So I'm negotiating my starting salary at a company where I've been freelancing for 6 months. I didn't think my salary was high enough, so I did some research - on Glassdoor and Payscale - and found that my pay was 5k below the median for my skill level. I mentioned this in a general way, and she asked me to send her data. Where is the best place for me to collect data like that? Can I just send her screenshots from those websites? It looks somewhat unprofessional
When I was in my corporate job, we had this handy trick to quash people's questions that we didn't like.
Whenever, in a meeting, someone wanted to suggest something or had a new idea, we used to ask for numbers or experimental results or data to support that idea if we didn't like the idea. Most of the times this discouraged the person because getting the data or experimental results means extra work. One may deem this as a dirty trick. But it mostly works.
In my opinion, it seems that she is trying to indirectly quash your action. Looks like she is trying to discourage you from justifying your salary raise.
So, instead of justifying your raise by using data collected from the internet, I would recommend that you use a different justification. If you were really that indispensable to the company, they wouldn't have asked for the aforementioned data.
If you're making a claim (in this case that the median salary for your skill level is 5k higher then their offer) then you have to be prepared to back that claim up. What they are asking for is not unreasonable. If you aren't confident enough that your supporting data will stand up to scrutiny, then why should they be?
The obvious course of action is to provide them with the same data that you used to arrive at your claim in the first place. If that's screen grabs from Glassdoor, Payscale etc then so be it. Probably a better way would be to give them the steps you took to get to that info as well e.g. "I searched on Glassdoor using the following criteria x,y,x - if you try this yourself you should see the same as I did in the attached screenshot".
If you are in the US, take a look at https://www.bls.gov/bls/blswage.htm which has data collected by the US Government about the average salaries for different jobs and in different states. While this won't give you detail about skill level, it will show you the average salary (and I think the full range) within your area.