In a research to determine the relationship..

Question 1 Report

In a research to determine the relationship between performance of students in an entrance examination and subsequent school performance, the results of ten randomly selected students wre obtained as follows;

Students	A	B	C	D	E	F	G	H	I
Performance in Entrance Examination	11	12	8	13	6	15	10	14	17
School Performance	5	10	9	7	4	8	6	14	11

1, Calculate the spearman's rank correlation coefficient

2. What would be the researcher's from the result in a?

Answer

1. To calculate the Spearman's rank correlation coefficient, we need to follow these steps:

Rank the data for both the entrance examination performance and school performance separately.
Calculate the difference between the ranks for each student.
Square the differences and add them up.
Use the formula to calculate the Spearman's rank correlation coefficient:

rho = 1 - ((6 * sum of squared differences)/(n*(n^2-1)))

where n is the number of data points (in this case, 10).

After ranking the data and calculating the differences, we get the following table:

Student	Entrance Exam Rank	School Performance Rank	Rank Difference (d)	d^2
A	6	4	2	4
B	7	8	-1	1
C	4	6.5	-2.5	6.25
D	8	3	5	25
E	3	10	-7	49
F	10	2	8	64
G	5	5.5	-0.5	0.25
H	9	1.5	7.5	56.25
I	2	9	-7	49
J	1	7	-6	36

The sum of the squared differences is 296.5, so we can calculate the Spearman's rank correlation coefficient:

rho = 1 - ((6 * 296.5)/(10*(10^2-1)))</

Read lesson note on Statistics (WAEC)

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