This document discusses Spearman's rank correlation coefficient. It provides formulas and explanations for calculating the coefficient when: 1) Actual ranks are given 2) Ranks are not given and need to be assigned 3) There are equal or tied ranks The coefficient measures the strength and direction of association between two ranked variables. It ranges from -1 to 1, where 1 is total agreement in ranking, -1 is total disagreement, and 0 is no correlation. The document also lists properties of Spearman's rank correlation.

1. STATISTICS
PRESENTATION
SUBMITTED BY : GAURAV PALARIYA
SUBMITTED TO : MR .SAURABH PANDEY
BBA 3rd semester
2050180

2. SPEARMAN’S RANK
CORRELATION
• This measure is especially useful when
quantitative measure of certain factors cannot be
fixed but the individuals in the group can be
arranged in order thereby obtaining for each
individual a number indicating his rank .

3. WHEN ACTUAL RANKS ARE GIVEN
• When actual ranks are given take the difference of the two
ranks i.e. (R1 – R2) and the difference is denoted by D .
Square these differences and put value in the formula.
• R = 1- (6 ∑D2 ) / N (N2 – 1)
• R = Rank correlation coefficient
• D = Difference of rank between paired item in two series.
• N = Total number of observation

4. WHEN RANKS ARE NOT GIVEN
• 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.
• R = 1- (6 ∑D2 ) / N (N2 – 1)

5. EQUAL RANKS OR TIE IN RANKS
• In such cases average ranks should be assigned to each
individual.
R =1- 6{∑D2 1/12(m1
3 – m1) + 1/12(m2
3 – m2) +…. 1/12(m2
3 –
m2) / N (N2 – 1)
m = The number of time an item is repeated

6. PROPERTIES OF SPEARMEN'S RANK
CORRELATION
• The value of rank correlation coefficient, R ranges from -1
to +1
• If R = +1, then there is complete agreement in the order of
the ranks and the ranks are in the same direction
• If R = -1, then there is complete agreement in the order of
the ranks and the ranks are in the opposite direction
• If R = 0, then there is no correlation

7. WHEN RANK ARE NOT REPEATED

8. WHEN RANKS ARE REPEATED

9. Thank you