LIMITATIONS OF
SPEARMAN'S RANK
CORRELATION
COEFFICIENT
Name : Sahasra Sagi
Class: 11A
Roll no : 19
1
INTRODUCTION
1. Spearman’s Rank Correlation is a statistical measure used to understand the strength
and direction of a relationship between two sets of ranked data. Unlike Pearson's
correlation, which works with actual values, Spearman’s Rank focuses on ranks, or
positions, of data points rather than their raw values.
2. It’s beneficial when dealing with ordinal data (data that can be ranked but doesn’t have
equal spacing, like rankings in a race). Spearman’s Rank is also helpful when data doesn’t
meet the strict requirements of other correlation measures, like linear relationships.
3. Even though Spearman’s Rank is widely used, it has certain limitations that can affect the
accuracy or relevance of results in specific situations. By understanding these
limitations, we can know when to use Spearman’s Rank effectively and when to consider
other options.
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LIMITATION 1 – DIFFICULTY WITH TIED RANKS
When multiple items have the
same rank (called “ties”),
Spearman’s Rank Correlation
becomes less accurate.
Adjustments are needed, but they
can reduce the precision of the
result.
Example Suppose you rank five students by
their math scores, but two
students have the same score.
Calculating an accurate correlation
becomes tricky since two items
have the same rank.
LIMITATION 2 – SENSITIVE TO NON-MONOTONIC 3
RELATIONSHIPS
Spearman’s Rank works well with
monotonic relationships (where
variables consistently increase or
decrease together). If the
relationship changes direction
(non-monotonic), it may give
misleading results.
Example Imagine ranking the hours of
sunlight and plant growth height. If
plants grow with sunlight only up to
a point and then stop, Spearman’s
Rank may fail to show this complex
relationship accurately.
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LIMITATION 3 – LIMITED TO RANKED DATA
Spearman’s Rank only works with
ordinal data (data that can be
ranked), so it’s not suitable for
interval or ratio data (data with
equal intervals or true zero
points) without conversion.
Example Suppose you have temperatures
measured in Celsius. You’d need to
convert these to ranks (high to low),
which loses some information and
may make results less meaningful.
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LIMITATION 4 – AFFECTED BY SAMPLE SIZE
Spearman’s Rank Correlation
becomes less reliable with small
sample sizes, as the correlation
may not represent the real trend
well. Larger samples provide more
stable results.
Example If you rank only five students’
scores, the result may not
accurately represent the trend. But
if you have 50 students, the
correlation is more dependable.
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CONCLUSION
Spearman’s Rank Correlation Coefficient is a helpful tool for measuring
1 relationships between ranked data, but it has its limitations. It struggles with
tied ranks, non-monotonic relationships, smaller sample sizes, and is limited to
ranked (ordinal) data.
Understanding these limitations helps us use Spearman’s Rank wisely and
2 consider alternatives when needed. By knowing its strengths and weaknesses, we
can make more accurate decisions in data analysis.
