正解: BCorrect: B
部門ごとの傾向と全体の傾向が逆転するのはシンプソンのパラドックスの典型で、応募先部門の分布という交絡因子が原因です。A reversal between subgroup and aggregate trends is the classic signature of Simpson's paradox, caused here by the confounding distribution of applications across departments.
この問題は1973年のカリフォルニア大学バークレー校の大学院入試データの分析に基づく有名な事例です。全体では女性の合格率が低く差別が疑われましたが、学科別に見ると多くの学科で女性の合格率がむしろ高く、女性が競争率の高い学科に多く応募していたことが原因でした。シンプソンのパラドックスは、集団を分割する変数（ここでは部門）が結果と説明変数の両方に関連しているときに生じます。選択肢Aは両方の数字が同時に正しくなりうることを理解していません。Cは部門別分析を不当に退けており、Dは構造的な要因を偶然と誤認しています。ビジネスでも、製品別・地域別の集計と全社集計で傾向が逆転することは頻繁にあり、意思決定前に層別分析を行う習慣が重要です。This question is based on the famous 1973 analysis of graduate admissions at the University of California, Berkeley. Overall acceptance rates suggested discrimination against women, but department-level data showed women often had higher acceptance rates; they had simply applied more to highly competitive departments. Simpson's paradox arises when a grouping variable, here the department, is associated with both the outcome and the explanatory variable. Option A fails to recognize that both sets of figures can be simultaneously correct. Option C wrongly dismisses the disaggregated analysis, and Option D mistakes a structural cause for chance. In business, trends frequently reverse between product- or region-level and company-level aggregates, so stratified analysis before decisions is an essential habit.
層別分析をすればパラドックスは解消しますが、どの変数で層別すべきかは統計だけでは決まらず、因果構造の理解が必要です。逆に層別を細かくしすぎると各セルのサンプルが小さくなり、偶然の差を過大解釈する新たな誤りも生じます。Stratification resolves the paradox, but which variable to stratify by cannot be determined by statistics alone; it requires understanding the causal structure. Over-stratifying shrinks each cell's sample size, creating a new risk of over-interpreting chance differences. In hiring, the pattern may also hide real inequities in why applicants sort into departments.
分析前に因果関係の仮説図（何が何に影響するか）を描き、交絡になりうる変数を事前に列挙します。集計結果を報告する際は全体値と主要な層別値を必ず併記し、逆転が見られたら「どの層の構成比が影響しているか」を説明する習慣をつけます。Before analysis, sketch a causal hypothesis diagram of what influences what and list potential confounders in advance. When reporting aggregates, always present the main stratified figures alongside them, and when a reversal appears, explain which subgroup composition is driving it. Then ask the follow-up question the paradox raises, such as why application patterns differ.