Application Assignment 9

Two-Way ANOVA

Example

For this assignment, we are going to revisit the data from our Chapter 4 assignment. As a reminder, the data you analyzed for Chapter 4 measured student ratings of customer satisfaction when they were randomly assigned to shop for specific items detailed in an assignment by Dr. Sylvia Niehuis (2005), as a white woman or as a Black woman. We found that students who were assigned to shop as a single Black woman for items such as bandages, hose, make-up, fashion magazines, and books were significantly less satisfied with their ability to find the items on their list, the price of the item compared to those available for white women, and the variety of options available compared to those available for white women.

Dr. Walker utilized this assignment with students taking statistics with her for several years. When she discussed the implications and limitations of the results with her classes, one question that always came up was, “Would the results be different if the data was collected in a different geographical location?” Some students hypothesized that there would be more availability and options in cities that had more racial diversity. After teaching statistics in two different states, Dr. Walker was finally able to allow students to analyze data to answer that question.

The dataset you will be working with for this assignment includes an additional variable “Class” to the dataset you worked with for Chapter 4. The first set of ratings are from students living in a city with over 700,000 people in the surrounding metro area in Ohio. According to the American Community Survey, the racial composition of this city is: white: 59.89%; Black or African American: 30.32%; Asian: 4.64%; Two or more races: 4.31%. The second set of ratings are from students living in a city with over 475,000 people in the surrounding metro area in Missouri. The racial composition of people living in this city are: white: 88.07%; Black or African American: 4.36%; Asian: 2.08%; Two or more races: 3.59%.

For this assignment, you will be testing to see if student customer satisfaction ratings are different depending on both location the data was collected (Ohio vs. Missouri) and the condition students were assigned to when shopping (white woman condition vs. the Black woman condition). Use an alpha level of .05.

Open the data file titled “Niehuis Statistics Adaptation Study Data (2 Way ANOVA)” in JASP to complete this assignment. If you import the .csv version instead of opining the JASP file directly, you can relabel Condition 1 “White Woman Scenario” and Condition 2 “Black Woman Scenario” as well as Class 0 to “Ohio” and Class 1 to “Missouri” to help with interpreting your results. Remember, higher scores indicate higher levels of customer satisfaction.

1. Write out the conceptual null and alternative hypotheses being tested in this example. Note that A = main effect of shopping condition, B = main effect of location, and AB = the interaction between condition and location.

H_0A:

H_0B:

H_0AB:

H_1A:

H_1B:

H_1AB:

2. Explain why a two-way ANOVA is the most appropriate statistical test for this research question.

3. Test the following statistical assumptions that apply for a two-way ANOVA. State how you tested each assumption and whether it was met. *Remember, you will use filtering + the split by option to isolate each of the four experimental groups. If you do find a violation of an assumption, you should acknowledge it, but you do not need to apply any filtering to your data to correct for it.

Normal distributions for all 4 groups

Outliers for all 4 groups

Homogeneity of variance

4. Report, using APA format, the results of your two-way ANOVA. Include a description of F test results to indicate significance for the main effects and interaction (using the variable names and context of the study) and include effect sizes along with an interpretation. Provide a follow-up split file analysis if the interaction is significant.
   Hint: Look at the “Putting it All Together” section in the JASP Guide for an example, but you do not have to report all group means or recap the assumptions.

5. Describe what the results of your statistical test mean in 1-2 sentences. Avoid the use of statistical jargon (e.g., significant difference, etc.).

Copy and Paste your JASP output for your assumption checks and main analyses below to receive credit for this assignment