Question

CHOOSING THE DESIGN OF AN EXPERIMENT

An optometrist is interested in the effects of different brands of eye drops. She wants to know if different drops affect the accuracy of a standard vision test.
Some researchers think that a new brand: Brand A may have more adverse effects on an individual’s ability to correctly report the letters in the vision test than the common brand: Brand B.
There is also some speculation that the effect of the drops on vision differs dramatically for individuals who are far-sighted compared to those who are near-sighted.
The optometrist hires you to design an experiment that tests the effect of the eye drops on test performance. You tell her there are two possible approaches to take: a randomized comparative approach or a matched pairs design.
Describe how you would use each design to test the effect of the eye drops on test performance on a random sample of patients.
Remember, there is a concern about the effects for near vs. far-sighted patients. As much as possible, use diagrams instead of words to summarize your experimental design.

Answer 1

**Randomized Comparative Approach:**

1. **Design:**

- **Randomly assign patients to two groups:**

- Group 1 (Brand A): Patients receive eye drops from Brand A.

- Group 2 (Brand B): Patients receive eye drops from Brand B (common brand).

2. **Subgroup Analysis:**

- After the initial analysis, further investigate the effects on near-sighted and far-sighted individuals separately.

3. **Diagram:**

```

---------------------------------

| Randomized |

| Comparative |

---------------------------------

| Group 1 |

| Brand A |

---------------------------------

| Group 2 |

| Brand B |

---------------------------------

```

**Matched Pairs Design:**

1. **Design:**

- **Pairing:**

- Pair each patient with a near-sighted individual and a far-sighted individual based on similar characteristics (e.g., age, initial vision score).

- Each pair consists of a near-sighted and a far-sighted individual.

- **Treatment Assignment:**

- Randomly assign one individual from each pair to receive Brand A.

- The other individual from the same pair receives Brand B.

2. **Subgroup Analysis:**

- Analyze results separately for near-sighted and far-sighted individuals.

3. **Diagram:**

```

---------------------------------

| Matched Pairs |

| Design |

---------------------------------

| Near-sighted | Far-sighted |

---------------------------------

| Brand A | Brand B |

---------------------------------

| Brand B | Brand A |

---------------------------------

```

Both designs allow for a comparison of the effects of Brand A and Brand B on vision test performance. The randomized comparative approach provides a straightforward comparison, while the matched pairs design controls for individual variability by pairing near-sighted and far-sighted patients.