Confusing P(A|B) with P(B|A) is often called the "confusion of the inverse". In statistical algebra, it is obvious. In ordinary English, it can be subtle.
Jessica Utts considered this confusion of the inverse one of seven topics that educated citizens needed to know about statistics.
The American Statistician, May 2003, V57, N2. Copy at:
www.ics.uci.edu/~jutts/AmerStat2003.pdf*********************************************
One example was an AP-UK press release (2009).. "Of the children who ate candies or chocolates daily at age 10, 69 percent were later arrested for a violent offense by the age of 34."
Where did they get this incredible statistic? They constructed it via a confusion of the inverse from this statistic: "69% of respondents who were violent by the age of 34 years reported that they ate confectionary nearly every day during childhood," Details at:
www.statlitblog.org/2009/10/ap-creates-crime-wave/------------------------------
Milo Schield
ASA Fellow
Editor and webmaster of
www.StatLit.orgMember, International Statistical Institute (ISI)
US Director, International Statistical Literacy Project (ISLP)
Vice-President of the National Numeracy Network (NNN)
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Original Message:
Sent: 08-15-2019 14:51
From: James Scanlan
Subject: Tales of two proportions
Page 67 of the U.S. Commission on Civil Rights 's July 2019 report Beyond Suspensions: Examining School Discipline Policies & Connections to the School to Prison Pipeline for Students of Color with Disabilities has this provocative statement that has been picked up in the media accounts of the report: "During the 2015–16 school year, 32 percent of black students with disabilities were suspended once, and almost 40 percent were suspended repeatedly…" The statement, of course, means that almost 72 percent of black students with disabilities received one or more suspensions.
But even a casual examination of Figure 8 on page 72 (which is the source for the 40 percent figure) should reveal that the 40 percent figure results from the report's confusing (a) the proportion a group makes up of persons experiencing an outcome with (b) the proportion of the group that experiences the outcome. I assume the same holds for the 32 percent figure. Actual figures would be around 20 percent for one or more suspensions and 10 percent for multiple suspensions.
Over the years, I have noticed the occasional confusion of these two proportions. My web pages Vignettes/Journalists and Statistics and Discipline Disparities/Rhode Island Disparities discuss two examples. I saw it once in a peer-reviewed article that I have since lost track of.
I would be interested in any cases where members have observed similar confusing of these two proportions, especially in any circumstance where the misreportage then took on a life of its own.
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James Scanlan
James P. Scanlan Attorney At Law
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