MATH 160 Cuyamaca College ANOVA F Test CFF of Individuals Stats Practice

I’m working on a statistics discussion question and need a sample draft to help me study.

Progress Check

Use this activity to assess whether you and your peers can:

• If conditions are met, use the ANOVA F-test to examine the relationship between a categorical explanatory variable that has more than two values and a quantitative response variable.
• State the conclusion of an ANOVA F-test in context.

Learn by Doing

The purpose of this activity is to give you guided practice in carrying out the ANOVA F-test using StatCrunch.

Some features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.

Use the rubric at the bottom of this page as a guide for completing this assignment.

A list of StatCrunch directions is provided after the Prompt section below.

Directions

Submit your work:

• Carefully read all sections below (beginning with the Context section and ending with the Prompt section).
• Commit a good-faith effort to address all items in the Prompt section below. Please be sure to number your responses.
• If directed to do so, embed all required StatCrunch output in your initial submission. Please do not submit StatCrunch output as an attachment.

Complete your assigned peer reviews:

• After you submit your initial good-faith attempt, continue to the ANSWER(S) page and review your instructor’s response. But please do not submit your corrected work yet.
• Within three days after the due date, return to this assignment and complete your assigned peer reviews (directions (Links to an external site.)).

Submit your corrected work:

• We all learn from mistakes (our own and our classmates’ mistakes). So please do not immediately correct your own mistakes. If possible, wait until you receive feedback from at least one of your peers.
• If necessary, correct your work and resubmit the entire assignment – including any required StatCrunch output. Your instructor will only review and grade your most recent submission, so please do not refer to a previous submission.

Context

Critical flicker frequency (CFF) and eye color

Computer screens and fluorescent bulbs flicker. If the frequency of the flicker is below a certain threshold, the eye detects the flicker, and it is annoying!

Different people have different flicker “threshold” frequencies (known as the critical flicker frequency, or CFF). The mean critical threshold frequency is important for product manufacturing as well as tests for ocular disease.

In 1973, researchers conducted a study to answer the following question.

Research question: Do people with different eye color have different threshold flicker sensitivity?

The 1973 study (“The Effect of Iris Color on Critical Flicker Frequency,” Journal of General Psychology [1973], 91–95) obtained the following data from a random sample of 19 subjects.

Color	Threshold Frequency (CFF)	Blue	Brown	Green
Brown	26.8	25.7	26.8	26.4
Brown	27.9	27.2	27.9	24.2
Brown	23.7	29.9	23.7	28
Brown	25.0	28.5	25	26.9
Brown	26.3	29.4	26.3	29.1
Brown	24.8	28.3	24.8
Brown	25.7		25.7
Brown	24.5		24.5
Green	26.4
Green	24.2
Green	28.0
Green	26.9
Green	29.1
Blue	25.7
Blue	27.2
Blue	29.9
Blue	28.5
Blue	29.4
Blue	28.3

In this spreadsheet the data is presented in two formats.

Stacked data: The quantitative data is stacked in one column. The first two columns show the data in a stacked format. Each variable is a column (one column for the explanatory variable eye color; one column for the response variable CFF) and each row is an individual. For example, the first row is a brown-eyed person with a CFF of 26.8.

Unstacked data: The quantitative data is distributed across the groups in multiple columns. The last three columns show the same data in an unstacked format. In this format, each column is a group defined by a value of the explanatory variable: one column for blue-eyed people, one column for brown-eyed people and one column for green-eyed people. Each column contains the response values (CFF) for that group.

The format of the data in the spreadsheet affects how we use StatCrunch to analyze it.

Variables

Color: This is the explanatory variable. The categorical data represents the groups we will compare.

CFF (flicker threshold sensitivity): This is the response variable. The quantitative data represents the frequency threshold at which the subject sees the flicker.

Data

Download the flicker (Links to an external site.) datafile. As always, ignore or close any prompt that invites you to login while downloading the file. Upload the datafile to StatCrunch.

Prompt

We will conduct an ANOVA F-test for the variables Colorand CFF. The flicker datafile is available in the Data section below. Also, the StatCrunch directions are provided in the list a the bottom of this page.

