MATH 160 CC Hypothesis for an ANOVA & Critical Flicker Frequency CFF Worksheet
Question Description
Context
Critical flicker frequency (CFF) and eye color
Computer screens and fluorescent bulbs flicker. If thefrequency of the flicker is below a certain threshold, the eye detectsthe 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 eyecolor; one column for the response variable CFF) and each row is anindividual. For example, the first row is a brown-eyed person with a CFFof 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 theexplanatory variable: one column for blue-eyed people, one column forbrown-eyed people and one column for green-eyed people. Each columncontains 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 tologin while downloading the file. Upload the datafile to StatCrunch.
Prompt
We will conduct an ANOVA F-test for the variables Color and 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.
- What are the hypotheses for the ANOVA test? Be sure that you define clearly the parameters.
- 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 CFFscores for each sample (because the samples are small). - Use StatCrunch to create side-by-side dotplots, histograms orboxplots (your choice) to examine the distribution of CFF scores foreach sample. You can use either data format; choose one (stacked data in the first two columns; or unstacked datain the the last three columns). To create the side-by-side graphs (foreither 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 StatCrunchdirections below.
- You will also need to compare the sample standard deviations. UseStatCrunch to find the summary statistics, means and standard deviationsfor the comparison groups (select the the appropriate DescriptiveStatistics StatCrunch directions from the list below). Then copy andpaste the table into your initial post and explain how the rule of thumb for comparing standard deviations is met.
- Use StatCrunch to carry out the ANOVA F-test (select the appropriateANOVA StatCrunch directions from the following two options).
Anova F-test Stacked Data Format OR
Anova F-test Unstacked Data FormatCopy and paste the output table into your initial post.
- State your conclusion in context of eye color and mean CFF.
Have a similar assignment? "Place an order for your assignment and have exceptional work written by our team of experts, guaranteeing you A results."