Question

You are thinking about wether or not an athletes finish in a race is related to how much protein they ate in their last meal before they performed. You collect information from 10 people and get the following data. “FIN” is where they finished in the race and “PROT” is the number of grams of protein in the last meal.

Person	FIN	PROT	+ -	RANK FIN	RANK PROT	D	D2
1	18	85	+	6	10	-4	16
2	28	59	+	8	5	3	9
3	8	33	+	4	2	2	4
4	11	62	+	5	6	-1	1
5	22	85	+	7	8	-1	1
6	7	52	+	3	4	-1	1
7	29	76	+	9	7	2	4
8	3	50	+	1	3	-2	4
9	34	86	+	10	9	1	1
10	5	21	+	2	1	1	1
SUM	165	619		55	55	0	42
St Dev	11.23	23.96		3.03	3.03	2.16	4.87

What is ΣD?   What is ΣD² ? What is N?   What is r_s ? Describe this correlation in a sentence:

Answer 1

1) Summation of D = 0 , D is the difference between the ranks of an individual

2) summation of D^2 =42 , D^2 is the difference between the ranks given to an individual squared .

3)N= total no. Of people = 10 ( N is the number of people who are ranked)

4) Spearman correlation -> 1 - 6(sum(D^2))/n(n^2 - 1)

1 - 6×42/10×99 = 1 - 0.2545= 0.7455

So rank correlation is 0.7455

This indicates a strong positive relationship between the ranks individuals obtained in the race finish and protein . That is, the higher you ranked in protien the higher you ranked in race also, and vice versa