SPSS contains several tests which (almost) all have different 'assumptions'. These assumptions are confusing for students, which is understandable.
The assumptions of the several tests you'll find at the description of these tests on this website. One could compare SPSS's assumptions with the driver's licence; in order for you to drive (to analyse a test), you will have to meet some conditions (assumptions) of the vehicle (SPSS test). If you don't meet these conditions, you will not be able to drive, because you would cause accidents. While using SPSS, off course you won't cause any accident, but the possibility exists that you will draw the wrong conclusion from the test.
Not every SPSS test has these strict conditions, as getting your moped licence doesn't have the same conditions as getting your driver's licence. Some test don't have any assumptions at all; for the same reason you don't need a licence to walk or to ride a bike. These SPSS tests without assumptions are 'non-parametric' tests. The functions of the several tests are in some cases different and therefore the assumptions may vary. To get your sailing licence you will have to be examined in an different way than getting your driver's licence.
Normality is one of the most occurring assumptions; this can be compared by driving on the right-hand side. The assumption of normality is a made in order to establish a normal distribution of the population being researched. A normal distributed test has the assumption of normal distributed data from the sample; this can be compared to the fact that everybody knows to drive on the right-hand side in traffic. Conducting a test (assuming normal distribution) with a sample which is non-normal can be compared with traffic in which people don't assume driving on the right-hand side; either way you probably won't get far. Unfortunately this is not all to it. When doing your thesis you'll probably have to deal with your mentor or professor.
Like different traffic regulations per country, different mentors apply different assumptions. This doesn't have to be a problem. When you know in which country (mentor) you are, you can adjust to the regulations (assumptions) which stand in the country (mentor). It's not always clear how different mentors deal with different assumptions; you'll have to try and find out. A good tip is to have the mentor confirm his reaction by email; this way you can fall back on those emails, when things are getting unclear about the assumptions. Bear in mind your mentor is the one who will criticize your work; don't correct your mentor about assumptions, one might not be well informed and doesn't like to be put right. When your data doesn't meet the assumptions and your mentor will argue that fact, you'll unfortunately have to apply a non-parametric test, like you'll have to ride a bike or walk when you don't have a licence. There's an alternative for every test; we'll elaborate on that on this website. In our opinion one should not take assumptions to seriously when it comes to student theses. Assumptions are formed for academics in which content is the most important issue.
In science very strict rules are applied when it comes to making a scientific assumptions and breakthroughs. Your thesis should be more of an exercise in which you can show you are capable of researching, formulating hypotheses, analyse these hypotheses (SPSS) and draw the right conclusions from these results. It's not your goal to create a scientific breakthrough when writing your thesis; this off course would be great, but it's not realistic to assume. Unless great violations have been made (one wouldn't put a blind man behind the wheel), the information about the assumptions not being followed (it's easy to spot an instruction car) should be sufficient. It's however important to motivate you choices; this way you can show that you know what you're doing. Furthermore 85% of the SPSS courses elaborate on tests with assumptions; most nonparametric tests are often not being taught. In comparison: it shouldn't be a problem for you to take your driving examination in a different car, but it's easier to take the exam in a familiar type of car.