Is this a parametric or non-parametric question?

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

2. When working with an Independence-oriented
problem like this:

3. When working with an Independence-oriented
problem like this:
To what degree is police-profiling independent of race?

4. When working with an Independence-oriented
problem like this:
To what degree is police-profiling independent of race?
Ethnicity of Person Arrested
1 = white, 2 = non-white
Profiled
1 = Yes, 2 = No
2 1
2 2
1 2

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

6. It is important to determine which method is
appropriate to use:
Parametric

7. It is important to determine which method is
appropriate to use:
Parametric
Non-Parametric

8. As a reminder,

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

10. 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.

11. 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

12. 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

13. Non-Parametric methods are used when we
examine sample statistics

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

15. 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.

16. 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

17. 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

18. 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.

19. 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 %

20. 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.

21. 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

22. Important Note
For a parametric method to be used BOTH the
data must be scaled and the distribution
normal

23. 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

24. 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.

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

26. 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.

27. 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
country
A 2 32
B 3 38
C 10 71
D 11 92
E 17 103
F 19 118

28. 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
country
The number contracting
“X” can range from 0 to
A 2 32
B 3 38
C 10 71
D 11 92
E 17 103
F 19 118
millions and the
intervals are equal.
Therefore the data in
this column is scaled.

29. 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
country
The number of flights
can range from 0 to
hundreds and the
intervals are equal.
Therefore the data in
this column is also
A 2 32
B 3 38
C 10 71
D 11 92
E scaled.
17 103
F 19 118

30. Government officials have claimed that persons in
the U.S. contracting Contagious The skew Disease for both of
“X” from
individuals from certain West these Artic distributions Countries is
is
way below the
independent of the number of + or flights – 2.0 cut off.
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
country
A 2 32
B 3 38
C 10 71
D 11 92
E 17 103
F 19 118

31. 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
country
A 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

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

33. 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.

34. 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 country
A 2 6th
B 3 5th
C 10 4th
D 11 3rd
E 17 2nd
F 19 1st

35. 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 country
The number contracting
“X” can range from 0 to
A 2 6th
B 3 5th
C 10 4th
D 11 3rd
E 17 2nd
F 19 1st
millions and the
intervals are equal.
Therefore the data in
this column is scaled.

36. 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 country
A 2 6th
B The number of flight
3 5th
C ranks is ordinal or rank
10 4th
ordered in nature.
D 11 3rd
E 17 2nd
F 19 1st

37. Government officials have claimed that persons in
the U.S. contracting Contagious The skew Disease for both of
“X” from
individuals from certain West these Artic distributions Countries is
is
way below the + or –
independent of the number of 2.0 flights cut off.
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 country
A 2 6th
B 3 5th
C 10 4th
D 11 3rd
E 17 2nd
F 19 1st

38. 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 country
A 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

39. Next example -

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

41. Government officials claim that the number of
illegal immigrants is independent of any one Central
American country.
Central American Country
1 = 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

42. Government officials claim that the number of
illegal immigrants is independent of any one Central
American country.
Central American Country
1 = 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

43. Government officials claim that the number of
illegal immigrants is independent of any one Central
American country.
Central American Country
1 = 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

44. Government officials claim that the number of
illegal immigrants is independent of any one Central
American country.
Central American Country
1 = 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.

45. Government officials claim that the number of
illegal immigrants is independent of any one Central
American country.
Central American Country
The skew for both of
these distributions is
way below the + or –
2.0 cut off.
1 = 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

46. Government officials claim that the number of
illegal immigrants is independent of any one Central
American country.
Central American Country
1 = Guatemala, 2 = Honduras, 3 = Nicaragua, 4 = El
Salvador 5 = Costa Rica, 6 = Panama
# of illegal
immigrants
from that
country
1 2,000
Even though the
2 distributions are
3,000
3 NORMAL, because the
10,000
data of one of the data
4 sets is NOMINAL, we
11,000
5 will use a
17,000
6 nonparametric method.
19,000

47. 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.