Aggregated Likert scale summary data - z-test?

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The discussion focuses on analyzing summarized Likert scale data without raw data, specifically considering the use of a z-test for proportions to compare groups based on their responses. The data is categorized into three "agree" levels on a 7-point scale, and the user is seeking guidance on appropriate statistical methods. There is a debate about whether to use parametric or non-parametric tests, with references to online calculators and articles suggesting that both approaches can be valid. The importance of avoiding Type I errors is highlighted, indicating that the choice of methodology may depend on the specific dataset. Ultimately, the analysis aims to determine if the groups are significantly different based on their responses.
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<Moderator's note: Moved from a homework forum.>

1. Homework Statement

I have some summarized Likert scale data from a report and my co-workers want to know what kind of comparison analysis we could do with it. I don't have the raw data.
Most of the questions are on a 7-point scale (Strongly disagree, disagree, slightly disagree, neither agree nor disagree, slightly agree, agree, strongly agree).
I have the number of responders for each group and I know the number of responders in each category. The report groups the responders into number and percentage who chose one of the 3 "agree" categories. It looks similar to my attachment.

Homework Equations


I'm wondering if I can use a z test for proportions to compare the groups and see if they are significantly different. I'm attaching a sample that looks similar to the data I have to work with.

The Attempt at a Solution


I was looking at an online calculator here: http://www.socscistatistics.com/tests/ztest/Default2.aspx
Thanks!
 

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http://blog.minitab.com/blog/advent...em-data-two-sample-t-test-versus-mann-whitney

I thought that the parametric test versus non-parametric test decision was a done deal. I guess not. This article (for minitab) discusses the use of both and asserts either one is okay. Apparently you can setup, run analysis, and see which statistical methodology is more likely to be reliable. Avoiding Type I error, for example.. Meaning the door can swing both ways depending on the data set.

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The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...

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