I clicked on an anti virus scanner pop up on my android? I was browsing Google when a message popped up saying something along the lines of me having a virus. Okay, I'm not stupid. I've seen these on a computer before. I also saw the word yahoo somewhere on the pop up? But, in my frenzy, I forgot to carefully inspect the thing. Anyways, I clicked "no thanks" instead of "scan now" or something, but thinking back, if this was some kind of virus pop up, clicking on either option would have been a bad idea.

After clicking no thanks, I closed the app and turned my phone off. So far, I haven't seen anything wrong, but I am still quite concerned. I have been thinking about backing my phone up onto my computer, and then restarting my phone, however, I'm not sure if that's a good idea. In the case that my phone has been infected, would it be possible for the virus to transfer over to my computer? Should I even be concerned? Has this happened to anyone else? Maybe I'm being paranoid, but I'd like to take as little chances as possible. Thanks.
Short answer
You did the right thing, and don't need to be afraid. That popup was most likely caused by some Javascript on the visited web site to make you download/install something really bad. It doesn't mean you're infected.
Explanation
There are a couple of things to consider. First, if the popup really said &quot;you have a virus&quot;, your reacting was fully correct (and the popup bluntly lying): There are no viruses for Android, at least not &quot;in the wild&quot;. I know, the term got mixed up, and when speaking about Anti-Virus people really mean &quot;an app against all kind of malware&quot;. But no serious AV app would speak of &quot;you have a virus&quot;, as that's technically incorrect.
Mixing in your &quot;fear&quot; from the second paragraph here: exactly that's what matches a virus definition, and makes it different from all other kinds of malware: the ability to &quot;multiply itself&quot;. As you 100% sure have no &quot;virus&quot; on your device, no need to be afraid about that.
For details on the above, please see e.g. Wikipedia:

the defining characteristic of viruses is that they are self-replicating computer programs which install themselves without the user's consent.

There you see why a virus is close to being impossible: on Android, the user is always asked for his &quot;consent&quot; when something is installed.
Now for the last part: Who should have caused that popup? Do you have any AV app installed and active? Your question does not suggest such. So if you have no such app installed, who should have popped up that warning? Android doesn't do that. So the most likely candidate was a part of the site you've visited. That's rather so-called Scareware trying to make you install something bad. Believe me, you did the right thing – and would possibly have been in trouble if you had acted differently.