A canine researcher investigated whether different training regimes affect the speed at which search-and-rescue dogs locate a hidden scent. One group of five dogs was trained using Method Alpha, while a second group of five dogs was trained using Method Beta. The time taken (in minutes) to locate the scent was recorded for each dog. The data and their corresponding ranks are shown in the table below.
| Method Alpha Group | Method Beta Group | ||||
|---|---|---|---|---|---|
| Dog | Time (mins) | Rank | Dog | Time (mins) | Rank |
| A | 10 | 1 | F | 15 | 3.5 |
| B | 14 | 2 | G | 18 | 5 |
| C | 15 | 3.5 | H | 21 | 7 |
| D | 19 | 6 | I | 26 | 9 |
| E | 22 | 8 | J | 28 | 10 |
| n1=5n_1 = 5n1=5 | n2=5n_2 = 5n2=5 |
Calculate the UUU value for the Mann-Whitney UUU 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.