Basically, you must start with your research problems/questions which if quantitative and if to be taken from a random sample, will be the bases of your hypotheses. Your statistical hypotheses will guide what statistical methods you are going to apply.

The shape of your data when plotted, and their measure could help you determine whether to use parametric or non-parametric tests.

I recommend that you begin by defining your research questions.  Like maybe one research question is something like "Which item on the survey have the biggest difference between University and Industry?" or another one might be "How does University responses agree with Industry responses?" or something like that. Only you can define your RQ's because you know what you're measuring.

Once you have your RQ's, you can then find a statistical test(s) for each RQ. If you have questions about this, you can post a new question with more information and it will be easier to answer that more specific question.

As far as parametric and non-parametric, I would encourage you to do both when possible. Hopefully, the results will match (both significant or both non-significant).

Lindsey -

Part of your question seems to be answered by describing the difference between a parametric test, and a nonparametric ('distribution-free') test. The former tends to have more 'power,' as distributional information is used. However, it may be that this is not always well justified, and this can sometimes harm your analysis/analyses to a degree. The latter, on the other hand, will lose information that you do have. You mentioned sign tests. These are notoriously 'under-powered' in that you are using very little of the information that is actually there. I once designed a test that was 'sign'-like in name only, because it actually used more of the information available than is typical of a sign test, and a leading nonparametric statistician got very upset before even knowing how it worked.

Within both types of tests above, you also have to see which test or tests will fit the application at hand. Some are for paired data, some for single data sets. Each is designed for a different purpose, though sometimes you may use more than one for a given application. The same test might be used for vastly different subject matter, or different tests used for data from similar sources. You have to look at the way each test works to decide if it is good for your purposes. If you search the Internet for each test by name and/or find a good textbook, the necessary conditions should be described.

Typically a textbook will tell you that power is important, and describe Type I and Type II errors, but then proceed to just look at isolated p-values, and only look at power when comparing tests. This is a big problem. A null hypothesis may typically be rejected by simply having a large enough sample size, but with a small enough sample size, it won't be rejected. That is why when testing to a given level, you should not use the same level in all cases. It depends upon your sample size. For some historical, and not justifiable reason, people tend to pick 0.05 for everything. That is not a good idea. Typically hypothesis or significance tests (whether from a Fisher or Neymann perspective) are misinterpreted. That is why I suggest using confidence intervals wherever possible. If you use p-values, it is best to get corresponding p-values for more than one simple hypothesis, as in 'sequential hypothesis tests,' and/or do some other sensitivity analyses.

A link is provided regarding misinterpretation of p-values.

I hope your project is enjoyable.

Cheers - Jim

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