if we had the data, we could compare the proportion of premium members in the cheaters list with the the proportion of premium members in the population of chess.com members and carry out a chi-square test to determine if the cheaters list is a random sample (with respect to the proportion of premium members) or whether it contains a bias.
Do premium members get a free ride?

if we had the data, we could compare the proportion of premium members in the cheaters list with the the proportion of premium members in the population of chess.com members and carry out a chi-square test to determine if the cheaters list is a random sample (with respect to the proportion of premium members) or whether it contains a bias.
Wouldn't work because the premium members and non paying members are self-selected groups, not random. They won't neccesarily cheat at the same rate.

the population is self selected of course but we can test to see whether the sample was taken randomly, i.e. whether the proportion of premium members in the sample is sufficiently different from the proportion of premium members in the population (of chess.com members).

i have read more than once in various places on chess.com where someone claims that chess.com is less likely to ban premium members than non-paying members. is there even a grain of truth in these claims?
No truth in these claims nowadays. People used to say this in the past but am aware of numerous premium-members who have been banned.

If you cheat and they catch you, you'll get banned, 100% guaranteed.
This is the bottom line.

the population is self selected of course but we can test to see whether the sample was taken randomly, i.e. whether the proportion of premium members in the sample is sufficiently different from the proportion of premium members in the population (of chess.com members).
Don't see how its possible. Just the simple fact that non paying members are more likely to be recreations of the same individual trying to cheat again and again (since there is a monetary cost to doing this while a premium member) would blow statistics out right there. if you don't know the extent to which this is happeneing then I dont think you can determine anything.
[Please restrict discussions of cheating to the Cheating Forum - mod]
http://www.chess.com/groups/home/cheating-forum
I know people who have been banned and have no idea why. They weren't cheating.
Yeah.....sure
lol