USCF is the chess federation for all of the United States. My question is if there is difference in a rating given in one state and another. For example, is a 1900 rated player in California on average better or worse than a 1900 in Indiana? I'd be interested in people's insights and/or data which draws you to your conclusion.
Ratings are not exactly "given", but determined from the outcome of games.
If 1) there is enough mixing (players from Indiana play against those from California, etc) and 2) if many games are played, the ratings should be comparable between states.
Conversely if a group of players is separated because they only play among themselves, this can lead to distortion of their ratings compared to players outside their group.
I can't speculate on whether ratings are worth more in one US state than another but I can outline the mechanism which could explain that phenomenon if observed.
When two players play a graded game (in an ELO type rating system) then the rating exchange is zero sum. That is, one player's rating loss is the other player's rating game. If one player's rating keeps on rising (perhaps because he is young and improving rapidly) then on average his opponents' ratings are declining even if their playing strength remains the same. Similarly if a highly rated player's rating keeps on declining (perhaps because of increasing age and declining health) then on average his opponents' rating are rising even if their playing strength remains the same.
In a state (or any particular area if you want to apply the analysis to other countries) rating points are "created" when either a new player starts playing rated games or when a rated player moves to the state / area. In ELO style rating systems when a new player receives a rating for the first time it does not involve removing rating points from his previous opponents. They are created out of thin air.
Similarly rating points are "destroyed" when either a rated player moves from the state / area or a rated player permanently gives up playing rated games.
This suggests several scenarios in which relative rating inflation / deflation could occur.
An economically poor area is likely to have new players come through the system as juniors, improve, reach say 2200 - 2400, finish school or university and then go off to the big city to earn serious bucks. Players in this area are likely to be underrated. Conversely the big city players are likely to be overrated.
A vibrant chess area which has lots of new players learning the game and joining / boosting the rating pool is likely to have rating inflation. Conversely an area where players are aging and stopping playing through poor health, family or work pressures and which has few new players learning to play or moving to the area is likely to have rating deflation.
The problem is that players do not play enough players in other regions to even out discrepancies due to number of kids and how fast they improve.
And while perhaps fixed/improved now, initial ratings make a huge difference. If everybody played in a national or big regional open for their first games they would have a higher rating than if they only played a small local tournament. This was a big problem early on in the ratings.
Also good players tend to group in the same places. EG When I played back when most of the masters were in NY. Some states might have a couple but the bulk of them were in NYC area where the TWO major chess clubs were. In DC there was one good club but the strength was far below NY.
Some states just do not attract people so they will have fewer strong players who like all people would prefer better weather and jobs where they live.
When I played in tournaments the south was always much easier then in the north. I was in DC which was middlish between those.
The same is true for Bridge players. The ones in the south are much easier and many people only get their LifeMaster (bridge) title after retiring to Florida where the competition is easier. Partly due to aging but overall the southern players are noticeably weaker.