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Exercises 25 to 28 refer to the following setting. Does the color in which words are printed affect your ability to read them? Do the words themselves affect your ability to name the color in which they are printed? Mr. Starnes designed a study to investigate these questions using the 16 students in his AP \(^{\text {R }}\) Statistics class as subjects. Each student performed two tasks in a random order while a partner timed: ( 1 ) read 32 words aloud as quickly as possible, and ( 2 ) say the color in which each of 32 words is printed as quickly as possible. Try both tasks for yourself using the word list below $$ \begin{array}{llll} \text { YELLOW } & \text { RED } & \text { BLUE } & \text { GREEN } \\ \text { RED } & \text { GREEN } & \text { YELLOW } & \text { YELLOW } \\ \text { GREEN } & \text { RED } & \text { BLUE } & \text { BLUE } \\ \text { YELLOW } & \text { BLUE } & \text { GREEN } & \text { RED } \\ \text { BLUE } & \text { YELLOW } & \text { RED } & \text { RED } \\ \text { RED } & \text { BLUE } & \text { YELLOW } & \text { GREN } \\ \text { BLUE } & \text { GREEN } & \text { GREEN } & \text { BLUE } \\ \text { GREEN } & \text { YELLOW } & \text { RED } & \text { YELLOW } \end{array} $$ Color words (4.2) Let's review the design of the study. (a) Explain why this was an experiment and not an observational study. (b) Did Mr. Starnes use a completely randomized design or a randomized block design? Why do you think he chose this experimental design? (c) Explain the purpose of the random assignment in the context of the study. The data from Mr. Starnes's experiment are shown below. For each subject, the time to perform the two tasks is given to the nearest second. $$ \begin{array}{cccccc} \hline \text { Subject } & \text { Words } & \text { Colors } & \text { Subject } & \text { Words } & \text { Colors } \\ 1 & 13 & 20 & 9 & 10 & 16 \\ 2 & 10 & 21 & 10 & 9 & 13 \\ 3 & 15 & 22 & 11 & 11 & 11 \\ 4 & 12 & 25 & 12 & 17 & 26 \\ 5 & 13 & 17 & 13 & 15 & 20 \\ 6 & 11 & 13 & 14 & 15 & 15 \\ 7 & 14 & 32 & 15 & 12 & 18 \\ 8 & 16 & 21 & 16 & 10 & 18 \\ \hline \end{array} $$

Step by step solution

01

Understanding the Study Type

In an experiment, a researcher manipulates one or more variables and controls others to determine their effect on a response variable. In this case, Mr. Starnes assigns the tasks of reading words and naming colors to the students, actively manipulating the order in which tasks are performed to compare the times. This contrasts with an observational study where the researcher merely observes subjects without manipulation.

02

Identifying the Design

Mr. Starnes used a completely randomized design for the experiment. This is because each student performed both tasks in a random order without any blocking based on characteristics such as reading speed or language. A completely randomized design was likely chosen to ensure simplicity and control for order effects without involving more complex grouping.

03

Explaining Random Assignment

Random assignment in this experiment involves randomly deciding the order in which each student performs the two tasks. This helps to ensure that any differences in task performance are due to the order they are conducted and not external variables such as fatigue or learning effects, thus allowing a clearer understanding of the effect of task type and sequence on performance time.

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Key Concepts

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

Random Assignment

Random assignment is a critical element in the setup of experiments. It refers to the process where subjects are randomly assigned to different groups or orders in an experiment.
This randomness helps ensure that any differences observed in outcomes across these groups are due to the variable or condition being tested, rather than some other uncontrolled factor.
In the study designed by Mr. Starnes, random assignment was used to determine the order in which the students performed the tasks.

• Random assignment balances out unknown factors across different groups or conditions.
• It minimizes biases that might influence the study outcome.
• Here, it controls for potential learning effects or fatigue that could skew results if students did the tasks in the same sequence.

By randomly assigning the order of tasks, Mr. Starnes ensured that each sequence had an equal chance of being tested by each student. Thus, any observed differences are more reliably attributed to the tasks themselves and their order.

Completely Randomized Design

A completely randomized design is one of the simplest and most straightforward experimental designs. In this design, all experimental subjects are assigned to treatment conditions randomly.
The goal is to eliminate potential bias by ensuring that the treatment each subject receives does not depend on any characteristic of the subject.
In Mr. Starnes's experiment, each student completed both tasks in a randomly assigned order.

• No grouping or blocking was done based on any student's potential abilities or characteristics.
• This design was most likely chosen to maintain simplicity while still providing reliable results.
• It helps in ensuring that things like prior knowledge or reading speed do not influence the study outcome unduly.

Completely randomized design is effective in studies where subjects are relatively homogeneous or when the number of subjects is enough to handle variability naturally.

Experiment vs. Observational Study

The main distinction between an experiment and an observational study lies in the control and manipulation of variables.
In an experiment, researchers actively intervene to test a hypothesis by manipulating one or more variables and observing the resulting changes.
Mr. Starnes's study is an experiment because he assigned specific tasks (reading words and naming colors) to students in varying orders.

• He controlled the order of task execution to observe its effect on task performance time.
• An observational study, on the other hand, would involve merely watching the students complete the tasks without any manipulation of variables.
• Experiments tend to provide stronger evidence for cause-and-effect relationships due to this level of control.

The deliberate manipulation present in Mr. Starnes’s study exemplifies why it is categorized as an experiment, rather than an observational study.