Question

A running-shoe manufacturer wants to test the effect of its new sprinting shoe on 100 -meter dash times. The company sponsors 5 athletes who are running the 100 -meter dash in the 2004 Summer Olympic games. To test the shoe, it has all 5 runners run the 100 -meter dash with a competitor's shoe and then again with their new shoe. The company uses the difference in times as the response variable. a) Suggest some improvements to the design. b) Why might the shoe manufacturer not be able to generalize the results they find to all runners?

Short answer

Increase sample size and randomize shoe trials. The current sample may not represent average runners due to their elite status.

Step-by-step solution

Understanding the Current Experiment Design

The company currently has 5 athletes run the 100-meter dash using both a competitor's shoe and their new sprinting shoe, with the difference in time taken as the response variable. This design allows them to observe individual differences in performance across the two shoe types for the same runners.

Suggesting Improvements to the Experiment Design

To improve the design, consider increasing the sample size by including more athletes, which provides a more diverse performance range and reduces variability due to individual differences. Randomly assign which shoe each athlete starts with to control for learning or fatigue effects. Additionally, ensure the runners have adequate recovery time between tests to minimize fatigue's impact on their performance.

Understanding Limitations in Generalizing Results

The study uses only 5 athletes from the Olympic games, a very specific and elite subgroup of runners. Results might not generalize to the broader population, as these athletes may respond differently to the shoes compared to amateur or non-professional runners.

Reasons for Limited Generalization

The small sample size and specific characteristics of Olympic athletes limit the ability to generalize findings. These athletes likely have optimal biomechanics and conditioning that may not represent the average runner's interaction with the shoe, potentially leading to skewed results when applied to a general population.

Key concepts

Sample Size

When conducting an experiment, one crucial factor to consider is the sample size. This refers to the number of participants in the study. In the original exercise, only 5 athletes were used, which is relatively small. A small sample size can lead to unreliable results because there's not enough data to account for natural variability among different individuals.
By increasing the number of athletes in the experiment, the shoe manufacturer can gather more data and produce results that are more dependable. Here are some key reasons why a larger sample size is beneficial:

• **Diversity**: A bigger group will likely include a mix of different skill levels, body types, and running styles, which helps in understanding the shoe's performance across a broader spectrum.
• **Accuracy**: More data points can reduce the influence of outliers or exceptional performers, leading to a more accurate average outcome.
• **Reliability**: With more participants, the findings are less likely to be affected by chance, providing more reliable evidence of the shoe’s effects.

Incorporating a larger and more representative sample size would strengthen the study and help the manufacturer draw more meaningful conclusions.

Generalization

Generalization refers to applying the findings of a study to a larger population. The ability to generalize results is vital in experimental design as it determines how valuable the study's conclusions are beyond the immediate participants.
In the given exercise, the results of the shoe test may not easily generalize to all runners because the study used only elite Olympic athletes. Olympians represent a very specialized and high-performing subset of runners. Their reaction to the shoes might not reflect how amateur or casual runners would perform.
Several factors contribute to this limited ability to generalize:

• **Specific Population**: Olympians likely have different training, biomechanics, and performance levels compared to the average runner. Studies on such specific populations may not apply to less trained individuals.
• **Niche Conditions**: The experiment conditions, such as the high level of pressure and competition at the Olympics, might differ significantly from everyday running scenarios.
• **Bodied Differences**: Physical conditioning and body mechanics can vary significantly between elite athletes and recreational runners, influencing how effective or noticeable the shoe's benefits are.

To improve generalizability, the manufacturer should conduct tests with a more varied participant base, encompassing a wide range of athletes.

Response Variable

In experimental design, the response variable is what researchers measure to determine the effect of an intervention. It represents the outcome of interest, influenced by the changes made during the experiment. In the shoe manufacturer's experiment, the response variable is the difference in 100-meter dash times when using the new shoe versus a competitor's shoe.
Using the difference in times as a response variable allows the researchers to focus on what matters most: whether the new shoe positively affects performance speed. However, it’s essential to ensure this variable accurately reflects the effect of the intervention. Some considerations include:

• **Validity**: Ensuring that the difference in time solely reflects the shoe's impact, rather than other factors like runner fatigue or environmental conditions.
• **Consistency**: Measuring the difference in consistent and controlled conditions to ensure that changes truly arise from the shoe and not extraneous variables.
• **Sensitivity**: Choosing a response variable sensitive enough to detect even small but significant changes caused by different shoe types.

Adjusting the experiment to accurately capture and reflect these differences will lead to more precise findings about the new shoe's performance.