A psychologist investigated whether caffeine consumption affects performance on a hand-eye coordination task. One group of five participants drank a caffeinated energy drink before the task, while a second group of five participants drank a placebo decaffeinated alternative. The number of errors made during the task was recorded for each participant. The data and their corresponding ranks are shown in the table below.
| Caffeine Group | Control Group (Placebo) | ||||
|---|---|---|---|---|---|
| Participant | Score | Rank | Participant | Score | Rank |
| A | 2 | 1 | F | 6 | 4.5 |
| B | 3 | 2 | G | 7 | 6 |
| C | 4 | 3 | H | 11 | 8 |
| D | 6 | 4.5 | I | 12 | 9 |
| E | 9 | 7 | J | 15 | 10 |
| n1=5n_1 = 5n1=5 | n2=5n_2 = 5n2=5 |
Calculate the U U\,U value for the Mann-Whitney U U\,U test for the data collected in this study. Show your workings.
You should use the formulae presented below.
U1=n1n2+n1(n1+1)2−R1 U_1 = n_1 n_2 + \frac{n_1(n_1 + 1)}{2} - R_1 U1=n1n2+2n1(n1+1)−R1 U2=n1n2+n2(n2+1)2−R2 U_2 = n_1 n_2 + \frac{n_2(n_2 + 1)}{2} - R_2 U2=n1n2+2n2(n2+1)−R2 U=the smaller of U1 and U2 U = \text{the smaller of } U_1 \text{ and } U_2 U=the smaller of U1 and U2513 exam-style questions on OCR A Level Psychology Data recording, analysis and presentation. Each one has a worked solution and a mark scheme showing where the marks go.