Is this a parametric or non- parametric question of Independence?
Jun 20, 2015
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.