Spearman’s Rank Order Correlation Coefficient
What is it and when is it used?
Spearman’s Rho is used when we are trying to find a ____________________ between two
____ _____________________. The two sets of data have to be _______________. The level
of measurement also has to produce ______________data.
Examples
Is there a relationship between the cost of chocolate and the taste?
Hypotehsise!
Experimental:
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
Null:
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
Probability level I am willing to accept is_____
Table to show___________________________ Graph to show______________________________________
__________________________________________ ___________________________________________________
(Complete with scores)

What do your descriptive results tell you?
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
(If we didn’t have a correlation, let’s pretend we did for the purposes of the next bit!)
Now for the inferential stats!
How does it work?
We need to rank two sets of data, compare the rank of each data set, and then using this to find a
correlation co-efficient. The closer the rank of the two sets of data, the stronger the
relationship.
How do we use it?
Using this test will give us an observed value (called a correlation co-efficient) between
__________ and __________, which shows the strength of the relationship.
1)
1) First calculate the sum of differences squared (⅀d²)
2) However, to know whether or not the result is significant, we need to look up our result on
a table of critical values. To do this we need two pieces of information.
a. Did you write a directional (one tailed) or non directional (two tailed) hypothesis?
b. How many ___________________ were in the study? This number is called N (number of chocolates
in our case!).
Using this information, we compare our observed value with the _______________ value on the table.
If our observed value is equal to or higher, we reject our _______________ hypothesis and accept
the _________________ hypothesis.
#cho
c
a) Price
per 100g
b) Mean
Taste score
c) Rank for
column (a)
d) Rank for
column (b)
Diff =
d
(ra-rb)
d²
1
2
3
4
5
⅀d²
Now the calculation
Σd2
= _______ N = _____
CV(5) = ______
)1(
6
1 2
2
−
Σ
−=
NN
d
rs
)1_____(____
____6
1 2
−
×
−=sr
_______
______
1 −=sr
sr = 1 - _______
sr = ________ this is a
positive / negative correlation.

If however, we predicted a positive correlation, but we found a negative correlation (or the vice
versa), we would still reject the _________________ hypothesis as the correlation was in the wrong
direction. We then use this information to state our conclusion.
OUR RESULTS: The calculated correlation coefficient of ________ is higher than/ less than the
critical value of ______ where N = ________ for a ____-tailed test. There is/is not a significant
correlation at p<0.___. Therefore I need to __________ the experimental hypothesis and
_______________ the null hypothesis because….
__________________________________________________________________________________________________
__________________________________________________________________________________________________
Extra practice! For the following, look up the critical value and write an appropriate conclusion
A. There will be a relationship between how many burgers a person eats and their self esteem.
Participants: 18 students. Observed value: +0.494
B. There will be a positive relationship between a person’s height, and their reaction time.
Participants: 7 men. Observed value: +0.699
C. There will be a negative correlation between the number of friends a person has on
Facebook, and the hours spent revising for an exam. Participants: 29 year 8 students.
Observed value +0.458