The conditional distribution of prostate cancer mortality, given a man's race, shows that black men and white men were, overall, about equally likely to die from prostate cancer. However, when we look at the study broken down by age groups older than and younger than 65, we find that in each age group, black men were more than twice as likely to die from prostate cancer than white men. This apparent contradiction is an example of

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Simpson's Paradox occurs when a trend appears in different groups of data but disappears or reverses when these groups are combined. In this case, the overall data shows no significant difference in prostate cancer mortality rates between black and white men. However, when the data is broken down by age groups, a significant disparity appears in each group, with black men being more likely to die from prostate cancer. This paradoxical situation can occur when the groups have different distributions and sizes, and the overall result is dominated by one group's data.

The Conditional Distribution of Prostate Cancer Mortality, Given a Man's