I'm female, and I'm honestly not trying to be PC when I say this--everyone needs to take safety precautions. Not just women.
The only two stories I know of where someone was attacked during a run happened to men, who were mugged.
I'm a woman. I live in a metropolitan area and I try to run in the day time--not sun rising, or sun setting, but daytime. (this can be hard for those who live in hot climate). I run on a paved trail that usually has a lot of bike and foot traffic. I always bring my phone and I've never felt unsafe.
I'd say try to find a buddy, or a space that you know will be populated. Honestly, running in populated areas is important for a lot of reasons. You could have a health issue, or need help. Not good to be out in the woods miles away from anyone or any cell service.
Switching up your routine is important too. Don't do the same runs every time you go out.