cream

Pass/Fail

Pass/Fail

1. Those who passed the test

Pass/Fail

1. Those who passed the test

2. Those who failed the test

The word “Nom” in “nominal” means “name”.

The word “Nom” in nominal means “name”. Essentially we are using data to name, identify, distinguish, classify or categorize.

Other names for nominal data are categorical or frequency data.

Here is how the nominal data would look like in a data set:


PersonsCarlyCelesteDonaldDunbarErnesta


Persons GenderCarlyCelesteDonaldDunbarErnesta


Persons GenderCarlyCelesteDonaldDunbarErnesta

1 = Male2 = Female


Persons GenderCarly 2Celeste 2Donald 1Dunbar 1Ernesta 2

1 = Male2 = Female

Persons Gender PreferenceCarly 2Celeste 2Donald 1Dunbar 1Ernesta 2

Persons Gender PreferenceCarly 2Celeste 2Donald 1Dunbar 1Ernesta 2

1 = Like ice-cream2 = Don’t like ice-cream

Persons Gender PreferenceCarly 2 1Celeste 2 1Donald 1 1Dunbar 1 2Ernesta 2 2

1 = Like ice-cream2 = Don’t like ice-cream


Religion


Religion

1 - Buddhist2 - Catholic3 - Jew4 - Mormon5 - Muslim6 - Protestant


Religion42561

1 - Buddhist2 - Catholic3 - Jew4 - Mormon5 - Muslim6 - Protestant

Now that we know what nominal data is,

What is nominal proportional data?

What is nominal proportional data?

Scaled

Ordinal


Nominal proportional data is simply the proportion of individuals who are in one category as opposed to another.

For example,

In the data set below:


3 out of 5 persons are female


Or 60% are female


That means 2 out of 5 are male


Or 40% are male

In such cases you may not see a data set,

you may just see a question like this:

A claim is made that four out of five veterans (or 80%) are supportive of the current conflict. After you sample five veterans you find that three out of five (or 60%) are supportive. In terms of statistical significance does this result support or invalidate this claim?

If you were to put these results in a data set it would look like this:

VeteransABCDE

Veterans SupportiveABCDE

Veterans SupportiveABCDE

1 = supportive2 = not supportive

Veterans SupportiveA 2B 2C 1D 1E 1


Veterans SupportiveA 2B 2C 1D 1E 1


If the question is stated in terms of percentages (e.g., 60% of veterans were supportive), then that percentage is nominal proportional data

If your data is nominal proportional as shown in these examples, select

If your data is nominal proportional as shown in these examples, select

Scaled

Ordinal


That concludes this explanation of scaled, ordinal and nominal proportional data.

Is the Data Scaled, Ordinal, or Nominal Proportional?

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