The document discusses Kendall's Tau, a nonparametric test used to measure the strength of association between two ranked variables that may contain ties. It provides a template for writing the null hypothesis for Kendall's Tau, which states that there is no statistically significant relationship between the rank-ordered variables. Two examples applying this template to problems investigating relationships between athletic performance variables are included.

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 [insert rank-ordered variable with ties] and [insert
variable rank-ordered variable with or without ties].

11. Here is a template for writing a null-hypothesis for a
Kendall’s Tau:
There is no statistically significant relationship between
the [insert rank-ordered variable with ties] and [insert
variable rank-ordered variable with or without ties].
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. 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 in the
relationship between the rank ordered results from the
biking and the running events. 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. Researchers are interested in the
relationship between the rank ordered results from the
biking and the running events. Here is the data for 10
individuals who competed.
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

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 in the
relationship between the rank ordered results from the
biking and the running events. Here is the data for 10
individuals who competed.
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

16. Problem
Researchers are interested in the relationship between
the rank ordered results from the biking and the
running events.
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between
the [insert independent variable] and [insert
dependent variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert independent variable] and [insert
dependent variable].

17. Problem
Researchers are interested in the relationship between
the rank ordered results from the biking and the
running events.
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between
the [insert independent variable] and [insert
dependent variable].
Null-hypothesis for this Problem
There is no statistically significant relationship between
the [insert independent variable] and [insert
dependent variable].

18. Problem
Researchers are interested in the relationship between the
rank ordered results from the biking and the running
events.
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data with or without ties].
Null-hypothesis for this Problem
There is no statistically significant relationship between the
[insert independent variable] and [insert dependent
variable].

19. Problem
Researchers are interested in the relationship between the
rank ordered results from the biking and the running
events.
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data with or without ties].
Null-hypothesis for this Problem
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data with or without ties].
s

20. Problem
Researchers are interested in the relationship between the
rank ordered results from the biking and the running
events.
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
Null-hypothesis for this Problem
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data with or without ties].
s

21. Problem
Researchers are interested in the relationship between the
rank ordered results from the biking and the running
events.
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
Null-hypothesis for this Problem
There is no statistically significant relationship between the
placements in biking and [insert variable for ranked
ordered data with or without ties].
s

22. Problem
Researchers are interested in the relationship between the
rank ordered results from the biking and the running
events.
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
Null-hypothesis for this Problem
There is no statistically significant relationship between the
placements in biking and [insert variable for ranked
ordered data with or without ties].
s

23. Problem
Researchers are interested in the relationship between the
rank ordered results from the biking and the running
events.
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
Null-hypothesis for this Problem
There is no statistically significant relationship between the
placements in biking and running events.
s

24. Null-hypothesis for this Problem
There is no statistically significant relationship between
the biking and running events.

25. Example 2

26. A researcher wishes to determine if a significant
relationship exists between last years college football
division 1 rankings (3 ties) and the rankings of coaches
salaries (2 ties).

27. A researcher wishes to determine if a significant
relationship exists between last years college football
division 1 rankings (3 ties) and the rankings of coaches
salaries (2 ties).
&

28. Problem
A researcher wishes to determine if a significant
relationship exists between last years college football
division 1 rankings and the rankings of coaches salaries (2
ties).
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
s

29. Problem
A researcher wishes to determine if a significant
relationship exists between last years college football
division 1 rankings and the rankings of coaches salaries (2
ties).
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
s

30. Problem
A researcher wishes to determine if a significant
relationship exists between last years college football
division 1 rankings and the rankings of coaches salaries (2
ties).
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
s

31. Problem
A researcher wishes to determine if a significant
relationship exists between last years college football
division 1 rankings and the rankings of coaches salaries (2
ties).
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
s

32. Problem
A researcher wishes to determine if a significant
relationship exists between last years college football
division 1 rankings and the rankings of coaches salaries (2
ties).
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
s

33. Problem
A researcher wishes to determine if a significant
relationship exists between last years college football
division 1 rankings and the rankings of coaches salaries (2
ties).
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
Null-Hypothesis
There is no statistically significant relationship between the
last years college football division 1 rankings and [insert
variable for ranked ordered data].
s

34. Problem
A researcher wishes to determine if a significant
relationship exists between last years college football
division 1 rankings and the rankings of coaches salaries (2
ties).
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
Null-Hypothesis
There is no statistically significant relationship between the
last years college football division 1 rankings and [insert
variable for ranked ordered data].
s

35. Problem
A researcher wishes to determine if a significant
relationship exists between last years college football
division 1 rankings and the rankings of coaches salaries (2
ties).
Template for a Kendall’s Tau Null-Hypothesis
There is no statistically significant relationship between the
[insert variable for rank ordered data with ties] and [insert
variable for ranked ordered data].
Null-Hypothesis
There is no statistically significant relationship between the
last years college football division 1 rankings and the
rankings of coaches salaries.
s

36. Null-hypothesis for this Problem
There is no statistically significant relationship between
the last years college football division 1 rankings and
the rankings of coaches salaries.