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11-Unit11

# Spearmans rank correlation method charles edward

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Unformatted text preview: les based on ranks given to the observations. This method is adopted when the variables are not capable of quantitative measurements like intelligence, beauty etc. in such cases, it is impossible to assign numerical values for change taking place in such variables. It is in such cases rank correlation is useful. Spearman’s rank correlation coefficient is given by rk = 1- 6 D2 / n (n2-1) Where D is the difference between ranks and n, number of pairs correlated. Concurrent Deviation Method In this method, correlation is calculated between direction of deviations and not their magnitudes. As such only the direction of deviations is taken into account in the calculation of this coefficient and their magnitude is ignored. The formula for the calculation of coefficient of concurrent deviations is given below: rc = +- 2C-n / n Sikkim Manipal University Page No. 208 Research Methodology Unit 11 Steps in the Calculation of Concurrent Deviation Find out the direction of change of x-variable. When a successive figure in the series increase direction is marked as + and when a successive figure in the series decrease direction of change is marked as -. It is denoted as dx. Find out the change in direction of y-variable. It is denoted as dy. Multiply dx and dy and determine the value of C. C is the number of positive products of dxdy (- X - or + X +). Use the formula rc = +- 2C-n / nto obtain the value of coefficient of rc. Problems 1. Calculate Karl Pearson’s co-efficient of correlation for the following data. X : 43 44 46 40 44 42 45 42 38 40 42 57 Y : 29 31 19 18 19 27 27 29 41 30 26 10 X Y dx dx2 dy Dy2 dxdy 43 29 3 -1 9 1 3 44 31 4 1 16 1 4 46 19 6 -11 36 121 -66 A(40) 18 0 -12 0 144 0 44 19 4 -11 16 121 -44 42 27 2 -3 4 9 -6 45 27 5 -3 25 9 -15 42 29 2 -1 4 1 38 41 -2 11 4 121 -22 40 A(30) 0 0 0 0 0 42 26 2 -4 4 16 -8 57 10 17 -20 289 400 -340 43 54 407 944 494 Sikkim Manipal University Page No. 209 Research Methodology Unit 11 Direct method r Covariance between x and y SD x SD y Covariance between x and y = xy / N - (x/N X y/N) Dx = standard deviati...
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