1. What are the hypotheses for the ANOVA test? Be sure that you define clearly the parameters.
2. Are the conditions that allow us to safely use the ANOVA F-test met? Explain.
   Note: To verify conditions, you will need to examine the distribution of CFF scores for each sample (because the samples are small).
3. Use StatCrunch to create side-by-side dotplots, histograms or boxplots (your choice) to examine the distribution of CFF scores for each sample. You can use either data format; choose one (stacked data in the first two columns; or unstacked data in the the last three columns). To create the side-by-side graphs (for either data format) see the list of StatCrunch directions below. Download the StatCrunch output window (your graph), upload it to your Stats-Classfolder, and then embed the .png file (your graph) in your initial post. To recall how to complete these tasks, see the list of StatCrunch directions below.
4. You will also need to compare the sample standard deviations. Use StatCrunch to find the summary statistics, means and standard deviations for the comparison groups (select the the appropriate Descriptive Statistics StatCrunch directions from the list below). Then copy and paste the table into your initial post and explain how the rule of thumb for comparing standard deviations is met.
5. Use StatCrunch to carry out the ANOVA F-test (select the appropriate ANOVA StatCrunch directions from the following two options).

   Anova F-test Stacked Data Format OR
   Anova F-test Unstacked Data Format

   Copy and paste the output table into your initial post.

6. State your conclusion in context of eye color and mean CFF.

List of StatCrunch Directions

Each link will open in a new window. To return to this discussion, either close the new tab or select the tab for this discussion.

• Purchase StatCrunch (You only need to do this once.)
• Open StatCrunch
• Download Excel Data File
• Upload Excel Data File to StatCrunch
• Download StatCrunch Output Window (no screenshots; please use these directions)
• Upload Files into Your Stat-Class Folder in Canvas
• Embed Pictures in a Discussion Post (no attachments; please use these directions)
• Side-by-side Boxplots Stacked Data Format
• Side-by-side Boxplots Unstacked Data Format
• Side-by-side Dotplots Stacked Data Format
• Side-by-side Dotplots Unstacked Data Format
• Side-by-side Histograms Stacked Data Format
• Side-by-side Histograms Unstacked Data Format
• Descriptive Statistics Multiple Categories Stacked Data Format
• Descriptive Statistics Multiple Categories Unstacked Data Format
• Copy & Paste a StatCrunch Table
• Anova F-test Stacked Data Format
• Anova F-test Unstacked Data Format

Rubric

Peer Reviewed Assignment w/ StatCrunch

Peer Reviewed Assignment w/ StatCrunch

Criteria	Ratings	Pts
This criterion is linked to a Learning OutcomeAddressing the Prompt	6 pts Full Marks All parts of the Prompt are addressed. Answers are correct. Statistical vocabulary is used appropriately. Writing is clear and thought process is easy to follow. 4 pts Partial Credit Some parts of the prompt are not addressed, are incorrect, or are unclear. 0 pts No Marks The prompt is not addressed.	6 pts
This criterion is linked to a Learning OutcomeStatCrunch Data	2 pts Full Marks Appropriate StatCrunch graphs and/or tables are provided as directed. 1 pts Partial Credit StatCrunch graphs and tables are inappropriate or missing important information. 0 pts No Marks No StatCrunch information is provided.	2 pts
This criterion is linked to a Learning OutcomeIndividual Penalty	0 pts No individual penalty -1 pts Individual penalty. Please see the instructor comments for more information.	0 pts
This criterion is linked to a Learning OutcomePeer Reviews	2 pts Full Marks You completed all assigned peer reviews (maximum of 2). For each peer review, the points you assigned in the rubric are appropriate. You included comments explaining the score you posted in the rubric. If you deducted points in the rubric, your comments explain what the author needs to do to earn a higher grade when the teacher grades the assignment. 1 pts Partial Credit Committed a good-faith effort to provide a high-quality peer review, but many necessary instructive comments are missing. 0 pts No Marks No peer review provided or the comments are not instructive.	2 pts
Total Points: 10