From 7f1005cc1666c8553d54cb9e1f9033f28336b433 Mon Sep 17 00:00:00 2001 From: Nutchanon J Date: Tue, 25 Oct 2022 14:26:11 +0700 Subject: [PATCH] new post --- _posts/2021-12-09-stats-in-court.md | 53 ++++++++++++++++++++++++++++ images/sally-clark.webp | Bin 0 -> 68426 bytes 2 files changed, 53 insertions(+) create mode 100644 _posts/2021-12-09-stats-in-court.md create mode 100644 images/sally-clark.webp diff --git a/_posts/2021-12-09-stats-in-court.md b/_posts/2021-12-09-stats-in-court.md new file mode 100644 index 0000000..a01a17a --- /dev/null +++ b/_posts/2021-12-09-stats-in-court.md @@ -0,0 +1,53 @@ +--- +title: "การตัดสินคดีผิดในสหราชอาณาจักร เหตุเพราะแพทย์เรียนสถิติมาไม่พอ" +tags: Technology +cardimage: "images/sally-clark.webp" +--- + +เรื่องนี้เป็นเรื่องของ Sally Clark แม่ผู้ถูกตัดสินว่าได้ฆ่าลูกอ่อนของตัวเองทั้งสองเมื่อเดือนพฤศจิกายน 1999 + +เธอสูญเสียลูกชายของเธอไปคนแรกเมื่อเดือนธันวาคม 1996 ในขณะที่ลูกชายของเธอมีอายุได้เพียงไม่กี่สัปดาห์ ความทุกข์ใจของเธอสาหัส ต่อมาเธอก็ตัดสินใจมีลูกคนที่สอง ซึ่งเป็นลูกชายเช่นกัน แต่ลูกชายคนที่สองของเธอก็ตายเมื่อเดือนมกราคม 1998 ด้วอายุเพียงไม่กี่สัปดาห์เช่นเดียวกับคนแรก + +เรื่องนี้ทำให้เธอถูกขึ้นศาลในฐานะที่เธอนั้นเป็นผู้ต้องสงสัยในคดีฆ่าลูกชายทั้งสอง โดยแพทย์ผู้เชี่ยวชาญ ท่าน Sir Roy Meadow ที่รับหน้าที่เป็นพยานผู้เชี่ยวชาญ (expert witness) ก็ได้กล่าวหาเธอทันทีว่าน่าจะเป็นผู้ที่กระทำการโหดเหี้ยมดังกล่าว + +เขาอ้างว่า (ด้วยสถิติที่เรียนมาตั้งแต่อยู่ ม.2 - อันนี้คิดเอง) โรคที่ทำให้เด็กทั้งสองตายนั้น ซึ่งทางฝ่ายจำเลยได้อ้างว่าน่าจะเป็น sudden infant death syndrome (SIDS) มีโอกาสที่จะเกิดกับเด็กทารกแรกเกิดเพียง 1/8500 เท่านั้น เพราะฉะนั้นหากเด็กทารกสองคนเกิดมาแล้วมีโรคดังกล่าวเหมือนกัน แสดงว่าโอกาสที่น่าจะเกิดขึ้นก็คือ + +(1/8500)^2 = 1/73000000 + +ซึ่งต่อมา ในปี 2001 ทางราชสมาคมสถิติของอังกฤษ (Royal Statistical Society) ก็ออกมาโต้ว่า สถิติดังกล่าวนั้นเป็นสถิติไม่มีหลักการเอาเสียเลย และเป็นการใช้สถิติแบบผิดหลักการอย่างมากในวงการยุติธรรมแห่งสหราชอาณาจักร + +# เรื่องแรก – เหตุการณ์ทั้งสองไม่ได้เป็นอิสระต่อกัน + +(ถ้า