OK--I struggled through some articles on population genetics and statistical methods and got some input from the FTDNA forums. I think that the Oracle analyses use several methods: factor analysis, cluster analysis and the main approach, which is called principal component analysis. It works something like this.

My pattern of values on a sample of Ancestry Informative SNPS (markers) is compared to a reference and the variance calculated. Then my pattern of variance is analyzed against those of a series of populations whose values have been established by a similar comparison. That analysis shows the percentage of the variation in my values that is explained by comparison with the various reference samples.

Oracle gives the best single population or major/minor population match. The smaller the number after the listed population the better the match.

Oracle 4 gives you several possible of how the various reference groups might combine to make up your variance pattern. It breaks the report down into 1, 2, 3, or 4 population group matches.

Oracle-x breaks you down into several populations by percentage, based on how well they explain the variation in your SNP pattern.

Still don't know about Options 1 and 2, but for me 2 better fits with my paper research. I also found Oracle-x to be the most consistent with my family history.

That's about all I can understand at the moment. If there's anyone out there with more depth in statistics, I'd appreciate any comments.

Jim