Page 180 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Self-Assessment

1. Indicate whether the following statements are True or False:
(i) Rank method can be used for finding correlation coefficient even when actual data is given.
(ii) If two items are to be assigned equal ranks, rank method of correlation coefficient cannot be
used.
(iii) The rank correlation coefficient was developed by spearman.
(iv) Rank correlation coefficient is obtained by the formula:
R = 16 D /N−∑ 2 3 − N .

(v) If difference of ranks in each pair is zero, show that the rank correlation coefifcient is+ 1.
11.3 Summary

• When there are two series of ranks for the same set of individuals, corresponding to two different
characters or two judges assigning ranks for the same character, one may be interested to know
if the two series are associated. The association between two series of ranks for the same set of
individuals is called rank correlation.
• This method of finding out covariability or the lack of it between two variables was developed
by the British psychologist Charles Edward Spearman in 1904. This measure is especially useful
when quantitative measures for certain factors (such as in the evaluation of leadership ability
or the judgment of female beauty) cannot be fixed, but the individuals in the group can be
arranged in order thereby obtaining for each individual a number indicating his (her) rank in
the group.
• The value of this coefficient also ranges between + 1 and – 1. When R is + 1 there is complete
agreement in the order of the rank and the ranks are in the same direction. When R is – 1 there
is complete agreement in the order of the ranks and they are in opposite directions.
• When we are given the actual data and not the ranks, it will be necessary to assign the ranks.
Ranks can be assigned by taking either the highest value as 1 or the lowest value as 1. But
whether we start with the lowest value or the highest value we must follow the same method in
case of both the variables.

+
56
• If two individuals are ranked equal at fifth place, they are each given the rank that is 5.5
2
++ 7
56
while if three are ranked equal at fifth place they are given the rank = 6. In other
3
words, where two or more individuals are to be ranked equal, the rank assigned for purposes
of calculating coefficient of correlation is the average of the ranks which these individuals would
have not got had they differed even slightly from each other.
• Where the data is of a qualitative nature like honesty, efficiency, intelligence, etc., this method
can be used with great advantage. For example, the workers of two factories can be ranked in
order of efficiency and degree of correlation established by applying this method.
• If N is fairly small (say, not large than 25 or 30), rank method is sometimes applied to interval
data as an approximation to the more time-consuming r. This requires that the interval data be
transferred to rank orders for both variables. If N is much in excess of 30, the labour required in
ranking the scores becomes greater than is justified by the anticipated saving of time through
the rank formula.

174 LOVELY PROFESSIONAL UNIVERSITY