Hello Nan,

The question of how best to scale perceived equality of situation depends in large part on how you intend to use these scaled scores. If your goal is to generate a score such that the highest numeric value is associated with the neutral category, and successively lower scores towards the extremes of the situation scale, then why not code them as 0,1,2,3,2,1,0 (for scale options of "Far less", "Moderately less", ..., "Far more", respectively)? I'd treat these as ordinal values.

Note that these values, as successive integers, may not align precisely with what more rigorously scaled values might turn out to be, but they are likely to be highly correlated (which was what Rensis Likert observed in his comparison of successive integer values for the response scale options; see below).

However, do recognize that neither individuals nor pairs of respondents (even if from opposing groups) actually behave in ways that are arithmetically complementary. For example, if individuals are given the following stimuli:

A. I believe that the 2020 U.S. Presidential election result was fraudulent.

B. I believe that the 2020 U.S. Presidential election result was not fraudulent.

And the response scale was used was your 7-point, "Agreement" scale, above, you'd expect those who chose "1" for stimulus A to have chosen "7" for stimulus B, right? But, the reality is, that's not what always (or, in some cases, even frequently) happens. Likewise, opposing view respondents won't necessarily choose complementary responses to the same stimulus. If this is relevant to the way you're framing your symmetry/equality scaling, then the values may be misleading as to the truth of the agreement/disagreement.

An alternative approach which might be worth considering is to use a polytomous item response theory model to calibrate the stimuli separately for each group, then compare them to see how they actually behave.

Good luck with your work.

Nan Cao Non-parametric tests for independence, such as Spearman's correlation or the chi-square test, should be used for ordinal data (individual Likert-scale items). Use parametric tests such as Pearson's r correlation or t-tests for interval data (overall Likert scale scores).

A Likert scale is made up of four or more Likert-type items that reflect related questions and are combined to form a single composite score/variable. Likert scale data may be examined as interval data, which means that the mean is the most accurate indicator of central tendency. To explain the scale, utilize means and standard deviations.

It depends on your items. You could also use the reverse scoring system.

Because you have ordinal data, the standard answer is to use a non-parametric equivalent of the t-Test, such as Mann-Whitney. However, recent simulation tests indicate that the results from the ordinary t-Test and the Mann-Whitney are likely to be equivalent if your sample is large enough.

https://blog.minitab.com/en/adventures-in-statistics-2/best-way-to-analyze-likert-item-data-two-sample-t-test-versus-mann-whitney

David Morse Hello Prof. Morse, Thank you for reminding about the arithmetically complementary may not be precise. I have considered this and I converted the scale so as to see if it can help the data sensitivity and eventually it works.

However, still it can’t prove this conversion is necessary and reasonable. And I did consider about transfer scale to 0-3, the validity analysis results are same as the 1,3,5,7 scale. I chose the later version only because want to keep the 1-7 range same as other measurement scale in this survey.

For using the polytomous item response theory model, I didn’t learn this before, so do you have any recommended tutorials for that? Does that mean that I should separately analysis the data from different groups and keep the original 1-7 scale. Thank you again for your kind reply.

Fatemeh Khozaei Hallo Prof. Khozaei, dank schoen for your advices on how to non-parametric tests and Likert Scale analysis.

Valentine Joseph Owan Thank you for your answer, Mr Owan. While it will also have the imprecisely arithmetical complementary problem as discussed above.

David L Morgan Thank you, Prof. Morgan. My data is ordinal, and from the link you shared, I could only do nonparametric tests because my collected data didn't show a continuous distribution. Besides, since the target group is small, my sample only has 106 responses so far.

Hello again Nan,

Here's some links to try for getting acquainted with polytomous IRT models:

1. https://www.uwo.ca/fhs/tc/labs/12.PolytomousIRT.pdf

2. https://files.eric.ed.gov/fulltext/EJ1246351.pdf

3. https://www.youtube.com/watch?v=1gglVK3a5MA

Good luck with your project.