Overview of Prompt 2:  After reading about a study conducted on concussed student-athletes, you think you’ve identified a possible problem in the setup of the concussion study. In order to confirm your intuition, you use two datasets available to you.  After exploring the data, and performing the appropriate statistical analysis using RStudio, you are asked to write a letter to the editor of the concussion study that clearly explains your statistical findings.

Background (Motivation): Recovery curve after concussion for student athletes

The (fictitious) Midwest Journal of Medicine recently published a study of the recovery curve after concussions for student athletes.  Student athletes complete a computer-based neurocognitive assessment when they first enter their university and are given a baseline concussion score.  If a student athlete becomes concussed, they are asked to perform the assessments again and again until their neurocognitive assessment score returns to their baseline score.

You believe that hand dominance may have an impact on the study results and observe that this wasnt controlled for in the original study.  To show the importance of controlling for hand dominance when performing computer-based evaluations, you decide to conduct your own study among undergraduate students at UM.

Your Study: Effects of hand dominance on various computer-based activities for undergraduate students at UM.

You have two different datasets available to you coming from a random sample of undergraduate students at UM.  Each student was asked to perform a series of two computer-based activities that measure reaction time (Links to an external site.) and memory (Links to an external site.).  Each student performed each activity twice; first using their dominant hand and again using their non dominant hand. You will be using these study results to evaluate if hand dominance has an effect on reaction time and memory when measured through these two computer based activities.

Below is a summary of the data collected for each activity:

It is attached below

Your Task

Write a 500 – 700 word letter to the editor of the concussion study published in the Midwest Journal of Medicine (according to these two guidelines, guideline 1 (Links to an external site.) and guideline 2 (Links to an external site.)).  Your letter to the editor should clearly explain your concern with the original concussion study, your experiments, and the findings from your experiments. Using your statistical findings comment on the impact of hand dominance on both reaction time and memory assessment.

Be sure to include the following:

The motivation for your letter.  Specifically, state the concern with the original concussion study.
An introduction to the outline of your experiment including:
The type of experimental design
The type and role for each of the experimental variables: hand used (dominant versus non-dominant) and completion time
Explain how we use dependent data when evaluating how hand dominance affects reaction time and memory assessment through the two computer based activities
Should randomness have been used in the hand dominance experimental design? If so, at what point? Refer to the screenshots  of the survey questions.
For one of the experiments (reaction time or memory assessment), perform a hypothesis test to assess whether there is a difference in completion time, on average, when undergraduate students at UM use their dominant vs. non-dominant hand, using a 5% significance level. Be sure to include:
Definition of the parameter of interest in context
Your hypotheses and results of your test.  You can include either a screenshot from R or a table of important values (test statistic, distribution, and p-value) calculated by hand.
An evaluation of the p-value and conclusion in context
Define alpha and power in context
Explain two ways in which you could increase the power of this test
For the other experiment, compute the 95% confidence interval to estimate the mean difference in completion time for all undergraduate students at UM when they use their dominant vs. non-dominant hand. Be sure to include:
Definition of the parameter of interest in context
Your confidence interval.
An explanation to the editor regarding whether or not the method for creating a confidence interval is reliable. This explanation shouldnt depend on your specific sample, but is for the method in general.
A clear explanation of how the confidence interval can be used to assess if hand dominance has an effect on completion time, on average, for all undergraduate students at UM 
An explanation to the editor about how you would make your interval more precise
A brief conclusion including:
A summary about whether there is a difference in performance, on average, when undergraduate students at UM use their dominant vs. non-dominant hands during reaction time and memory tests
Recommendations to the original concussion researchers about how they can adjust a similar future study on concussions.

The two data files are attached as well memory and reaction time.

The table data is attached as well

The format of the letter should follow these two guidelines from the two links

https://www.naeyc.org/our-work/public-policy-advocacy/letter-editor-template

https://journals.sagepub.com/doi/full/10.1177/2050640620956921