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Speed Skating Suits (Example 3) Speed skating is a sport in which it is important to have a suit that minimizes wind drag as much as possible, as the difference between winning and losing a race can be as small as a thousandth of a second. In the 2014 Winter Olympics, U.S. speed skaters used a suit called the Mach 39 , and none medaled despite high expectation before the games. For the 2018 Winter Olympics, a new suit design called the H1 was developed. Suppose the designers wanted to test if skaters would be faster in the H1 or the Mach \(39 .\) They have 10 Olympic speed skaters and 10 recreational speed skaters on whom to test the suits. a. Identify the treatment variable and the response variable. b. Describe a simple randomized design (not blocked) to test whether the H1 suit decreases race times. Explain in detail how you will assign skaters to treatment groups. c. Describe a blocked design using the types of skaters that could be used to test whether the \(\mathrm{Hl}\) suit decreases race times. What advantage does the blocked design have? d. Describe a design that uses the skaters as their own controls to reduce variation.

Step by step solution

01

Identify the treatment and response variable

The treatment variable is the type of speed skating suit (H1 vs. Mach 39). On the other hand, the response variable is the speed of the skaters, which could be measured using their race times.

02

Simple randomized design

For a simple randomized design, the 20 skaters can be randomly assigned to use either H1 or Mach 39, ensuring an equal chance of either suit being used. The race times of the skaters can then be recorded and a comparison between the two groups can be performed to determine if there's any significant difference in the times.

03

Blocked design

In the blocked design, the difference in the skill level of the speed skaters, defined as Olympic and recreational skaters, is taken into account. This design groups the skaters based on their skill level. Thus, 5 Olympic skaters would use the H1 suit and the other 5 would use Mach 39 and similarly for recreational skaters. Comparison of the race times is done within the blocks and the results are then combined. This design utilizes the information on the skaters' skill level and could increase the precision of the results.

04

Design using skaters as controls

Each skater can serve as their own control, by letting them race in both suits and recording the time in each. The sequence of which suit is worn first could be randomized to prevent any bias. Since each skater wears both suits, the effect of individual differences can be controlled for.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Treatment and Response Variables

Understanding the concepts of treatment and response variables is fundamental in experimental design. Let's consider an example in speed skating: designers have developed two suit designs, the Mach 39 and the H1, intending to minimize wind resistance and improve speed. In this scenario, the treatment variable is the type of suit worn by the skaters, as it is the factor being manipulated to observe a potential effect.

The response variable, on the other hand, is the measurable effect of this treatment, which in our case is the skaters' race times. By comparing the response variable under the influence of different treatment variables, we aim to conclude whether one suit outperforms the other in reducing race times. Being able to clearly identify these variables is crucial for setting up a coherent and reliable study.

Simple Randomized Design

A simple randomized design is a basic yet powerful tool for experimental studies. It involves randomly assigning subjects to different treatment groups to ensure that each subject has an equal chance of receiving any particular treatment. The key aim here is to mitigate the effects of bias and unobserved variables.

For the speed skating suits, a simple randomized design would involve assigning the 20 skaters to either the Mach 39 or H1 suit randomly. This could be done, for example, by using a random number generator or drawing names from a hat. By randomizing skaters to each type of suit, any systematic differences between groups are minimized, making it more likely that differences in race times can be attributed to the suit design itself, rather than extraneous factors.

Blocked Design

Moving on to a more nuanced experimental strategy, a blocked design takes into account the natural groupings or 'blocks' within the experimental subjects that could affect the response variable. In our exercise, the skaters are divided into two blocks based on their skill level – Olympic skaters and recreational skaters.

In a blocked design, treatment is applied within these blocks. For instance, a random assignment of 5 Olympic skaters to the H1 suit and 5 to the Mach 39 suit occurs, and the same process is replicated for the recreational skaters. The main advantage of this approach is the increased accuracy of the results. By accounting for the skill level, the blocked design minimizes the variability within the groups, which might otherwise overshadow the effect of the treatment variable.

Control in Experimental Design

Incorporating control into experimental design is essential for isolating the treatment effect from the variability due to extraneous factors. One way to do this is by using the participants as their own controls, which is particularly useful when experimenting with effects that may be influenced by individual differences.

In the context of speed skating suits, having each skater race in both the H1 and the Mach 39 serves this purpose. This within-subject design ensures that variables like fitness level, experience, and natural speed are held constant, as each skater's performance in one type of suit can be directly compared to their performance in the other. To avoid biased results due to learning effects or fatigue, the order of the suit tests should be randomized. This method is highly effective in reducing intra-subject variation, allowing the precise measurement of the suit's effect on race times.