Unfortunately, I am the expert on anal glands
I have expressed a great deal of anal glands with dogs. I dont know statistically, but I didnt notice that male dogs had a bigger issue with this, it seemed equal. My female Yorkie has them done once a month. But I do know that small dogs seem to have more problems then bigger dogs. I would say that for every 10 dogs I have expressed, one has been a big dog.
Anal glands are two sacs just inside dogs anus's (at the 3 and 9 oclock position), and fill with the worst nasty smelling liquid I have ever smelled in my life. Most dogs dont have problems and can express this liquid (or sometimes a pastey type consistancy) naturally while defecating.
If your dog is smelling foul even after a bath, scooting their rear end on the carpet, or licking their behind, this may be a sign that they may need to be expressed. Atleast where I worked, we didnt express them unless there was a problem, but some groomers might. A Vet or a groomer can easily do this for you.
Unless you want me to, I won't go on about how you can express them on your own, unless you ask, because the smell can be so bad that the person will puke.
BTW, My dogs stools do not differ depending on how full her anal sacs are, and atleast I have never heard it making any difference about the hardness of their stool.