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Ryan, Engineer
Category: Math Homework
Satisfied Customers: 8982
Experience:  B.S. in Civil Engineering
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Conduct ANOVA and Chi-Square on the following information:

Customer Question

Conduct ANOVA and Chi-Square on the following information:
(Likert Scale used: Strongly Agree= 1, Agree=2, Neutral=3, Disagree=4, Strongly Disagree=5)
Average of responses from different generational groups vs Questions
Submitted: 1 year ago.
Category: Math Homework
Expert:  Ryan replied 1 year ago.
Hi, Thank you for using the site. I'll be happy to help you with this. Do you have any additional information that goes with this problem? Thanks, Ryan
Customer: replied 1 year ago.
Hi Ryan,
I did a small study using the Likert Scale, and I need to produce ANOVA and Chi-square results. Basically, the study is about how the different generational groups find social media useful in finding new companies/brands.
Expert:  Ryan replied 1 year ago.
Ok. I can run the analyses and post the results for you. I'll have to leave it to you to determine whether it is appropriate for your purposes to use ANOVA with Likert Scale data. This is an issue of contention among statisticians, so there is no clear-cut answer for whether it is valid or not.
Customer: replied 1 year ago.
Yes, an ANOVA and Chi-Square, please.
Thank you.
Expert:  Ryan replied 1 year ago.
Ok. I'll get those posted for you as quickly as I can.
Expert:  Ryan replied 1 year ago.
Hi, Here are the results: ANOVA/Chi-Square Note that you are getting seemingly contradictory results from the two different test. Keep in mind though that the two methods are asking slightly different questions. The ANOVA test is comparing the mean response across all questions for each age group. The result here tells you that at least mean response is different from the other means, but it doesn't tell you which one. Clearly, from looking at the data, the mean for the Baby Boomers is the highest, and the mean for the Gen Z group is the lowest. The test doesn't tell you which one is the "different" one though. Additional post-hoc tests would be needed to compare each pair of groups. Also, as mentioned earlier, there is controversy about using a ANOVA test for Likert Scale data, so these results may not be completely valid. The Chi-Square test is asking if there is any dependency between the responses and the age group of the respondents. Clearly, there is a trend toward lower results as you move across the age groups, with the Baby Boomers having the higher values and the Gen Z group having lower values. In this case, the Chi-Square test is telling you that the differences are not large enough to conclude that there is a dependency. I hope this helps. Please feel free to ask if you have any additional questions about this. Thanks, Ryan