# Combine results from many likert scales in order to get a single response variable - PCA? CFA?

I'm helping a friend design his research. He'll use a Google Forms questionnaire with several questions (from 0 to 5, Likert scale) to assess anxiety of students' before taking two different tests. The questionnaire has about 10 questions, all underlie anxiety and all go from 0 (strongly disagree) to 5 (strongly agree), and students will take either test A or test B (the tests are the same, but in different languages). The question is to verify if anxiety can be explained by type of test. Hence, I'm thinking about performing an Ordinal regression (using R's clm) to test it in a second moment.

• The thing is, after we have the data, what would be an appropriate approach to combine all results into a single "anxiety" measure? in order to be able to fit the model afterwards?

• Hypothetical data:

ID      test   Q1 ... Q10
PART1    A      1      3
PART2    A      2      4
PART3    B      5      1
PART4    B      4      2

### We'd like to model "Anxiety" taking into consideration Q1 to Q10:

clm(ANXIETY ~ test)


Notes:

• sts will take either test A or test B, so this is not a repeated-measures design
• I've thought of running a pilot study with a few sts and run a Cronbach's alpha to assess reliability/consistency, but I still don't know what to do afterwards to combine all questions into a single variable.
• This is more of a theoretical question, but R tips would be much appreciated. Thanks!

I've seen many similar questions here, hopefully this isn't a duplicate, but I still don't know what path would be the most adequate. like this from 2015, this from 2012,this from 2017 and this from 2015

• Seems like a fairly straightforward application of structural equation modeling... Commented Nov 26, 2022 at 16:30
• One aspect of this is that one can wonder to what extent this should actually be determined by the data, i.e., to what extent the data contain information about how an overall scale should be put together. For example, if two items are highly correlated, this may mean that they're measuring the same thing (in which case they should probably be implicitly downweighted, as PCA will do), but it may also mean that they measure really different aspects of anxiety that happen to be correlated in the data, in which case they should probably not be downweighted. Commented Nov 29, 2022 at 11:48
• But why do you need to combine the 10 items into one measure (so early)? If Q1 in A correspinds to Q1 in B (and so further), why not test the effect of AvsB on each item separetely? Commented Dec 4, 2022 at 11:30