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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 H1 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 Response and Treatment Variables

Treatment Variable: The type of suit worn by the skaters (Mach 39 or the H1).\nResponse Variable: The race times of the speed skaters.

02

Describe a Simple Randomized Design

Randomly assign 10 suits of each type (H1 and Mach 39) to the 20 skaters. Record the race times for each skater. It's important to ensure that the assignment of suits is completely random so there's no bias in the experiment.

03

Describe a Blocked Design

In a blocked design, we would first partition the skaters into two blocks: Olympic skaters and Recreational skaters. Then, within each block, we randomly assign 5 suits of each type (Mach 39 and H1). Recording the race times for each skater, a suitable statistical test is later used to evaluate the effect of suits on racing times within each block. The advantage of this design is that it can control the variability related to types of skaters.

04

Describe a Design Using Skaters as their own Controls

Each skater wears both suits (Mach 39 and H1) in random order and their race time is recorded both times. By having each skater serve as his own control, we can reduce variability associated with differences among skaters.

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Key Concepts

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

Randomized Design

In the realm of statistics, a randomized design is a fundamental approach used to measure the effect of different treatments. Here, the process involves randomly assigning subjects to various treatment groups. This randomness helps to ensure that there is no bias in the allocation. For instance, in the speed skating experiment, 20 skaters are randomly assigned to wear either the Mach 39 or the H1 suit. Each suit is randomly distributed among the participants, with 10 skaters assigned to each suit type.

This type of experimental design is powerful because it provides a fair comparison between the two groups. By removing any patterns or predictability in the assignment, the results are more likely to reflect true differences due to the treatment rather than any external factors. Moreover,

• Randomized design helps balance unknown factors among groups.
• Minimizes bias and confounding variables.
• Ensures each participant has an equal chance of receiving any treatment.

Therefore, it is a preferred strategy in many scientific studies, as it lays the groundwork for making unbiased estimates and conclusions.

Blocked Design

A blocked design is an advanced technique in experimental design that partitions or "blocks" subjects into groups that have similar characteristics. This method greatly reduces the variability within each block, making the experiment more sensitive to the treatment effects. In the speed skating exercise, the skaters are divided into two blocks: Olympic and Recreational skaters.

Within each block, the skaters are then randomly assigned to either the H1 or Mach 39 suit. This ensures that each group has a balanced representation of the two suit types. The advantage of a blocked design is particularly noticeable in its ability to

• Control for known sources of variability among subjects.
• Enhance the precision of results by comparing similar sets of subjects.
• Improve the power of statistical tests within each block.

In essence, blocked designs are beneficial when there are distinct groups or categories within the subjects. By addressing these differences explicitly, researchers can more accurately assess the treatment's effect.

Control in Experiments

Control in experiments is crucial for obtaining valid and reliable results. One way to achieve control is by using designs where subjects serve as their own controls. This method involves having each participant experience all treatment conditions under study. In our speed skating scenario, each skater wears both the Mach 39 and the H1 suit with the order of suits being randomized.

This "within-subject" design reduces variability caused by individual differences between skaters. Some key benefits include:

• Minimized influence of extraneous variables since each participant serves as their own baseline.
• Efficient comparison with fewer subjects needed.
• Increased sensitivity to detecting treatment effects.

This control measure is quite powerful because it helps to isolate the influence of the variable being tested. It's especially effective when individual variability is a significant concern in the experiment. Using self-control designs can result in more reliable and interpretable outcomes.