Back to the female/psychic question, cultural attitudes in the Unity toward young girls and boys could also play a role. 

More specifically, perhaps the Advent believes girls are stronger in this regard and these subconscious attitudes reinforce their own cultural gender roles (subconscious thoughts being shared more strongly in the Unity) and children could be encouraged to take different paths based on this. Of course, different sects may have different ideas about this as well.

We've had stereotypical gender roles in our cultures historically, although that has been changing.

Well if you actually look at the Advents children indoctrination into society it is actually severely liberal. The children grow up to be what they strive to be. But in my opinion its genetic, remember the advent are post-human but still human so most likely they have the same structure as us as well. And if you study on the woman brain they actually have much better multi-tasking ability then us males.

I think it should be noted that males secrete less serotonin making us more fidgity. Oxtocin is also more prevalent in females making them have more quick responses to situations.

Not entirely relevent to the discussion, but I kinda disagree with this. First of all, everyone is different; such blanket statements for some reason always feel too narrow for diversity to play a role when it is usually the deciding factor. Now, your right that on average statistics show that women excel at multi-tasking, and that is backed up by everyday experiences. However, I believe that men are, in general, just as good at multi-tasking, it's just focused in a different manner.

For example, I enter a room and immediately size it up, look for potential hiding places, see who might have a weapon, what might be laying around to use as a weapon, what the best escape route might be. When I'm trying to solve a problem, it often helps to think about a bunch of other problems; it helps make connections, and gets me to the bare minimum solutions much quicker. I often find myself imagining the feel of objects as I push it, lift it, or as it falls.

You might not have exactly the same sensations, but I would point out that these are difficult to discribe, as they are more 'thoughts' than words. And that is the key difference I think between the average man and the average woman. Women's multi-tasking is conducive to their social talents, and I think men's multi-tasking is conducive to their tactical talents. The tests/studies, being taken by someone not inside your head, thus reflects higher marks for the more sociable type.

Now, as I said, this is my opinion. For the exact same reason, I can't know whats going on inside a woman's head (many have tried :p), and I could very well be wrong. I do think that regardless, it is an important observation.

And with Unity being a "social thing" it would explain better why women rise to the top in an Advent culture.

oh, of course. Theres also much less need for those male talents in our modern society then there used to be. I would believe it if someone said the male Advent do have a practical niche for tactics. However, it doesnt have to be that way. To be able to best utilize resources, you have to know how to use them yourself (you don't have to be an expert, but you should be able to handle yourself with them). Depending on how far down the ladder males are in Advent society, they might not have the exposure, experience, and/or talent to use the resources they would ultimately manage.

However, that might be looking at it from a militaristic viewpoint. I suppose that if the Unity is a religion that manages to permeate every facet of Advent society, including technology and war tactics; That would play into womens strengths as well, no matter the males status. An example of this might be the Ori from stargate, and I've always had the same vibe with the Advent as the Ori.

If you don't know of the Ori, they are an extremely relgious society reminiscant of Catholicism in the dark ages. All other beliefs are evil. What makes them dangerous is that in alot of ways, their beliefs have justification. If you are devout, you might one day become a prior and be granted powers of telekinesis, mind reading, and instant healing. Both biological and technological knowledge is used to sell the belief that these powers are the result of envoking the gods. The truth is the same as the original stargate: advanced beings manipulate these beliefs and those that believe it through the use of their advanced knowledge.

This brings us back to the original question: How does the Unity and/or Advent powers work, exactly? After you have that, the Advent religion can layered to bring additional story interests and in turn reveal more about the Advent society. Do they know how their powers work? Does the average Advent citizen know? Are there Advent secrets? Can there be secrets in a telepathic society? How pervasive is the telepathy? Do they have a hive-mind, strong subliminal messaging, or is the joint telepathy like people on the internet (although, one could argue that's a hive-mind )? How do they 'research' things? How do they view the beliefs of others? Where do they go on Christmas?

Well you even said it yourself the common statistic says women are etc etc. Might have effect, not saying males are bad at it, im sure some advent males excel over most advent females. Im just saying this is to help the Op

At the end of the day the men dominate the females in the bed-room.