Null-hypothesis for a Kendall’s Tau

Conceptual Explanation

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

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

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.

As you may recall, a Kendall’s Tau is like a Pearson correlation but is used with Rank-ordered data.

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

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.

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

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

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].

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.

Example 1

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.

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

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

ProblemResearchers are interested in the relationship between the rank ordered results from the biking and the running events.

Template for a Kendall’s Tau Null-HypothesisThere is no statistically significant relationship between the [insert independent variable] and [insert dependent variable].

Null-hypothesis for this ProblemThere is no statistically significant relationship between the [insert independent variable] and [insert dependent variable].

ProblemResearchers are interested in the relationship between the rank ordered results from the biking and the running events.

Template for a Kendall’s Tau Null-HypothesisThere is no statistically significant relationship between the [insert independent variable] and [insert dependent variable].

Null-hypothesis for this ProblemThere is no statistically significant relationship between the [insert independent variable] and [insert dependent variable].

ProblemResearchers are interested in the relationship between the rank ordered results from the biking and the running events.

Template for a Kendall’s Tau Null-HypothesisThere 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 ProblemThere is no statistically significant relationship between the [insert independent variable] and [insert dependent variable].

ProblemResearchers are interested in the relationship between the rank ordered results from the biking and the running events.

Template for a Kendall’s Tau Null-HypothesisThere 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 ProblemThere 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

ProblemResearchers are interested in the relationship between the rank ordered results from the biking and the running events.

Template for a Kendall’s Tau Null-HypothesisThere 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 ProblemThere 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

ProblemResearchers are interested in the relationship between the rank ordered results from the biking and the running events.

Template for a Kendall’s Tau Null-HypothesisThere 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 ProblemThere is no statistically significant relationship between the placements in biking and [insert variable for ranked ordered data with or without ties].s

ProblemResearchers are interested in the relationship between the rank ordered results from the biking and the running events.

Template for a Kendall’s Tau Null-HypothesisThere 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 ProblemThere is no statistically significant relationship between the placements in biking and [insert variable for ranked ordered data with or without ties].s

ProblemResearchers are interested in the relationship between the rank ordered results from the biking and the running events.

Template for a Kendall’s Tau Null-HypothesisThere 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 ProblemThere is no statistically significant relationship between the placements in biking and running events.s

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

Example 2

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).

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).

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ProblemA 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-HypothesisThere 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

ProblemA 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-HypothesisThere 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

ProblemA 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-HypothesisThere 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

ProblemA 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-HypothesisThere is no statistically significant relationship between the [insert variable for rank ordered data with ties] and [insert variable for ranked ordered data].Null-HypothesisThere is no statistically significant relationship between the [insert variable for rank ordered data with ties] and [insert variable for ranked ordered data].s

ProblemA 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-HypothesisThere is no statistically significant relationship between the [insert variable for rank ordered data with ties] and [insert variable for ranked ordered data].Null-HypothesisThere is no statistically significant relationship between the [insert variable for rank ordered data with ties] and [insert variable for ranked ordered data].s

ProblemA 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-HypothesisThere is no statistically significant relationship between the [insert variable for rank ordered data with ties] and [insert variable for ranked ordered data].Null-HypothesisThere is no statistically significant relationship between the last years college football division 1 rankings and [insert variable for ranked ordered data].s

ProblemA 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-HypothesisThere is no statistically significant relationship between the [insert variable for rank ordered data with ties] and [insert variable for ranked ordered data].Null-HypothesisThere is no statistically significant relationship between the last years college football division 1 rankings and [insert variable for ranked ordered data].s

ProblemA 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-HypothesisThere is no statistically significant relationship between the [insert variable for rank ordered data with ties] and [insert variable for ranked ordered data].Null-HypothesisThere is no statistically significant relationship between the last years college football division 1 rankings and the rankings of coaches salaries.s

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