An educational psychologist conducted a study comparing two different learning techniques: Group A used active recall (flashcards) to study for a quiz, while Group B used passive rereading (textbooks).

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

Table 1: Quiz scores and ranks for active recall and passive rereading groups

Group A (Active Recall)		Group B (Passive Rereading)
Quiz Score	Rank	Quiz Score	Rank
28	15	15	2
24	11	19	5.5
25	12	21	8.5
29	16	12	1
21	8.5	18	4
27	14	22	10
26	13	17	3
19	5.5	20	7
Total		Total

Mann-Whitney $U\,$ formulae:

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

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

(where $U\,$ is the smaller of $U_a\,$ and $U_b$ )

Show your working.

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

Table 1: Quiz scores and ranks for active recall and passive rereading groups

Group A (Active Recall)		Group B (Passive Rereading)
Quiz Score	Rank	Quiz Score	Rank
28	15	15	2
24	11	19	5.5
25	12	21	8.5
29	16	12	1
21	8.5	18	4
27	14	22	10
26	13	17	3
19	5.5	20	7
Total		Total

Mann-Whitney $U\,$ formulae:

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

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

(where $U\,$ is the smaller of $U_a\,$ and $U_b$ )

Show your working.

Methods

Question 74

Table 1: Quiz scores and ranks for active recall and passive rereading groups

Mann-Whitney $U\,$ formulae:

Methods

Question 74

Table 1: Quiz scores and ranks for active recall and passive rereading groups

Mann-Whitney $U\,$ formulae:

Methods

Question 74

Table 1: Quiz scores and ranks for active recall and passive rereading groups

Mann-Whitney U U\,U formulae:

Methods Questions

Methods

Question 74

Table 1: Quiz scores and ranks for active recall and passive rereading groups

Mann-Whitney U U\,U formulae:

Methods Questions

Mann-Whitney $U\,$ formulae:

Mann-Whitney $U\,$ formulae: