Example 1: In A-ville, there are 1000 Whigs, of whom 30% can juggle, and 100 Tories, of whom 20% can juggle. In B-ville, there are 100 Whigs, of whom 60% can juggle, and 1000 Tories, of whom 50% can juggle. So a given Whig is more likely to be able to juggle than a given Tory?

Example 2: The first half of the season, Ruth has a batting average of.280 on 100 at-bats, while Gehrig has a batting average of.270 on 200 at-bats. In the second half of the season, Ruth bats .190 on 200 at-bats, while Gehrig bats .180 on 100 at-bats. So Ruth's average for the season is higher than Gehrig's?

Example 3: In A-ville, 30% of both parties can juggle; there are 1000 Whigs and 100 Tories. In B-ville, 60% of both parties can juggle; there are 100 Whigs and 1000 Tories. Thus, the same percentage of each party in each village can juggle; but the percentage of Whigs who can juggle is substantially less than the percentage of Tories who can juggle.