An anxiety researcher conducted a study comparing the effectiveness of two therapeutic interventions: Group X received Cognitive Behavioral Therapy (CBT), while Group Y received Mindfulness-Based Stress Reduction (MBSR).

Complete Table 1 and calculate the Mann-Whitney $U\,$ statistic for the data in Table 1.

Table 1: Anxiety reduction scores and ranks for CBT and MBSR groups

Group X (CBT)		Group Y (MBSR)
Anxiety Reduction Score	Rank	Anxiety Reduction Score	Rank
31	16	29	15
28	14	25	11
27	13	23	9.5
26	12	18	5.5
23	9.5	16	4
22	8	14	3
20	7	13	2
18	5.5	11	1
Total		Total

Mann-Whitney $U\,$ formulae:

U_x = n_x n_y + \frac{n_x(n_x+1)}{2} - \sum R_x

U_y = n_x n_y + \frac{n_y(n_y+1)}{2} - \sum R_y

(where $U\,$ is the smaller of $U_x\,$ and $U_y$ )

Show your working.

Complete Table 1 and calculate the Mann-Whitney $U\,$ statistic for the data in Table 1.

Table 1: Anxiety reduction scores and ranks for CBT and MBSR groups

Group X (CBT)		Group Y (MBSR)
Anxiety Reduction Score	Rank	Anxiety Reduction Score	Rank
31	16	29	15
28	14	25	11
27	13	23	9.5
26	12	18	5.5
23	9.5	16	4
22	8	14	3
20	7	13	2
18	5.5	11	1
Total		Total

Mann-Whitney $U\,$ formulae:

U_x = n_x n_y + \frac{n_x(n_x+1)}{2} - \sum R_x

U_y = n_x n_y + \frac{n_y(n_y+1)}{2} - \sum R_y

(where $U\,$ is the smaller of $U_x\,$ and $U_y$ )

Show your working.

Methods

Question 32

Table 1: Anxiety reduction scores and ranks for CBT and MBSR groups

Mann-Whitney $U\,$ formulae:

Markscheme

Methods

Question 32

Table 1: Anxiety reduction scores and ranks for CBT and MBSR groups

Mann-Whitney $U\,$ formulae:

Markscheme

Methods

Question 32

Table 1: Anxiety reduction scores and ranks for CBT and MBSR groups

Mann-Whitney U U\,U formulae:

Methods Questions

Methods

Question 32

Table 1: Anxiety reduction scores and ranks for CBT and MBSR groups

Mann-Whitney U U\,U formulae:

Methods Questions

Mann-Whitney $U\,$ formulae:

Mann-Whitney $U\,$ formulae: