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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.

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Directions

Use the drop-down menu to learn about the three steps needed to complete this assignment.

Three steps to complete the assignment

Step 1: Review the Rubric

• Before you submit your work, review the rubric at the bottom of this assignment.
• Use the rubric as a checklist to determine whether you are ready to submit your work.

Step 2: First Draft

• Commit a good-faith effort to address each item in the Prompt section below.
• Please be sure to number your responses and include “white space” between problem numbers. This improves the readability and flow of your work. I cannot give feedback and grade jumbled work.
• Use either of the following options to submit your work.
  OPTION 1: You can submit a text-entry assignment (i.e. typing your answers in Canvas). To learn how to submit a text-entry assignment, use these (opens in a new tab).
  OPTION 2: You can upload your paper-and-pencil work (or the digital equivalent). To learn how to upload your paper-and-pencil work, use these (opens in a new tab). WARNING – some file types may not be visible on my end. So to learn which files you can upload, be sure to use the directions link I provided for this option.
• Not ready to submit a good-faith effort yet? Avoid frustration – use the link to the Questions, Answers, & Tips discussion board (at the bottom of this page) to post questions about this assignment (or visit the discussion board to answer your classmates’ questions). You can also contact me directly (see the homepage for my contact information).

Step 3: Optional Final Draft

• After you submit your good-faith attempt to fully respond to the questions in the Prompt section below, advance to the ANSWER(S) page.
• You can use the ANSWER(S) page to correct your work and resubmit this assignment any time before I begin grading the problems. However, to earn full credit, you are not required to submit a final draft for this assignment. But if you do submit a final draft, I will only grade it if you submitted a good-faith effort on your first draft.
• Warning – I will only grade your most recent submission. So if you choose to submit a final draft, please do not leave anything out, and please do not direct me to read an earlier submission. To maximize your score, your most recent submission (at the time I begin grading) must be complete.

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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], 9195) obtained the following data from a random sample of 19 subjects.

Critical Flicker Frequency

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.

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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.

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Data

• Open the flicker data set in the Stats at Cuyamaca College group on StatCrunch ( – opens in a new tab).

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Prompt

We will conduct an ANOVA F-test for the variables Color and CFF. The flicker datafile is available in the Data section above. 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 clearly define the parameters.
2. Are the conditions that allow us to safely use the ANOVA F-test met? Explain and provide any supporting evidence.
   Hint: The sample sizes are small. Therefore, to verify conditions, you will need to examine the shape of the distribution of CFF scores for each sample.
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 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 and embed it in the textbox with your responses. 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 descriptive statistics, means, and standard deviations for the comparison groups (select the appropriate Descriptive Statistics StatCrunch directions from the list below). Then copy and paste the table into the textbox 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).

   OR

   Copy and paste the output table into the textbox.

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

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List of StatCrunch Directions

Click here for StatCrunch Directions

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

• (no screenshots; please use these directions)
• (no attachments; please use these directions)

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Module 24 Discussion Board

Use the Module 24 (opens in a new tab) to ask questions or provide feedback about the problems in any Module 24 activity – including this peer-reviewed assignment.

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Review Feedback

• Instructor feedback is only available after an assignment is graded.
• Use these (opens in a new tab) to learn how to review feedback.

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Click the “Next” or > button to continue.

Content by Cuyamaca College math faculty and licensed under the .

Rubric

Formative Assessments w/ StatCrunch

Formative Assessments w/ StatCrunch

Criteria	Ratings	Pts
This criterion is linked to a Learning OutcomeAnswering the Prompt	8 ptsFull CreditThe first submission demonstrates a good-faith effort to address each part of the Prompt. Either in the first draft or the optional final draft, all parts of the “Prompt” are addressed and the responses demonstrate attainment of the learning objectives in the “Progress Check” section of the assignment. The answers are correct. The writing/work is clear. The explanation/work is reasonable, well-organized, and easy to follow.6.5 ptsMostly CorrectThe first submission demonstrates a good-faith effort to address most of the Prompt. In the optional final draft all parts of the “Prompt” are addressed, and the responses demonstrate attainment of the learning objectives in the “Progress Check” section of the assignment. The answers are mostly correct. The writing/work is clear. The explanation/work is reasonable, well-organized, and easy to follow. 3.5 ptsOne or more incorrectThe first submission demonstrates a good-faith effort to respond to a smaller portion of the Prompt. In the first draft or the optional final draft, one or more parts of the “Prompt” are not addressed or are incorrect. Or, answers do not demonstrate attainment of the learning objectives in the “Progress Check” section of the assignment. Or, answers are correct, but the writing/work is unclear, incorrect, or difficult to follow.0 ptsNo MarksThe first submission does not demonstrate a good-faith effort to address the Prompt.	8 pts
This criterion is linked to a Learning OutcomeStatCrunch	2 ptsFull CreditStatCrunch graphs and/or tables are correct and embedded with your work.1 ptsPartial CreditStatCrunch graphs and/or tables are incorrect or missing important information. 0 ptsNo CreditNo StatCrunch information is embedded with your post. Or all StatCrunch work is incorrect.	2 pts

Total Points: 10

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