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Why are there numbers at all? For two reasons. One is that quantitative data confirm the argument or story line that otherwise might be told only logically, dramatically, or even poetically. More precisely, the numbers document the case by providing occasions for disconfirmatory evidence to show up; when it fails to do so, we gain confidence in the argument. From this perspective then, this study is only secondarily quantitative; the numbers are the court of last resort, so to speak. The second reason for numbers is to aid in discovery.

This change over is my main focus, but the degree of pre-1960s "establishment" to be "disestablished" differed by denomination and by region. Hence, the abruptness of the shift can be highlighted by showing where it has been felt least as well as where it has been felt most. The data on which my argument rests come from telephone surveys with 2,620 adults, randomly selected in the states of Massachusetts, North Carolina, Ohio, and California. (The interview schedule is reproduced as Appendix B.

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A Mathematician Explains by Logsdon M.I.

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