Question

STATISTICS CHOOSING THE DESIGN OF AN EXPERIMENT

The Academy of Sports Medicine Physicians is interested in determining whether a new training regimen will help long-distance runners improve their performance in marathons. This organization comes to you for some advice on how to design an experiment to test whether this new regimen is more effective than the standard regimen. You have access to a sample of long- distance runners on the track teams at ten different universities. You hope to conduct the experiment over the course of two years because the regimen takes a long time to learn and because you want to include new runners in the sample as they join the track team. You also believe that the effect of the regimen on performance may differ for men and women.

Your challenge is to design an experiment that uses a randomized approach to measure the effect of the new regimen on performance.

Remember, your design should take into account your concerns about different effects for men and women and should be set up so that new subjects can be properly included in the experiment. Create an experiment that will address these concerns.

Pay particular attention to the factors, explanatory and response variables, any blocks or matching characteristics, and the treatment conditions used in the experiment.

You may want to create a diagram that summarizes your experimental design (this is not required.)

Answer 1

**Experimental Design:**

1. **Factors and Levels:**

- **Factor 1: Training Regimen**

- Level 1: Standard regimen

- Level 2: New regimen

- **Factor 2: Gender**

- Level 1: Male

- Level 2: Female

2. **Explanatory Variable:**

- Training Regimen (Standard or New)

3. **Response Variable:**

- Long-distance running performance (measured by marathon completion time or another relevant metric).

4. **Blocking or Matching:**

- **Blocking Factor: University**

- Randomly assign individuals within each university to the two treatment groups.

- This helps control for university-specific variations and ensures a balanced representation of each regimen at each university.

- **Matching Characteristic: Gender**

- Ensure a balanced representation of both genders within each treatment group at each university.

5. **Treatment Conditions:**

- **Group 1: Standard Regimen**

- Male and female runners following the standard training regimen.

- **Group 2: New Regimen**

- Male and female runners following the new training regimen.

6. **Inclusion of New Subjects:**

- Allow for the continuous inclusion of new subjects over the two-year period.

- Newly joined runners can be randomly assigned to either the standard or new regimen within their respective universities and gender groups.

**Diagram:**

```

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

| Randomized Experiment Design |

|----------------------------------------------------------------|

| University 1 |

|----------------------------------------------------------------|

| | Standard Regimen |

| Gender |--------------------------------------------------------|

| | Male Runners | Female Runners |

|----------------------------------------------------------------|

| | Newly Joined | Existing Runners | Newly Joined | Existing Runners |

|----------------------------------------------------------------|

| | | | | |

| Standard Regimen | Standard Regimen | New Regimen | New Regimen |

|----------------------------------------------------------------|

| University 2 |

|----------------------------------------------------------------|

| | Standard Regimen |

| Gender |--------------------------------------------------------|

| | Male Runners | Female Runners |

|----------------------------------------------------------------|

| | Newly Joined | Existing Runners | Newly Joined | Existing Runners |

|----------------------------------------------------------------|

| | | | | |

| Standard Regimen | Standard Regimen | New Regimen | New Regimen |

|----------------------------------------------------------------|

| ... |

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

```

This design allows for a rigorous evaluation of the new training regimen's impact on long-distance running performance, considering potential gender differences and accommodating the inclusion of new subjects over the two-year period. The randomized approach helps control for confounding factors, and the blocking by university ensures that the results are representative across different academic institutions.