Unformatted text preview: relationship between the variables.
4. If the correlation is +1 or –1, it signifies that there is a high
degree of correlation. (+ve or –ve) between the two variables.
If r is near to zero (ie) 0.1,-0.1, (or) 0.2 there is less correlation.
207 Rank Correlation:
It is studied when no assumption about the parameters of
the population is made. This method is based on ranks. It is useful
to study the qualitative measure of attributes like honesty, colour,
beauty, intelligence, character, morality etc.The individuals in the
group can be arranged in order and there on, obtaining for each
individual a number showing his/her rank in the group. This
method was developed by Edward Spearman in 1904. It is defined
as r = 1 − 3
r = rank correlation coefficient.
Note: Some authors use the symbol ρ for rank correlation.
D2 = sum of squares of differences between the pairs of ranks.
n = number of pairs of observations.
The value of r lies between –1 and +1. If r = +1, there is
complete agreement in order of ranks and the direction of ranks is
also same. If r = -1, then there is complete disagreement in order of
ranks and they are in opposite directions.
Computation for tied observations: There may be two or more
items having equal values. In such case the same rank is to be
given. The ranking is said to be tied. In such circumstances an
average rank is to be given to each individual item. For example if
the value so is repeated twice at the 5th rank, the common rank to
be assigned to each item is
= 5.5 which is the average of 5
and 6 given as 5.5, appeared twice.
If the ranks are tied, it is required to apply a correction
factor which is
(m3-m). A slightly different formula is used
when there is more than one item having the same value.
The formula is
r= 1− 6[ΣD 2 + 1
(m3 − m) + (m 3 − m) + ....]
n3 − n
208 Where m is the number of items whose ranks are common
and should be repeated as many times as there are tied
In a marketing survey the price of tea and coffee in a town based on
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