Sir Roy Meadow ตั้งใจเรียนตอนอยู๋โรงเรียนกว่านี้ เขาน่าจะรู้ว่า - คิดเอง) กฎการคูณที่จะใช้หาโอกาสในการเกิดเหตุการณ์นั้น เหตุการณ์ทั้งสองต้องเป็นอิสระต่อกัน คือความน่าจะเป็นที่ลูกคนแรกจะตายจากโรค จะต้องเป็นอิสระไม่ขึ้นกับความน่าจะเป็นที่ลูกคนที่สองจะตายจากโรคเดียวกัน ซึ่งเห็นได้ชัดว่าไม่จริงอยู่แล้ว เพราสาเหตุทางพันธุกรรม ฯลฯ ก็มีผลเกี่ยวเนื่องกันมา + +# เรื่องที่สอง – แพทย์ไม่รู้จัก Bayes’ Rule + +(ถ้า Sir Roy Meadow ตั้งใจเรียนสถิติตอนอยู่ปีหนึ่ง แทนที่จะเอาเวลาไปทุ่มเรียนแต่ชีวะ เขาน่าจะรู้ว่า - คิดเอง) โอกาสที่แม่จะเป็นผู้บริสุทธิ์แต่มีหลักฐาน หรือ P(บริสุทธิ์|มีหลักฐาน) กับโอกาสที่มีหลักฐานแต่แม่เป็นผู้บริสุทธิ์นั้น หรือ P(มีหลักฐาน|บริสุทธิ์) มีค่าไม่เท่ากัน ถ้าเขียนเป็นสมการก็น่าจะได้ประมาณนี้ คือ + +P(บริสุทธิ์|มีหลักฐาน) != P(มีหลักฐาน|บริสุทธิ์) + +โดยที่ถ้าเป็นศาล ค่าโอกาสที่อยากทราบคือ โอกาสที่แม่จะเป็นผู้บริสุทธิ์แต่มีหลักฐาน หรือ + +P(บริสุทธิ์|มีหลักฐาน) + +โดยถ้ามีค่าใกล้หนึ่ง แสดงว่าแม่ไม่น่าจะมีความผิด สมการของ Bayes จะออกมาหน้าตาประมาณนี้ คือ + +P(บริสุทธิ์|มีหลักฐาน) = P(มีหลักฐาน|บริสุทธิ์) * P(บริสุทธิ์)/P(มีหลักฐาน) + +โดยที่ถ้าใช้ Law of total probability จะได้ว่า + +P(มีหลักฐาน) = P(มีหลักฐาน|บริสุทธิ์) * P(บริสุทธิ์) + P(มีหลักฐาน|กระทำผิด) * P(กระทำผิด) + +หากลองคิดดู โอกาส P(กระทำผิด) ที่แม่ในสหราชอาณาจักรจะจิตใจอำมหิตฆ่าลูกอ่อนสองคนในเวลาที่ไล่เลี่ยกันนั้นมีโอกาสน้อยมาก เพราะฉะนั้นหากค่าของ P(กระทำผิด) เข้าใกล้ศูนย์ จะได้ว่า + +P(มีหลักฐาน) = P(มีหลักฐาน|บริสุทธิ์) * P(บริสุทธิ์) + +และทำให้ P(บริสุทธิ์|มีหลักฐาน) มีค่าเข้าใกล้หนึ่ง + +ประเด็นปัญหาของความเข้าใจผิดทางสถิตินี้คือ ถึงแม้ว่าโอกาสที่ P(มีหลักฐาน|บริสุทธิ์) หรือโอกาสที่ลูกทั้งสองของแม่คนเดียวกันจะมีโรค SIDS พร้อมกันจะมีค่าน้อยมาก ๆ แต่โอกาสที่ P(บริสุทธิ์) ของเธอก็มีมากเช่นกัน ดังนั้นการจะด่วนสรุปว่า P(บริสุทธิ์|มีหลักฐาน) จะน้อยเพราะว่า P(มีหลักฐาน|บริสุทธิ์) น้อยนั้นเป็นเรื่องที่ด่วนสรุปมากเกินไป + +# Aftermath + +หลังจากการยื่นอุทธรณ์ ศาลอังกฤษก็ได้พิจารณาตัดสินคดีนี้อีกครั้ง และทำให้ Sally Clark พ้นโทษในปี 2003 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