The document discusses Spearman's Rho, a statistical test used to determine the relationship between two variables when at least one is ordinal. It provides examples of writing the null hypothesis for Spearman's Rho. The null hypothesis states that there is no statistically significant relationship between the variables being tested. Two examples are provided: one testing the relationship between team rankings and average point output, and one testing the relationship between states' poverty rankings and the number of charter schools per capita.

1. Null-hypothesis for a
Spearman’s Rho
Conceptual Explanation

2. With hypothesis testing we are setting up a null-hypothesis
–

3. With hypothesis testing we are setting up a null-hypothesis
– the probability that there is no effect or
relationship –

4. With hypothesis testing we are setting up a null-hypothesis
– the probability that there is no effect or
relationship – and then we collect evidence that leads
us to either accept or reject that null hypothesis.

5. As you may recall, a Spearman’s Rho is a value that
makes it possible to statistically test the relationship
between two variables, with at least one of those
variables being rank ordered (ordinal).

6. As you may recall, a Spearman’s Rho is a value that
makes it possible to statistically test the relationship
between two variables, with at least one of those
variables being rank ordered (ordinal).
Person Time in
biking phase
Place in
running phase
A 4.5 hours 2nd
B 5.5 hours 1st
C 6.0 hours 3rd
D 6.3 hours 4th
E 7.0 hours 5th

7. As you may recall, a Spearman’s Rho is a value that
makes it possible to statistically test the relationship
between two variables, with at least one of those
variables being rank ordered (ordinal).
Person Time in
biking phase
Place in
running phase
A 4.5 hours 2nd
B 5.5 hours 1st
C 6.0 hours 3rd
D 6.3 hours 4th
E 7.0 hours 5th

8. Here is a template for writing a null-hypothesis for a
Spearman’s Rho:

9. Here is a template for writing a null-hypothesis for a
Pearson Correlation:
There is no statistically significant relationship between
the [insert variable] and [insert variable].

10. Example 1

11. Problem
You have been asked to determine the relationship
between the ranking of teams and their average
offensive output in terms of points.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert variable] and [insert variable].

12. Problem
You have been asked to determine the relationship
between the ranking of teams and their average
offensive output in terms of points.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
School Top 10
Brown State 1
Brigham Young Academy 2
Alaska Tech 3
Northern Rhode Island U 4
Western Utah U 5
Bluegrass State 6
Etc. Etc.
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert variable] and [insert variable].

13. Problem
You have been asked to determine the relationship
between the ranking of teams and their average
offensive output in terms of points.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
School Top 10
Brown State 1
Brigham Young Academy 2
Alaska Tech 3
Northern Rhode Island U 4
Western Utah U 5
Bluegrass State 6
Etc. Etc.
Points
33.2
31.3
29.5
35.9
27.3
24.1
Etc.
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert variable] and [insert variable].

14. Problem
You have been asked to determine the relationship
between the ranking of teams and their average
offensive output in terms of points.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert variable] and [insert variable].

15. Problem
You have been asked to determine the relationship
between the ranking of teams and their average
offensive output in terms of points.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert variable] and [insert variable].

16. Problem
You have been asked to determine the relationship
between the ranking of teams and their average
offensive output in terms of points.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert variable] and [insert variable].

17. Problem
You have been asked to determine the relationship
between the ranking of teams and their average
offensive output in terms of points.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
[insert variable] and [insert variable].

18. Problem
You have been asked to determine the relationship
between the ranking of teams and their average
offensive output in terms of points.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
[insert variable] and [insert variable].

19. Problem
You have been asked to determine the relationship
between the ranking of teams and their average
offensive output in terms of points.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
team rankings and [insert variable].

20. Problem
You have been asked to determine the relationship
between the ranking of teams and their average
offensive output in terms of points.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
team rankings and [insert variable].
s

21. Problem
You have been asked to determine the relationship
between the ranking of teams and their average
offensive output in terms of points.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
team rankings and the average point output.

22. Null-hypothesis for this Problem
There is no statistically significant relationship between
team rankings and the average point output.

23. Example 2

24. Problem
You have been asked to determine if there is a
relationship between states’ poverty rankings and the
number charter schools per capita.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert variable] and [insert variable].

25. Problem
You have been asked to determine if there is a
relationship between states’ poverty rankings and the
number charter schools per capita.
Template for a Spearman's Rho Null-Hypothesis
States Poverty Ranking Charter Schools per
There is no statistically significant relationship capita (10,000 people)
between
the [insert variable] and [insert variable].
Washington 50th 6.2
Massachusetts 49th 5.9
Connecticut 48th 5.4
Oregon 47th 5.1
Minnesota 48th 4.9
Etc. Etc. Etc
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert variable] and [insert variable].

26. Problem
You have been asked to determine if there is an inverse
relationship between states' poverty rankingsand the
number charter schools per capita.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert variable] and [insert variable].

27. Problem
You have been asked to determine if there is an inverse
relationship between states' poverty rankingsand the
number charter schools per capita.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert variable] and [insert variable].

28. Problem
You have been asked to determine if there is an inverse
relationship between states' poverty rankingsand the
number charter schools per capita.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert variable] and [insert variable].

29. Problem
You have been asked to determine if there is an inverse
relationship between states' poverty rankingsand the
number charter schools per capita.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
[insert variable] and [insert variable].

30. Problem
You have been asked to determine if there is an inverse
relationship between states' poverty rankingsand the
number charter schools per capita.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
[insert variable] and [insert variable].

31. Problem
You have been asked to determine if there is an inverse
relationship between states' poverty rankingsand the
number charter schools per capita.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
states' poverty rankingsand [insert variable].

32. Problem
You have been asked to determine if there is an inverse
relationship between states' poverty rankingsand the
number charter schools per capita.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
states' poverty rankingsand [insert variable].

33. Problem
You have been asked to determine if there is an inverse
relationship between states' poverty rankingsand the
number charter schools per capita.
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship between
the [insert variable] and [insert variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
states' poverty rankingsand the # of charter schools per capita.

34. Null-hypothesis for this Problem
There is no statistically significant relationship between
states' poverty rankings and the number of charter
schools per capita.