Null Hypothesis for Spearman's Rho (Independence)

Null-hypothesis for a Spearman's Rho

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 Spearman's Rho is like a Pearson correlation but is used with Rank-ordered data.

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

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.

Here is a template for writing a null-hypothesis for a Spearman's Rho:

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].

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.

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.

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 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.

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.

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.

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

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

ProblemAre the rank ordered results from the biking and the running events are independent of one another?

Template for a Spearman's Rho Null-HypothesisThere is no statistically significant relationship between the [insert variable] and [insert variable].

ProblemAre the rank ordered results from the biking and the running events are independent of one another?

Template for a Spearman's Rho Null-HypothesisThere is no statistically significant relationship between the median [insert variable] and the median [insert variable].

ProblemAre the rank ordered results from the biking and the running events are independent of one another?

Template for a Spearman's Rho Null-HypothesisThere is no statistically significant relationship between the median [insert variable] and the median [insert variable].

ProblemAre the rank ordered results from the biking and the running events are independent of one another?

Template for a Spearman's Rho Null-HypothesisThere is no statistically significant relationship between the median [biking even rankings] and the median [insert variable].

ProblemAre the rank ordered results from the biking and the running events are independent of one another?

Template for a Spearman's Rho Null-HypothesisThere is no statistically significant relationship between the median [biking event rankings] and the median [running event rankings].

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