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Frequency Format Hypothesis

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47 pointsAgraillo11 comments

It's important to remember that a substantial fraction (at least 20% -- 1 in 5 [0]) of the adult population is really uncomfortable with percentages. Percentages are abstract, but it is easy for me to think of 5 relatives and estimate how many can do simple math.

[0] https://www.theguardian.com/education/2016/mar/07/a-fifth-of...

That article is about adults being uncomfortable with both fractions and percentages. Considering “20%” just means “20 in 100,” I doubt “1 in 5” is going to be much more comfortable for these adults.

the information leaflets for medication are written here (Germany) in case numbers and not in percentages, following a "1 in X" scheme (1 in 100, 1 in 1000, 1 in 10000) which I think kind of makes sense for inclusiveness, on the other side I do think this way is almost as if providing values on a logarithmic scale, due to the X in "1 in X" being given in base-10 magnitudes.

I wonder if it would actually be more intuitive to use dice for comparison. Like 1/36 would be the probability to roll doubles of 6, 1/216 would be the probability to roll triples of 6, etc. Rolling 6 dices to 6 would be 1/46656 and 7 dices to 6 would be 1/279936, ...

At least my generation has played enough Yatzeeh to have a feel for dice-throwing :-)

I think the point of that article (and the larger point about math anxiety) is that many people do not realize that 20% "just means" 20 in 100. And it probably gets worse for percentages < 1%.

From my encounters with mathematically unskilled people: The usage of percentages is very confusing. As in in it is used in "1 in 100" but also there is this "6% increase" which is used for factors 1.06, and that the reciprocal calculation is not a "6% decrease" but a "5.6% decrease". Then on top come usages of yearly or monthly interest rates, etc.

In each context, the percentage needs to be handled and understood differently, which means that even though percentages are everywhere, the knowledge does not automatically "solidify" upon being exposed to percentages for these folks.

The "1 in 5" example is the most prominent one (introduced at the start of the article), but I was more impressed with another one - "Do you say the word hello or charisma more". Similar is this. Try remembering two of your acquaintances (friends) and tell with whom you talked more last year. In many cases you would give the exact answer, but it comes not from the explicit knowledge somewhere in the "symbolic storage", it would be probably derived implicitly from two (or more) "neuron clouds" related to these two individuals. Just to leave the symbolic world whatsoever, let them be unnamed persons like a cashier in the shop. You still can derive this information. For me it's a special thing about the frequency and probably some other kind of properties/data. Being discrete/symbolic for the human tasks, they can come from a non-symbolic memory storage

Really? I've always been the opposite for some reason. I find it easier to visualize 20% of a pie chart, or of a crowd, or a length, etc. It's a lot harder for me to think about 1/5 of a crowd or 1/5 of a length.

It's tangentially related to this, but I've seen posts on social media over the years of how people visualize different kinds of information. For example, some people think of the months of the year in a vertical fashion, others horizontal.

I'm curious if this is something similar where some people find a certain way of thinking of probability easier than others.

Think of it this way: if I said that 0.001 or 0.1% of people had a certain congenital disease; that may seem like not many people at all. Say it as 1 in every 1000 people, or about 330,000 people in America, and it seems like a lot of people.

I agree with you on that. If it's less than 1% then it does make more sense to think of it that way.

5 out of 3 people have difficulty with improper fractions.

That sounds a lot like prompt engineering for humans.

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