Complete Table 2 and calculate the Mann-Whitney $U\,$ value for the results of Dr Aris's investigation.

Use the following formulas for the Mann-Whitney $U\,$ test:

U_a = n_a n_b + \frac{n_a(n_a + 1)}{2} - R_a

U_b = n_a n_b + \frac{n_b(n_b + 1)}{2} - R_b

where:

$n_a\,$ and $n_b\,$ are the sample sizes of Group A and Group B respectively ( $n_a = 9, n_b = 9$ )
$R_a\,$ and $R_b\,$ are the sum of the ranks for Group A and Group B respectively
the final test statistic $U\,$ is the smaller of $U_a\,$ and $U_b\,$

Table 2:

Condition A: No blue-light exposure		Condition B: Blue-light exposure
Coordination score (out of 20)	Rank	Coordination score (out of 20)	Rank
19	18	18	16.5
18	16.5	11	8.5
17	15	10	7
16	13.5	8	5.5
14	11.5	8	5.5
16	13.5	7	4
13	10	6	3
14	11.5	5	2
11	8.5	3	1
Total		Total

Complete Table 2 and calculate the Mann-Whitney $U\,$ value for the results of Dr Aris's investigation.

Use the following formulas for the Mann-Whitney $U\,$ test:

U_a = n_a n_b + \frac{n_a(n_a + 1)}{2} - R_a

U_b = n_a n_b + \frac{n_b(n_b + 1)}{2} - R_b

where:

$n_a\,$ and $n_b\,$ are the sample sizes of Group A and Group B respectively ( $n_a = 9, n_b = 9$ )
$R_a\,$ and $R_b\,$ are the sum of the ranks for Group A and Group B respectively
the final test statistic $U\,$ is the smaller of $U_a\,$ and $U_b\,$

Table 2:

Condition A: No blue-light exposure		Condition B: Blue-light exposure
Coordination score (out of 20)	Rank	Coordination score (out of 20)	Rank
19	18	18	16.5
18	16.5	11	8.5
17	15	10	7
16	13.5	8	5.5
14	11.5	8	5.5
16	13.5	7	4
13	10	6	3
14	11.5	5	2
11	8.5	3	1
Total		Total

Methods

Methods Questions