Null Hypothesis for Spearman's Rho (Independence)

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 like a Pearson
correlation but is used with Rank-ordered data.

6. As you may recall, a Spearman's Rho is like a Pearson
correlation but is used with Rank-ordered data.
Individuals Rank order for
Biking Event
Rank order for
Running Event
Bob 1st 1st
Conrad 2nd 1st
Dallen 2nd 2nd
Ernie 3rd 3rd
Fen 4th 4th
Gaston 5th 4th

7. As you may recall, a Spearman's Rho is like a Pearson
Correlation but is used with Rank-ordered data. It,
however, does not handle tied rankings as does a
Kendall’s Tau.

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
Spearman's Rho:
There is no statistically significant relationship between
the median [insert variable] and the median [insert
variable].

10. Here is a template for writing a null-hypothesis for a
Spearman's Rho:
There is no statistically significant relationship between
the median [insert variable] and the median [insert
variable].
Note – as long as both or at least
one of the variables has rank-ordered
ties then a Spearman's
Rho would be used.

11. Here is a template for writing a null-hypothesis for a
Spearman's Rho:
There is no statistically significant relationship between
the median [insert variable] and the median [insert
variable].
Also, the null-hypothesis is the aim of a
research question that focuses on the
independence between rank ordered
and another variable.

12. Example 1

13. An iron man competition consists of three consecutive
events: Biking 110 miles, Swimming 2.5 miles and
Running 26.2 miles.
Researchers are interested if the rank ordered results
from the biking and the running events are
independent of one another to show how diverse the
athletes in the completion are.
Here is the data for 10 individuals who competed.

14. An iron man competition consists of three consecutive
events: Biking 110 miles, Swimming 2.5 miles and
Running 26.2 miles.
Race organizers are interested in showing the diversity
in athlete abilities by determining if the rank ordered
results from the biking and the running events are
independent of one another.
Here is the data for 10 individuals who competed.

15. An iron man competition consists of three consecutive
events: Biking 110 miles, Swimming 2.5 miles and
Running 26.2 miles.
Race organizers are interested in showing the diversity
in athlete abilities by determining if the rank ordered
results from the biking and the running events are
independent of one another.
Here is the data for 10 individuals who competed.

16. Individuals Rank order for
Biking Event
Rank order for
Running Event
Bob 1st 1st
Conrad 2nd 3rd
Dallen 3rd 2nd
Ernie 4rd 4th
Fen 5th 5th
Gaston 6th 6th

17. Individuals Rank order for
Biking Event
Rank order for
Running Event
Bob 1st 1st
Conrad 2nd 3rd
Dallen 3rd 2nd
Ernie 4rd 4th
Fen 5th 5th
Gaston 6th 6th
Note that
there are
NO TIES

18. Problem
Are the rank ordered results from the biking and
the running events are independent of one
another?
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship
between the [insert variable] and [insert
variable].

19. Problem
Are the rank ordered results from the biking and
the running events are independent of one
another?
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship
between the median [insert variable] and the
median [insert variable].

20. Problem
Are the rank ordered results from the biking
and the running events are independent of one
another?
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship
between the median [insert variable] and the
median [insert variable].

21. Problem
Are the rank ordered results from the biking
and the running events are independent of one
another?
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship
between the median [biking even rankings] and
the median [insert variable].

22. Problem
Are the rank ordered results from the biking and
the running events are independent of one
another?
Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship
between the median [biking event rankings]
and the median [running event rankings].

23. Template for a Spearman's Rho Null-Hypothesis
There is no statistically significant relationship
between the median biking event rankings and
the median running event rankings.