I think it can swing both ways.. it's pretty much a given, that women like to shop, but not all women like to shop online, and I am pretty sure that amongst the ones that do, that they are more than capable of paying for their purchases themselves.
Personally, I like to shop online because I find that the "brick-and-mortar" stores charge higher prices for the same stuff.. Some stores, such as Best Buy, even have the nerve to charge top dollar for something that is not only considerably old, refurbed, but that you can get a newer, more up-to-date model of the same type, for LESS than what you would pay for that item at the store.
That was the experience my husband and I had when we were looking to buy a car alarm. We decided on the model, and then I did my homework online and found a place that not only sold the same model 80% less than what Best Buy was charging for it, and BRAND NEW, (while Best Buy was selling it refurb'd) but they had the newer unit, 3 models newer than the one we decided on, at 60% off the price of what Best Buy was charging for the older model.
So, I added the newer model to my cart and was about to purchase it, when, I saw that the place that was selling it online, had 2 locations in Long Island. So, I called the guy to find out if it was in stock, refused his upsell because the only difference between the one we wanted and the one he was trying to upsell, was the remote. All of the core features were the same. (I checked this on the alarm manufacturer's website itself beforehand.. And I didn't think that the pretty, color LCD screen on the key fob justified the $150 jump in price.) after he told me that it was in stock, my husband and I drove over and picked it up.
Shopping online helps me to get more bang for my buck.. and to be a more informed consumer. If I hadn't done my research, then we would have ended up paying more money at Best Buy for what would have been a mediocre alarm system, and we would have had to wait at least 2 weeks for the free "basic install" from Geek Squad, as opposed to saving more than $250 and then getting it installed by our mechanic the same day for $130.
I also like shopping online because I can use discount or coupon codes at checkout which gives me more opportunity to save on merchandise that has already been marked down in price. So I just end up saving more money on the total cost, as well as offsetting the cost of shipping and any applicable taxes, although if it clothing then I don't have to worry as there is no tax on clothing < $150 in my state.