And those "website" invitations do not produce valid results. I know of no successful station that even tabulates such results. It's strictly done for listener involvement and loyalty building.
Based on some of the responses, I will add (again) that random research does not give valid results. It may, however, help spot trends and has some value particularly when radio station users also spend a lot of time discovering new music online. In other words, it can give a "heads up" warning about new songs or artists or even trends, but can't tell you how to determine current music rotations.
I'm always fascinated by research. When I am asked online to take a poll or survey, I purposely put my age in the range I believe the pollster is looking for, typically a 44 year old male "with some college" and employed fulltime and with (if asked) an income between $45 k and $60 k annually. That gets me in, and I get to look at how the research is structured, the wording of questions, the options on responses and so on.
But the fact is that the researcher has no way of knowing that I ceased to be 45 over a quarter century ago...
This is one of the issues Nielsen fights every day in the PPM world. Families get rewarded only if everyone participates. So, if someone does not cooperate and the family wants that new microwave or some other premium or incentive, they have another family member carry the meter. Or one person alternates their meter and the other person's meter. Or they tie the meter to the dog's collar. Or a ceiling fan.
And the PPM participants are carefully recruited. Yet there are all kinds of pitfalls that can distort the research. When you have self-recruited participants, the distortions multiply. In any field, volunteers are not representative of the overall population. Are the fine people who volunteer to help the Red Cross do blood drives the same as people who don't do community service?
Given the opportunity, getting listener "votes" on new songs or getting them to do a "dream set" of 10 songs or such is a great promotion. Some of the results can be used... I've used the "dream set" to do once a day a music sweep but the set was picked to match the station's library first. And the person who picked the set got a T-Shirt that said "I programmed WWWW's Dream Set" (not my real wording, of course). Done today, I'd feature the person on the station website and paint them as "the WWWW listener family... join him/her/them every day on WWWW for your favorite music".
But in the end, that raw un-recruited research data is not valid except for things like the "dream set" or as a hint about trends and breaking songs. But it's fun for some listeners, and can help less experienced programmers understand the audience a bit better. So it is not invalid, totally.
In Spanish, there is an expression "bueno el culantro pero no tanto". It means "Coriander is great, but in moderation". Same goes for self-recruited research... it can be a tool but not the final product.