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This question How would you explain statistical significance to people with no statistical background? provides some good ideas for explaining statistical significance to a lay audience in a limited period of time.

I seek similar ideas and examples for visual displays for that same purpose.

Joel W.
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    something along the tails of bell curve. the trouble is explaining the null hypothesis. if I were to defend, that would be my line of attack. i'd get into discussion of "under the null" and alternative hypo, and try to make the statistician angry first, then to look like a condescending arse. "People vs. OJ" has a great scene with forensics guy in it – Aksakal Nov 20 '18 at 19:57
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    @Aksakal I am concerned about a lay group understanding a typical graph, especially when we are talking about area under the curve. – Joel W. Nov 20 '18 at 20:50
  • it should boil down to the trust to an expert, i doubt that you'll ever be truly explain significance to the jury. people get confused about p-values all the time here – Aksakal Nov 20 '18 at 21:47
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    "Trust to an expert" is a bad argument to a jury! Relevant: https://www.americanscientist.org/article/do-we-really-need-the-s-word – kjetil b halvorsen Nov 21 '18 at 09:51

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Interesting question.

A jury presumes the defendat to be innocent (until proven guilty) and then looks at evidence that could invalidate that presumption. The more evidence the jury will see that invalidates the presumption of innocence, the more compelled they would feel to reject that presumption and conclude that the accused is guilty as charged. If the evidence is insufficient to pass the threshold of "beyond a reasonable doubt", then the jury will not be able to reject their initial presumption of the accuser's innocence in favour of his guilt.

A statistician presumes there is no effect/no difference and then looks at evidence in the data that could invalidate that presumption. The statistician weighs all the available evidence and comes up with a number (called p-value) which encapsulates the strength/weight of the evidence against the presumption of no effect/no difference. The number can be compared against the numeric equivalent of the threshold of "beyond a reasonable doubt" (e.g., 0.05). If the number falls beyond this threshold (i.e., the evidence is strong), the statistician will feel compelled to reject his initial presumption of no effect/no difference and conclude that the data provide evidence of an effect/difference.

Perhaps you can summarize the above parallelism visually with a side-by-side diagram. One shows the jury having to deliberate around the presumption of innocence, the other shows the statistician having to deliberate around the presumption of no effect/no difference. Both parties need to gather evidence that could invalidate this presumption and weigh its strength. The stronger the evidence, the more compelled each party would feel to reject their initial presumption and conclude that the opposite presumption must hold. The jury weighs the available evidence in more subjective ways - the statistician weighs the evidence in a more objective way via a single number. The smaller this number, the stronger the weight of evidence. Both parties must make a decision and reach a verdict/conclusion. While the jury can find the defendant not guilty, the statistician will generally abstain from concluding that there is no effect/no difference. The statistician will simply conclude there is no evidence in the data of an effect/difference, although it is possible in some cases to refine that statement.

Isabella Ghement
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