High School “Fixed mindsets” might be why we don’t understand statistics

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SUMMARY

The discussion centers on the impact of fixed mindsets on the public's understanding of statistics, particularly in high-stakes situations like jury trials. The case of Sally Clark, wrongfully convicted based on flawed statistical reasoning by Sir Roy Meadow, exemplifies the dangers of misinterpreting statistical data. A study published in Frontiers in Psychology attributes these misunderstandings to a resistance to change and an over-reliance on familiar methods learned in school. Key statistical concepts such as "mean value" and "standard deviation" are highlighted as essential for accurate data interpretation.

PREREQUISITES
  • Understanding of basic statistical concepts, including "mean value" and "standard deviation."
  • Familiarity with the implications of statistical reasoning in legal contexts.
  • Knowledge of the relationship between statistics and physics, particularly concepts like "center of gravity" and "moment of inertia."
  • Awareness of cognitive biases, specifically fixed mindsets and their effects on problem-solving.
NEXT STEPS
  • Research "The Flaw of Averages" to understand the limitations of relying solely on mean values.
  • Study the role of standard deviation in data analysis to enhance statistical literacy.
  • Explore cognitive psychology literature on fixed mindsets and their impact on learning and decision-making.
  • Examine case studies where statistical misinterpretation led to significant real-world consequences.
USEFUL FOR

This discussion is beneficial for educators, legal professionals, psychologists, and anyone interested in improving their statistical reasoning skills and understanding the implications of cognitive biases in decision-making.

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https://arstechnica.com/science/2018/10/fixed-mindsets-might-be-why-we-dont-understand-statistics/

The article outlines our difficulty of understanding statistics in everyday problems or while on juries.

In 1999, an English solicitor named Sally Clark went on trial for the murder of her two infant sons. She claimed both succumbed to sudden infant death syndrome. An expert witness for the prosecution, Sir Roy Meadow, argued that the odds of SIDS claiming two children from such an affluent family were 1 in 73 million, likening it to the odds of backing an 80-1 horse in the Grand National four years in a row and winning every time. The jury convicted Clark to life in prison.

But the Royal Statistical Society issued a statement after the verdict insisting that Meadow had erred in his calculation and that there was "no statistical basis" for his stated figure. Clark's conviction was overturned on appeal in January 2003, and the case has become a canonical example of the consequences of flawed statistical reasoning.

A new study in Frontiers in Psychology examined why people struggle so much to solve statistical problems, particularly why we show a marked preference for complicated solutions over simpler, more intuitive ones. Chalk it up to our resistance to change. The study concluded that fixed mindsets are to blame: we tend to stick with the familiar methods we learned in school, blinding us to the existence of a simpler solution.
 
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Tell me about it. Most people (and that includes a lot of academicians) understand the concept of "mean value" - full stop. What they do not understand is that:
  • The "mean value" is equivalent to the "center of gravity" in physics - nice to know, but only of restricted usefulness
  • In order to say something useful about a set of data, you must include the "standard deviation" (which is equivalent to the "moment of inertia" in physics).
I could go on for several pages, but I would only get frustrated thinking about it.

(For the record - I am not a statistician. I learned about the importance of these things in Physics 101 - Measurement Theory).
 
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Svein said:
Tell me about it. Most people (and that includes a lot of academicians) understand the concept of "mean value" - full stop. What they do not understand is that:
  • The "mean value" is equivalent to the "center of gravity" in physics - nice to know, but only of restricted usefulness
  • In order to say something useful about a set of data, you must include the "standard deviation" (which is equivalent to the "moment of inertia" in physics).
I could go on for several pages, but I would only get frustrated thinking about it.

(For the record - I am not a statistician. I learned about the importance of these things in Physics 101 - Measurement Theory).
There is a book detailing poor knowledge and understanding of Statistical terms and ideas :" The Flaw of Averages" details the over-reliance on the mean at the exoense of other measurements. If you go to the north pole for 1 year and a coat will last you 3 months on average, will you only take 4 coats with you, or will you consider the variability ( variance/sd)? Sure, to all here in PF this is likely trivial but apparently not so much so outside of PF.