This question is relevant for people who suffer psychologically and who consider to take up a psychotherapy. There are indeed several treatment options. In Germany, four types of psychotherapy are scientifically accepted by the authorities and are paid by the health insurcance. So, what type of treatment should one choose?
But this question is also asked by stakeholders and politicians - they have to decide how the limited money in health care is spend most wisely.
Now - has it any effect? We have to formulate this question a bit more precisely to be able to answer it well.
A well-worded question is for example: "Are patients with complex mental health problems who receive analytic psychotherapy with at least 50 sessions, after that mentally healthier than patients who received another treatment?" The answer is: Yes. Scientists gathered all studies together which had investigated this issue and analysed the results (Leichsenring, 2011, British Journal of Psychiatry). This is called a meta-analysis. The researches found 10 studies for their meta-analysis. In total, 971 patients had been treated in these studies. All these studies combined the authors concluded that long-term psychotherapy is more effective in this group of patients than short-term psychotherapy.
And what about short-term psychoanalytic therapy? Here we also have a meta-analysis (Abbass, 2014, Cochrane Library). The authors collected 33 studies with a total of 2173 patients where short-term psychoanalytic therapy was compared to care as usual, to waiting or to minimal contacts. Taken these studies together, we see that short-term psychoanalytic therapy improves psychological suffering in many areas: the patients were less depressed, less anxious and felt better overall compared to patients who did not received analytic treatment. Somatic symptoms however could not be reduced.
There are of course many more questions we can (and should) ask to be able to judge the effectiveness of analytic psychotherapy. We need many high-quality studies for that.
Sometimes it is difficult for non-experts to understand scientific studies and papers. And often it is also difficult to get access to those papers. To help them understand what researchers found out, the International Psychoanalytical Association provides an overview of published studies which is updated regularly and free of charge for all, the "Open-Door-Review". Experts find that this provides good evidence for the effectiveness of psychoanalyis.
Another excellent source is the Cochrane Collaboration. Here, high-quality studies are searched and analysed in a systematic way (so-called "systematic reviews"). Each review is summarised in an easy language so that non-experts are able to understand it. For example, the study of Abbass (2014) mentioned above can be found here.