Short cut method

Example

Steps for Calculation• Choose convenient values as assumed mean of two series, X

and Y.

• Deviations(now dx and dy instead of x and y) are obtained from the assumed means.

• Obtain the sum of dx and dy columns, that is, ∑dx and ∑dy.

• Deviations dx and dy are squared up and their totals ∑ dx2 and ∑ dy2 are obtained.

• Finally obtain ∑ dxdy which is the sum of the products of deviations taken from the assumed means in the two series.

Sollution

• This shows a high degree of correlation between amounts of radio time(x) and number of electrical appliances sold(y).

• If we examine carefully the formula used for the shortcut method with that used with actual arithmetic mean are used, we would find that (∑dx * ∑dy)/N is the correction factor in the numerator and (∑dx)² /N and (∑dy)²/N are the correction factors introduced in the denominator on account if the use of assumed means in place of actual means.

Spearman’s Rank Correlation Method

Meaning• If the values are ranked in decreasing or increasing order,

the correlation between these ranks in rank correlation and the coefficient of correlation computed between these ranks is called coefficient of rank correlation.

r = 1 - 6∑D2

(N3 – N)

∑D2 =total of sqaures of the diff. between ranksN =number of pairs of observationr =coefficient of rank correlation

Calculation of Coefficient of Rank Correlation

1. If the ranks are given

2. If the ranks are not given

The following are the marks of 8 students in statistics and mathematics. Find the coefficient of correlation

Marks in Statistics

25 43 27 35 54 61 37 45

Marks in Mathematics

35 47 20 37 63 54 28 40

Solution

r = 1 - 6∑D2

(N3 – N) = 1 - 6 x 14 64 - 8

= 1 – 0.1667 = 0.8333

Problem of Equal Ranks

• It is possible sometimes that the values may be repeated twice or thrice in the series. In such cases average rank is assigned to the similar items.

• The average rank is calculated by dividing the sum of the ranks by the n numbers of repetition.

• Then the rank correlation is calculated by adding 1/12(m3-m) in the simple correlation of rank formula.

Merits of Rank Coefficient of Correlation Method

1. Simplicity2. Compulsory Calculation3. Useful for data of qualitative measures4. Same result

Demerits of Rank Coefficient of Correlation Method

1. Unsuitable for group frequency distribution2. Unsuitable if values of the series exceed 303. Lacking precision