Questionnaires often contain questions which are similar but worded differently. Usually these questions are located in different parts of the questionnaire, intended to weed out participants who don't take the questionnaire seriously, but I've seen examples where related questions are placed together in a block, as well.
What is the purpose of these questions and, more importantly, how are they analysed?
For example, if the purpose of the survey is to find correlations between different variables on a Likert scale, then how can one go about analysing the data?
Assuming that simple linear regression is appropriate, for example, does one simply try out different 'versions' of the regressor (i.e. the different versions of the same question) and see which one results in the smallest p-value (for $H_0$: $\beta_1$ = 0, $H_A$: $\beta_1$ > 0)?
Or is there some other way to go about this?
Edit: To clarify, I am NOT asking how to conduct hypothesis tests on Likert scales or when I can assume them to be interval rather than ordinal, etc., nor am I asking for how to deal with multiple variables. My question was specifically asking about how similar questions on a questionnaire are dealt with, e.g. if Question 1 is Are you satisfied with our services?, Question 2 is Are you happy about our services?, and Question 3 is How good do you think our services are?
Edit 2: In fact, I don't mind if I get a answer about using logistic regression on true-or-false questions or something. My focus is on repeated questions, not on linear regression or the Likert scale.
Edit 3: Imagine I have four questions like these:
- Do you like our services? No 1 2 3 4 5 Yes
- Are you satisfied with our services? No 1 2 3 4 5 Yes
- Do you think our services are good enough? No 1 2 3 4 5 Yes
- Will you come to our store again? No 1 2 3 4 5 Yes
and I want to know the relationship between how people like our services and whether they'll be back. (Assume also that I'm sure simple linear regression is applicable. I've used each of 1-3 as regressor, found the least-square estimates of $b_0$ and $b_1$ each time, ensured the error is normal with the chi-squared goodness-of-fit test, ensured the relationship is linear with the F-test for lack of fit, dealt with outliers, etc.)
How should this relationship be analysis? If the responses to the first three questions are distributed very differently (say, significantly different mean or variance through Student's t- and F-tests), what is to be done about it? What if $H_0$ can be rejected for one or two questions but not the others - what can be done about this? Thanks.