Is this a parametric or non-parametric question of Independence?

When working with an Independence-oriented problem like this:

When working with an Independence-oriented problem like this:

To what degree is police-profiling independent of race?

When working with an Independence-oriented problem like this:

To what degree is police-profiling independent of race?

Ethnicity of Person Arrested1 = white, 2 = non-white

Profiled 1 = Yes, 2 = No

2 12 21 2

It is important to determine which method is appropriate to use:

It is important to determine which method is appropriate to use:

Parametric

It is important to determine which method is appropriate to use:

Parametric

Non-Parametric

As a reminder,

Parametric methods are used when we examine sample statistics as a representation of population parameters

Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is normal and the data is scaled.

Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is normal and the data is scaled.

Normal Distribution

Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is normal and the data is scaled.

Scaled Data

Non-Parametric methods are used when we examine sample statistics

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data is ordinal / nominal.

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data is ordinal / nominal.

Skewed Distributions

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data is ordinal / nominal.

Skewed Distributions

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data is ordinal / nominal.

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data is ordinal / nominal.

Or ranked data like percentiles %

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data is ordinal / nominal.

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data is ordinal / nominal.

1 = American

2 = Canadian

Important Note

For a parametric method to be used BOTH the data must be scaled and the distribution normal

Important Note

If either the data is ordinal OR the distribution is skewed, non-parametric methods should be used.

For a parametric method to be used BOTH the data must be scaled and the distribution normal

Important Note

If either the data is ordinal OR the distribution is skewed, non-parametric methods should be used.

For a parametric method to be used the data must be scaled AND the distribution must be normal.

Here is an example of a parametric “independence” question:

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

West Artic Country # of persons from US contracting “X” from a

person from this country

# of flights per year from this

countryA 2 32

B 3 38

C 10 71

D 11 92

E 17 103

F 19 118

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

West Artic Country # of persons from US contracting “X” from a

person from this country

# of flights per year from this

countryA 2 32

B 3 38

C 10 71

D 11 92

E 17 103

F 19 118

The number contracting “X” can range from 0 to

millions and the intervals are equal.

Therefore the data in this column is scaled.

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

West Artic Country # of persons from US contracting “X” from a

person from this country

# of flights per year from this

countryA 2 32

B 3 38

C 10 71

D 11 92

E 17 103

F 19 118

The number of flights can range from 0 to hundreds and the

intervals are equal. Therefore the data in

this column is also scaled.

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

West Artic Country # of persons from US contracting “X” from a

person from this country

# of flights per year from this

countryA 2 32

B 3 38

C 10 71

D 11 92

E 17 103

F 19 118

The skew for both of these distributions is

way below the + or – 2.0 cut off.

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

West Artic Country # of persons from US contracting “X” from a

person from this country

# of flights per year from this

countryA 2 32

B 3 38

C 10 71

D 11 92

E 17 103

F 19 118

Because the data is scaled and the

distribution is normal, this is a parametric test

Here is an example of a non-parametric “independence” question:

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

West Artic Country # of persons from US contracting “X” from a

person from this country

Rank of # of flights per year

from this countryA 2 6th

B 3 5th

C 10 4th

D 11 3rd

E 17 2nd

F 19 1st

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

West Artic Country # of persons from US contracting “X” from a

person from this country

Rank of # of flights per year

from this countryA 2 6th

B 3 5th

C 10 4th

D 11 3rd

E 17 2nd

F 19 1st

The number contracting “X” can range from 0 to

millions and the intervals are equal.

Therefore the data in this column is scaled.

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

West Artic Country # of persons from US contracting “X” from a

person from this country

Rank of # of flights per year

from this countryA 2 6th

B 3 5th

C 10 4th

D 11 3rd

E 17 2nd

F 19 1st

The number of flight ranks is ordinal or rank

ordered in nature.

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

West Artic Country # of persons from US contracting “X” from a

person from this country

Rank of # of flights per year

from this countryA 2 6th

B 3 5th

C 10 4th

D 11 3rd

E 17 2nd

F 19 1st

The skew for both of these distributions is way below the + or –

2.0 cut off.

Government officials have claimed that persons in the U.S. contracting Contagious Disease “X” from individuals from certain West Artic Countries is independent of the number of flights coming in from those countries.

West Artic Country # of persons from US contracting “X” from a

person from this country

Rank of # of flights per year

from this countryA 2 6th

B 3 5th

C 10 4th

D 11 3rd

E 17 2nd

F 19 1st

Even though the distributions are

normal, because the data for one of the data

sets is ordinal / rank ordered we would use a

nonparametric test

Next example -

Government officials claim that the number of illegal immigrants is independent of any one Central American country.

Government officials claim that the number of illegal immigrants is independent of any one Central American country.

Central American Country1 = Guatemala, 2 = Honduras, 3 = Nicaragua, 4 = El

Salvador 5 = Costa Rica, 6 = Panama

# of illegal immigrants from that country

1 2,000

2 3,000

3 10,000

4 11,000

5 17,000

6 19,000

Government officials claim that the number of illegal immigrants is independent of any one Central American country.

Central American Country1 = Guatemala, 2 = Honduras, 3 = Nicaragua, 4 = El

Salvador 5 = Costa Rica, 6 = Panama

# of illegal immigrants from that country

1 2,000

2 3,000

3 10,000

4 11,000

5 17,000

6 19,000

Government officials claim that the number of illegal immigrants is independent of any one Central American country.

Central American Country1 = Guatemala, 2 = Honduras, 3 = Nicaragua, 4 = El

Salvador 5 = Costa Rica, 6 = Panama

# of illegal immigrants from that country

1 2,000

2 3,000

3 10,000

4 11,000

5 17,000

6 19,000

Because these numbers are used as identifiers and do not signify an amount, the data is

considered NOMINAL

Government officials claim that the number of illegal immigrants is independent of any one Central American country.

Central American Country1 = Guatemala, 2 = Honduras, 3 = Nicaragua, 4 = El

Salvador 5 = Costa Rica, 6 = Panama

# of illegal immigrants from that country

1 2,000

2 3,000

3 10,000

4 11,000

5 17,000

6 19,000

The number of illegal aliens can range from 0 to thousands and thus

constitute equal intervals. Therefore this

data is SCALED.

Government officials claim that the number of illegal immigrants is independent of any one Central American country.

Central American Country1 = Guatemala, 2 = Honduras, 3 = Nicaragua, 4 = El

Salvador 5 = Costa Rica, 6 = Panama

# of illegal immigrants from that country

1 2,000

2 3,000

3 10,000

4 11,000

5 17,000

6 19,000

The skew for both of these distributions is way below the + or –

2.0 cut off.

Government officials claim that the number of illegal immigrants is independent of any one Central American country.

Central American Country1 = Guatemala, 2 = Honduras, 3 = Nicaragua, 4 = El

Salvador 5 = Costa Rica, 6 = Panama

# of illegal immigrants from that country

1 2,000

2 3,000

3 10,000

4 11,000

5 17,000

6 19,000

Even though the distributions are

NORMAL, because the data of one of the data sets is NOMINAL, we

will use a nonparametric method.

Note – if needed click on the link below the link to this presentation to receive instruction as to how to assess the skew of your data set.