This video discusses calculating rank correlation coefficients between two data sets. It explains how to calculate ranks when values are repeated or not repeated, and uses Spearman's formula to determine the correlation coefficient. Three example problems are worked through: finding the rank correlation between two students' exam scores, correcting a mistake in calculated rank differences, and interpreting the result of rank correlation between two assessments. The key steps are assigning ranks, determining differences between ranks, and applying Spearman's formula to quantify the correlation between the two variables.

1. RANK CORRELATION
GRADE 11 MATH
COLLEGE MATH
R

2. PREVIEW:
THIS VIDEO ILLUSTRATES THE METHOD OF CALCULATING RANK
CORRELATION.
BOTH CASES WHEN RANKS ARE REPEATED AND NOT REPEATED ARE
DISCUSSED.
SO TAKE A PEN AND PAPER AND WORK WITH ME THROUGH THIS
VIDEO.

3. Correlation coefficient between 2 series of ranks is called rank correlation coefficient. The formula for
the coefficient of rank correlation was given by Spearman. Spearman’s rank correlation coefficient is
given by
Where D difference between 2 ranks

4. Question 1
The marks obtained by 2 students in Physics and Maths are as follows .
Compute the ranks in the 2 subjects and the coefficient of correlation
of ranks.
English 35 23 47 17 10 43 9 6 28
Maths
30 33 45 23 8 49 12 4 31

5. English Maths D =
35 30 3 5 - 2 4
23 33 5 3 2 4
47 45 1 2 - 1 1
17 23 6 6 0 0
10 8 7 8 - 1 1
43 49 2 1 1 1
9 12 8 7 1 1
6 4 9 9 0 0
28 31 4 4 0 0
12

6. High degree of rank correlation

7. Question 2
The coefficient of rank correlation of marks obtained by 10 students in
Physics and Chemistry was found to be 0.5. It was later discovered that
the difference in ranks in 2 subjects obtained by one of the students
was wrongly taken as 4 instead of 8. Find the correct coefficient of rank
correlation
r = 0.5

8. Correct

9. r =

10. Question 3
The following table gives 2 kinds of assessments. Find Spearman’s
coefficient of rank correlation and interpret the result
Assess
1
30 20 40 50 30 20 30 50 10 0
Assess
2
15 40 40 45 20 30 15 50 20 10

11. Ass 1 Ass 2
30 15 5 8.5 - 3.5 12.25
20 40 7.5 3.5 4 16
40 40 3 3.5 - 0.5 0.25
50 45 1.5 2 - 0.5 0.25
30 20 5 6.5 -1.5 0.25
20 30 7.5 5 2.5 2.25
30 15 5 8.5 - 3.5 6.25
50 50 1.5 1 0.5 12.25
10 20 9 6.5 2.5 6.25
0 10 10 10 0 0
56

12. 50 is repeated 2 times
30 is repeated 3 times
20 is repeated twice
40 is repeated twice
20 is repeated twice
15 is repeated twice
Where m is the number of times a rank is repeated

15. For more videos , subscribe to my channel