For me, the golden, unbreakable rule is, never use any statistics if you do not really understand what they mean! This might seem obvious, but it is surprising how frequently statistics get misused or misinterpreted to support an argument that actually has no real basis in fact. The famous saying that there are three types of lies – “lies, damned lies, and statistics” is attributed to Prime Minister Disraeli, but when properly used, statistics can be clear, unequivocal, and very supportive in communicating complex data simply. The main problem(s) are often started by people deliberately selecting the information that they want to hear and then seeking for statistical back-up which looks impressive and difficult to challenge. Secondary problems occur when people either do not properly understand what the real statistics are saying, or when people choose to deliberately select or twist the statistical information which seems to support their preferred point of view. Ultimately, all three problem areas both devalue the use of statistics and also take us even further away from a clearer understanding of the situation that we are trying to interpret and communicate.
A good “rule of thumb” is to stick to the simplest means of statistically expressing the results that you want to communicate. Percentages, pie-charts, and histograms might look fairly unadventurous if you are trying to impress an examiner, but they have the advantage that they are quick to produce, clear to interpret, and easy to understand. Fancy calculations may look more impressive, but they are frequently harder to produce, more difficult to fully understand, and have a greater chance of either the creator or the reader making errors of interpretation. A common error is to quote percentages rather than give simple numerical values for small population samples. If 7 out of 12 of your interviewees agree, say “7 out of 12 agree that…” rather than “58.33%…” A difference of 1 person immediately gives an 8% error and is clumsier. Keeping it simple gives both a truer impression of the data and an easier comparison with other results. Similarly, I have seen some very impressive and complex diagrams, complete with 3-D shading and vector trends, which actually do not tell us very much at all because the detail is lost in the artistic flamboyance. They look fancy but add nothing to the discussion.
Quite often, certain disciplinary areas will have their own conventions as to which statistical procedures are common, or preferred, and how they are presented. The supervisors should be able to advise on these common standards, and the benefit is usually that the new research data can both make use of earlier research results, and can be easily contrasted and compared with already published data in the discipline. Some statistical procedures can look complicated to calculate, but are actually quite straightforward to use. All universities will have opportunities for research students to attend courses on statistical methods which are appropriate for different subject areas of research, so students should get training early in the research to avoid any subsequent false starts. There are lots of self-guide short courses on the web, and of course in text-books, but self-tuition is also open to misunderstanding, so it is always best, in the first exploration at least, to work through the procedure(s) alongside someone who is already very familiar with the statistical technique(s). Bear in mind, contrary to some current political rhetoric, there are no “alternative facts” simply facts that you acknowledge and facts that you might prefer to ignore. Research is about improving knowledge, not picking just the bits that you like.