The short answer: No. Just don’t do it.
The longer answer: If your English is strong enough for you to convincingly insert made-up statistics into your essays, then it is probably unnecessary for you to do so. Basically, if you write at a solid Band 7.5/8+ level; have experience citing statistics in English in your writing for work or school; and want to have some fun with the test, then by all means, go ahead and make up a study or two. If you are among the other 97% or so of test-takers, focus on improving your grammar, vocabulary, organization, and ability to explain your ideas clearly.
I suspect that for most test-takers who decide to invent statistics or other types of research, the thought process goes something like this:
Research from prestigious universities looks very impressive, so if I make up a study from, say, Oxford or Harvard, then that’ll make my argument really strong. And a common number like 75% will look fake, so I’ll make up something really random like, I don’t know, 68.3% because that’ll seem more convincing.
If you’ve been thinking of doing this, please be aware that not only will countless other IELTS candidates use the exact same logic (there is nothing original about this strategy!), but also that citing invented statistics from World Famous University X will by itself do nothing to strengthen your essay or impress an examiner if your writing contains many errors in grammar and vocabulary and is not organized in a clear way.
You earn high marks in Task Achievement and Coherence & Cohesion by providing solid points to support your argument, and by explaining those points in an appropriate amount of detail (not too little, not too much). The strength and internal logic of your reasoning are what count—there is absolutely no expectation that candidates will bring specific, statistical knowledge to the exam, and so, contrary to the assertions of some tutors, this type of evidence will not help you obtain a high score.
Then, there are the linguistic traps. I’m going to focus on two of the main ones here.
The first involves articles. Although this may seem like a very subtle, picky point, it is actually not a small matter: names of English-language universities are governed by strict rules involving the use of the, and they may differ between institutions in the UK and North America.
For example, you can say The University of Oxford or Oxford University, but you cannot say University of Oxford (without the article) or The Oxford University. On the other hand, Harvard University is always Harvard University, not The Harvard University or The University of Harvard.
While one misused article or misstated name will not of course ruin your score, you should be aware that these kinds of avoidable mistakes can contribute to a poor general impression. If you are writing about a world-famous institution, there is an expectation that you will know how to refer to it. I point this out because I have seen university names mangled in many essays, and because difficulty in this area is virtually always accompanied by serious grammar and vocabulary mistakes.
The second issue is stylistic. Unless you have a lot of experience citing research in university-level essays, you will probably not be familiar with the types of standard phrases used to introduce this kind of material in a sophisticated way, e.g., As a team of Cambridge University researchers discovered… or Recent findings from a study conducted by researchers at the University of Alberta suggest…
Before you get any ideas, if you do try to learn such “formulas”, they will stick out as obviously memorized if the rest of your writing contains noticeable errors in grammar and vocabulary—which, if you’re looking for easy ways to game the test, is almost certainly what you actually need to worry about. And sticking to simpler constructions (e.g., For example, professors at Oxford University found that 37.2% of people try to recycle every day) will do little to move you into a high band if the rest of your essay is not already very strong.
To be clear, it is perfectly fine to bring your general outside knowledge into the test—in fact, when the directions ask you to consider your “knowledge or experience,” that’s precisely what you’re being asked to do. It’s fine to make general statements such as, Research has consistently demonstrated that the vast majority of dieters quickly regain the weight they have lost or A recent article from the BBC emphasized the difficulty that dieters have in keeping weight off, no made-up figures needed.
If you are worried about not having enough to say about common IELTS topics (e.g., the environment, technology, education, health and fitness), then you need to make time to read about them in English every day. If you actually have actual knowledge about a subject, then the question of whether you should make things up becomes irrelevant.