A clinical psychologist conducted a study comparing two different therapeutic interventions for generalized anxiety disorder. Group X received Cognitive Behavioural Therapy (CBT), while Group Y received Mindfulness-Based Stress Reduction (MBSR). The scores represent the reduction in anxiety levels after 6 weeks (higher scores indicate greater improvement).

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
32	15	18	2
28	11	23	5.5
29	12	26	9
35	16	14	1
25	8	21	4
31	14	27	10
30	13	20	3
23	5.5	24	7
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
32	15	18	2
28	11	23	5.5
29	12	26	9
35	16	14	1
25	8	21	4
31	14	27	10
30	13	20	3
23	5.5	24	7
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 233

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

Mann-Whitney $U\,$ formulae:

Methods

Question 233

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

Mann-Whitney $U\,$ formulae:

Methods

Question 233

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

Mann-Whitney U U\,U formulae:

Methods Questions

Methods

Question 233

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: