We are not strangers to the
concept of correlation, as it implies the relationship between two variables.
The number of fans sold by a superstore with the rise of humidity on a summer
period is a case in point.
In the above example, we can
quantify the variables involved - they take numbers. So, we plot a graph of the
two variables to see a relationship between the two and they go a step further
to justify it in a mathematical manner to make it statistically
Variables cannot be
represented by numbers, though. yet, they can arrange them in a certain order so
that the pattern makes sense to people who are interested in them.
Some bottles of wine can be
arranged by the response to their taste. The arrangement makes sense to people
who are fond of wine, despite the absence of an index to measure it.
In these circumstances,
Spearman's rank comes to our rescue. It can easily be used to determine the
relationship of two variables that escape numbers. Since it is universally
accepted as a trusted method, we can easily cash in on this encouragingly simple
Since we do not have numbers
for the variable, we assign numbers to them, in a sensible way. They are
There are five wine bottles A,
B, C, D and E in the order of taste. We can assign ranks to them in the order of
5,4,3,2,1 or 10, 8.6, 4,2 . These are arbitrary values assigned to variables in
a sensible way; there are not hard and fast rules about it. However, the simpler
The ranking system must be
extended to both sets of variables. Then a formula must be used to find the
Spearman's rank, value of which determines the correlation.
|Ranks of variable X||Ranks of variable Y||Ranks of variable X - Ranks of variable Y
Spearman's rank (rs) = 1 -
6∑d2 / [n(n2-1)]
The value of lies between o and 1 (inclusive)
Spearman's Rank Calculator
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Please work out the following questions to complement what you have just learnt.
1)The height of some baby girls are as follows:
87, 88.8, 90.9, 87.4, 88.7, 90.8, 91.5, 92.2, 88.4 and 94
The corresponding weight in (kg) are 12.7, 11.8, 12, 12.2, 12.4, 12.5, 12.6, 12.7, 12.8 and 13. Find Spearman's Rank.
2)The height of some baby boys are as follows:
92.1, 90.5, 89.8, 93.1, 89.2, 92.4, 95.1, 90.7, 93.9 and 93.8
The corresponding weight in (kg) are 14.1, 13.2, 13.3, 13.4, 12.5, 13.6, 13.7, 13.8, 14 and 14.4. Find Spearman's Rank.