Thread by @chrissanders88

A lot of tips about good writing are rooted in the psychology of your reader. For example, if you want your reader to understand a risk (a probability), is it better to express that as a relative frequency (1 in 20) or a percentage (5%)?
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Typically, people understand risk better as a frequency. For example, consider the likelihood of a kid dropping out of high school. You could say that 5% of kids drop out, or that 1 in 20 does. Why is the latter more effective?
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First, it's something you can more easily visualize. There's some evidence you might be converting the percentage into the frequency representation in your head anyway. Weber et al (2018) talked about this here: frontiersin.org/articles/10.33…
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Next, it's more tangible to many audiences. We can all think of 20 people. Some may have 20 folks in their family or workplace.

Imagine if you're a teacher. If your class size is 20, you could interpret that as though one of YOUR students could drop out.
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Even if your class size is different than 20, the frequency representation gives you a clear basis for judgment. If your class size is 30, you know that there is an even stronger chance one of your kids could be one that drops out. You could even have two!
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This representation also makes it more intuitive to compare risks. While the average dropout rate across the US is 5%, it is 35% for students with a disability. Said another way, 7 out of 20 students in the latter group will not graduate. 6 more than average!
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And, not for nothing, lots of folks are just bad at statistics, appreciating differences in them at varying scales, or getting at their true meaning. This stuff is hard, particularly if you don't do it all the time. I struggle with this all the time.
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Researchers wield this knowledge well -- I read a study recently that described interventions for getting nurses to wash their hands more. They pointed out that 1 in 20 hospital patients get an infection in the hospital, and hand washing can significantly help prevent that.
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That's relevant because nurses visualize those 20 patients. On some floors, they may see that many in a day or over a couple of days. It means more, intuitively, than 5%. It *humanizes* the problem and simplifies interpretation.
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There are things to be careful of with this approach. It usually involves rounding. That's okay in some places but not in others. Sometimes you want to provide the frequency and give the percentage in an appendix or as supporting data.
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You also have to make sure the quantities (the denominator) are reasonable for the audience. An X out of 20 (classroom) or X out of 250 (school) frequency might be relevant for a teacher, whereas an X out of 10000 might not be.
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In general, most folks can relate personally to smaller denominators. Not as many can relate to larger ones. We see folks struggle with that a lot now with COVID stats. A lot of those (and other things policymakers rely on) are X out of 100,000 frequencies.
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Lastly, it becomes annoyingly easy for folks to manipulate quantities in ways that trick people. That usually means oversimplifying complex issues, comparing unrelated things, or ignoring skewed data. That's a broader discussion.
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I'll caveat a lot of this, again, by saying this is going to be somewhat situational. Relative frequencies humanize statistics and people relate to them more. You have to understand your audience to make the most effective use of the strategy.
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All told, thinking about the representation of statistics is pretty common these days in research when designing interventions. But, it's also applicable to any form of writing that describes risk and needs to achieve a goal. That encompasses most infosec writing.
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Here's some more background on the scientific case for using frequencies to express probabilities: persuasivelitigator.com/2018/10/explai…
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And, If you want to learn more about stats in a way that isn't boring, I recommend Naked Statistics by Charles Wheelan: smile.amazon.com/dp/B007Q6XLF2/….

We're all in the probability business, so it's helpful to understand how to talk about it.

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