Spearman's rank correlation coefficient measures the strength of association between two ranked variables using a non-parametric statistical approach. It assesses monotonic relationships, where one variable increases or decreases in relation to another, without necessarily being linear. The method has advantages such as simplicity and applicability to various data types, but also limitations like approximate calculations and challenges with larger samples.

1. Spearman’s
Rank-Difference Correlation
K.THIYAGU, Assistant Professor, Department of Education,
Central University of Kerala, Kasaragod

2. The Spearman’s Rank Correlation Coefficient is the
non-parametric statistical measure
used to study the
strength of association
between the
two ranked variables.
This method is applied to the ordinal set of numbers, which
can be arranged in order, i.e. one after the other so that
ranks can be given to each.
Spearman’s Rank Correlation
It was developed by Charles Spearman; this it is
called the Spearman rank correlation.
Spearman's rank correlation coefficient denoted
by the Greek letter  (rho)
It assesses how well the relationship
between two variables can be
described using a monotonic function.

3. Charles Edward Spearman
Born 10 September 1863,
London, United Kingdom
Died 17 September 1945 (aged 82),
London, United Kingdom
Known for g factor, Spearman's rank correlation
coefficient, factor analysis
Notable
students
Raymond Cattell, John C. Raven,
David Wechsler
Influences Francis Galton, Wilhelm Wundt

4. While Pearson's correlation assesses linear relationships,
Spearman's correlation assesses monotonic relationships
(whether linear or not).
A monotonic relationship is a relationship that does one of the
following: (1) as the value of one variable increases, so does
the value of the other variable; or (2) as the value of one
variable increases, the other variable value decreases
Monotonic Relationships

8. Monotonic relationships are where:
• One variable increases and the other increases.
Or,
• One variable decreases and the other decreases.
Monotonic variables increase (or decrease) in the same
direction, but not always at the same rate.
Linear variables increase (or decrease) in the same
direction at the same rate.

9. If an increase in the independent variable
causes a decrease in the dependent
variable, this is called a monotonic inverse
relationship. An inverse relationship is the
same thing as a negative correlation.
A monotonic direct relationship is where
an increase in the independent variable
causes an increase in the dependent
variable. In other words, there’s a positive
correlation between the data.

10. D = Difference of ranks
N = Number of Observations
Formula for the Spearman’s Rank Correlation Co-efficient
When the ranks are repeated the formula is
where m1, m2, ..., are the number of
repetitions of ranks

11. Example
English
(mark)
Maths
(mark)
Rank
(English)
Rank
(maths)
d d2
56 66 9 4 5 25
75 70 3 2 1 1
45 40 10 10 0 0
71 60 4 7 -3 9
62 65 6 5 1 1
64 56 5 9 -4 16
58 59 8 8 0 0
80 77 1 1 0 0
76 67 2 3 -1 1
61 63 7 6 1 1

12.  It is easy to calculate.
 It is simple to understand.
 It can be applied to any type of data.
Qualitative or Quantitative. Hence
correlation with qualitative data such as
honesty, beauty can be found.
 This is most suitable in case there are two
attributes.
Merits

13.  It is only an approximately
calculate measure as actual
values are not used for
calculations.
 For large samples, it is not a
convenient method.
 Combined r of different
series cannot be obtained as
in case of mean and S.D.
 It cannot be treated further
algebraically.
Demerits

14. Thank You
K.THIYAGU, Assistant
Professor, Department of Education,
Central University of Kerala, Kasaragod