My teaching evaluations arrived and female students statistically gave me worse scores than male students. Is there any possible explanation?
I would hesitate to draw any conclusions whatsoever from one semester. File this away, and check whether it becomes a pattern, and if it does then think about it then when you have more information.
Although there's not a single incident that you're aware of, I wouldn't be at all surprised if something being "amplified among a group of students" is exactly what happened. It's easy to have a miscommunication with a student that leaves them with a negative impression of you, and for that to spread among their friends. Unless there's a trend in other classes I wouldn't jump to the conclusion that this has anything to do with gender specifically, it may well just be that one group of friends which is mostly or entirely female didn't like you.
Also, I commend you for thinking about this and for seriously considering whether you need to change something in your teaching. I just think you might be overthinking it at this point.
Here are a few possible lines of thought. Of course, we would need much more data and context to know if any were actually the case.
Don't forget the null hypothesis. If you carried out this survey for other lecturers (of each gender) for the same course, other courses, other departments, other universities, would we indeed find that your result is anomalous, and by how much? We may have no reason to think it isn't, but unless we know, we don't really know what phenomenon is under discussion.
How do you know your survey is valid? Which factors in your teaching did you measure? Are they measurable numerically?
As you suggested and Noah responded to, "amplification" is a possibility. Classroom culture is a factor at every level of teaching. I found this especially during practice teaching in a middle school, where the same students and teacher are together all day and it's hard to have multiple atmospheres or moods coexist in the classroom. The verbal and tacit feedback they get from each other promotes uniformity. One class decides they like a teacher, and it's easy to teach the group even if a few students privately feel differently. One class decides they don't, and it becomes very hard to win them back as a group.
Even when the whole class doesn't respond alike, subgroups often respond alike. In the high school classes I'm teaching now, there are friend groups that break along some classic lines, and each group rather than each student tends to have a certain attitude towards the course and the teacher. I could imagine that gender is a possible subgrouping. Such a group was created just recently in my English course on the basis of content when we watched and discussed a movie on how women are depicted in advertising. The overall class cohesion meant it was a temporary divide, but a subtler cause of division could be harder to heal.
Being overly respectful is not likely to be seen as condescending. But standoffishness (even unintentional) is not the same thing as respect. I have an idea of the careful line you're trying to hold by not sitting too close and not shaking hands, and it's a good thought. But consider that a conscious attempt not to overengage can come off as stiff or cold. Some people avoid others because they dislike them or feel disdain for them, which is not the impression you want your students to have.
If you feel more confident that you can comfortably interact with the young men without crossing boundaries than you do with the young women, there might well be a difference in how warm each group perceives you to be. You might even be unconsciously reducing the number of interactions with the girls. Students are highly sensitive to cues about whether their teachers like them.
The same neutral approach could also be an issue in terms of content. Qui tacet consentire videtur. You don't always know what you're saying by not saying anything. I was teaching English in a high school and we were reading essays on gun control. Suddenly, the Stoneman Douglas shooting happened, and the government responded about arming teachers and whatnot. To be silent about it would be to invite the students to construe — on their own, without evidence — what I thought of the issues. So the discussion was opened.
Note that in such a discussion, you don't have to even reveal your own opinions, but give the floor respectfully and affirm what's said and the right to speak of various people, especially those who tend to be intimidated or talked over by the class as a whole. But you can also make direct contributions if you want. It's a great idea to prepare students on these issues that they'll grapple with as adults, bringing insight from whichever field you're working in. Anthropology, biology, history, literature, statistics, business — many fields have inroads if you want to show your hand, rather than hide it, for the positive effect it might have on skeptics.
I think any more requires knowing about your results, your students, and your class.
Here's a suggestion if you want richer, non-useless student feedback from these students, since the people who were there have more insight than you can convey to us here. You could invite a few students who you think were highly engaged and who had good connections with their peers to sit and share more detailed feedback on the class, if they're interested. "After reading through the anonymous surveys, I'm hoping to explore some points further. I think you might have a valuable perspective to offer, based on your participation in class."
You could then ask some open, non-leading questions, not about your results themselves ("Why was there a gender divide?") but about possible factors ("How did you perceive the teacher-student interaction? Did you sense any favouritism?").
You can also ask colleagues, who will sometimes hear from students or even inquire about how the new hire is doing. They may have some things to share through the grapevine. Another answerer's suggestion of inviting a colleague to sit in on a class and take notes on your teaching is also great. I think here too I'd avoid giving them too strong a lead to look for, beyond the premise that you want feedback; whatever they notice will be more significant if it comes up without prompting.
Do keep in mind what you've said — that you don't know what the significance of your results is. (Not that it stops you from making positive moves.)
It could be almost any of the suggestions already suggested, but my hunch from the information provided (in particular, that the complaints "are mostly about the organization of the teaching or the course being demanding"), is that it may tend to be one of two things:
Communication style. You may organize and explain ideas in a style that more typical men in your culture use more and follow more easily than typical women in your culture do.
The minor/major point mentioned in the comment by @darijgrinberg . For example, if your male students are mostly majoring in related subjects, but your female students are mainly taking your course to meet some requirement but they're not particularly interested in the subject, or if they have less experience with courses in your field, your course may seem less intelligible to them because you may not be explaining things for people less familiar with the assumptions and language of your subject, making the teaching seem more disorganized and harder from their perspective.