How to choose the best statistical analysis

#1
Hi Everyone!,
I am currently doing a study and as part of it, I have to develop a questionnaire with the following structure: Given a change in "Factor A" how will it affect "Factor B"?. I have realized that I have many factors (and therefore my questionnaire is quite long). Then, I would like to perform a statistical analysis to check if some of these factors are independent so I can eliminate some questions, and therefore reduce the questionnaire's size. For instance, if after an statistical analysis I obtain that Factor 1 and Factor 2 are independent i could eliminate 2 questions: (1) Given a change in "Factor 1" how will it affect "Factor 2"? and (2) Given a change in "Factor 2" how will it affect "Factor 1"?

To perform the analysis, I have data regarding factors presented in past accidents as follows:
- Accident 1: Factor 1, Factor 2, Factor 4, Factor "n"
- Accident 2: Factor 2, Factor 3, Factor "n"
...
Is there any statistical test that would allow me to determine if two factors (e.g. Factor 1 and Factor 3) are independent by considering how often they appear together in an accident?
 
#2
There are a couple of things that are important to consider here, and they're based in a couple of questions you should ask yourself as well as some considerations. Most of these questions/considerations could be answered by understanding the specifics of your analyses (i.e: what is your actual project, data being collected, etc.).
  • What kind of data are you getting from the questions?
    • Quantitative? (ie: Are you asking, "On a scale of 1-5, how does this make you feel?")
    • Qualitative? (ie: "Which of the words best describes how this made you feel" in which you would then look at the frequency of each answer as quantitative data)
  • Are your "factors" the questions themselves, or are multiple questions relating to specific factors
    • ie: Is "Factor n = Question n" or is "Question 1-3, 7, 10 = Factor 1"?
So before helping you further, we'd need answers to those questions, as they're all important questions!

Right now, I think that the only way to figure that out, BEFORE giving out the questionnaire, is to non-statistically ask yourself whether or not you can find questions that are redundant or otherwise irrelevant. From a statistical standpoint though, the only way you're going to figure out which are important, independent, etc. is to collect the data and analyze it afterwards to figure out which questions can be considered unimportant/redundant/irrelevant. Note that this would be analyzed POST-questionnaire. I think that this could be really helpful though, because it will allow you to reduce the number of variables/factors going into your study. It will also help your data analyses, because you would ideally want to have a larger sample size than you do factors/variables (meaning there are more people answering the questions than questions themselves).
 
#3
Hi everyone,

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