# anova f test using statcrunch 1

## 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.

Here are the directions and grading rubric for the discussion board exercises.

A list of StatCrunch directions is provided at the bottom of this page.

### 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], 91â€“95) obtained the following data from a random sample of 19 subjects.

 Color ThresholdFrequency (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.

### 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.

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-Class folder, 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).

Copy and paste the output table into your initial post.

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