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I realize that "school" is also a collective noun in its singular form... which may account for the greater use of the singular. I'm just thrown by the pattern, or lack thereof... mainly in no searches showing for the plural California public schools.
The search stats are monthly, for "Exact Query Matching: Show my ad when a search contains these keywords and no others." 4,200/month is a threshold value, so I can understand that if "California public schools" was hovering around 4,200 it might vanish entirely. Still, the pattern doesn't make sense to me.
schools -- 2,781,300
public schools -- 259,700
private schools -- 92,200
California schools -- 50,300
California public schools -- 0
California private schools -- 4,200
school -- 11,335,900
public school -- 134,800
private school -- 80,000
California school -- 96,900
California public school -- 8,400
California private school -- 0
I'm also guessing that there should be some correspondence between singular and plural ratios... Here too, the ratios puzzle me. I expect anomalies in Overture data, but don't expect them from Google. Is it possible that there are anomalies in Google data too, or am I greatly oversimplifying?
Maybe I'm about to answer my own question.... but thinking out loud, I could say that between schools and California schools, the ratio is 50:1. Between public schools and California public schools, a 50 to 1 ratio would give a little over 5,000 for the latter, but if the threshold is 4,200, it's not inconceivable that a slight shift from 5,000 could make this appear to drop to 0. Looking at private school, I noticed in Overture that when private was used as a modifier for school(s), state names appeared much more frequently... so, back in Google, California private schools showing 4,200 searches is a little more than twice what one would expect at 50:1, but maybe not unexpected.
Etc etc... I could make plausibility arguments for almost all the stats this way, but it does feel like an exercise in rationalization... and I'm still wondering about the data....