Null hypothesis for Kendall's Tau (Independence)

1. Null-hypothesis for a
Kendall’s Tau
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 Kendall’s Tau is like a Pearson
correlation but is used with Rank-ordered data.

6. As you may recall, a Kendall’s Tau 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 Kendall’s Tau is like a Pearson
correlation but is used with Rank-ordered data. It
differs from a Spearman’s Rho in that it handles tied
rankings whereas Spearman’s does not.

8. As you may recall, a Kendall’s Tau is like a Pearson
correlation but is used with Rank-ordered data. It
differs from a Spearman’s Rho in that it handles tied
rankings whereas Spearman’s does not.
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

9. Here is a template for writing a null-hypothesis for a
Kendall’s Tau:

10. Here is a template for writing a null-hypothesis for a
Kendall’s Tau:
There is no statistically significant relationship between
the median [insert variable] and the median [insert
variable].

11. Here is a template for writing a null-hypothesis for a
Kendall’s Tau :
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 Kendall’s Tau
would be used.

12. Here is a template for writing a null-hypothesis for a
Kendall’s Tau:
There is no statistically significant relationship between
the median [insert variable] and the median [insert
variable].
You may remember that when rank-ordered
variable is being compared with
another variable the median is used.

13. Here is a template for writing a null-hypothesis for a
Kendall’s Tau :
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.

14. Example 1

15. 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.

16. 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.

17. 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.

18. 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

19. 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
Note the
tied
rankings

20. 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
Note the
tied
rankings

21. Individuals Rank order for
Biking Event
Rank order for
Running Event
Bob 1st 1st
Conrad 2nd Note the
1st
Dallen 2nd tied
2nd
rankings
Ernie 3rd 3rd
Fen 4th 4th
Gaston 5th 4th

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

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

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

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

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

27. Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship
between the median biking event rankings and
the median running event rankings.