A cognitive psychologist is testing the influence of the use of imagery on the m

Question

A cognitive psychologist is testing the influence of the use of imagery on the

memory of students. He collected the following data on a memory test after the

learning situation where imagery was used on half of the participants. Rank the

scores and perform a MannWhitney test at .05, using the 5 steps of hypothesis

testing. (Hint: Use the formula to generate the U value for each sample.)

With Imagery Without Imagery

10 12 6 7

9 14 8 5

9 11 10 7

8 12 8 6

I am struggling with the ranking and assigning points especially. Please be clear as to how this is calculated.

Explanation / Answer

H0: Both data have the same probability distribution (or median).
Ha: They have different probability distributions (or medians).

Rank the combined data: Keep track of the group while ranking. Ranks are shown in parenthesis.

5   6   6   7   7   8   8   8   9   9   10   10   11   12   12   14   

5- 1

6 - 2.5 {two times , 2 and 3 ,so average = 0.5*(2+3) =2.5}}

similarly 8 - {rank 6,7,&8 ,hence average 7 }

similarly others

10 1 [11.5]
12 1 [14.5]
9 1 [9.5]
14 1 [16]
9 1 [9.5]
11 1 [13]
8 1 [7]
12 1 [14.5]
6 2 [2.5]
7 2 [4.5]
8 2 [7]
5 2 [1]
10 2 [11.5]
7 2 [4.5]
8 2 [7]
6 2 [2.5]

Add ranks of group 1: T1 = 95.5
Add ranks of group 2 : T2 = 40.5
Select the larger rank Tx = 95.5
n1 = 8
n2 = 8
nx = 8 (group that gave the larger total is group 1)

U = n1 n2 + n1 (n1+1) / 2 - Tx
U = (8)(8) + 8(9)/2 - 95.5
U = 4.5 (test statistic)

The critical value at 5% level (from the table in the link) is 13.
Since the computed value is less than the critical value , reject H0 *
(This differs from the conventional parametric hypothesis tests)

The results indicate a significant difference in ranks between the two groups, so they have different probability distributions (medians).

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