Wikipedia talk:Two times does not mean two times more

In the first section

Along with the maths, the essay mixes chatty comments like how well cooked the cookies are and how lucky the eater is. So this isn't a formal essay. But it gets a little bogged down with referring to "in the first section" and sometimes the description gets confused: The lucky person is going to eat 200% as many cookies as our first section. Sections don't eat cookies, and there wasn't a person in the first section. The commentary seems a bit like someone is speculating about food photos they found on the internet (which I guess they did) rather than using the images as illustrations in a story they want to tell. So how about introducing characters with names. Each section has a character. Some are better at baking than others and some are greedier or hungrier than others. Perhaps the person with five and a half cookies is going to share them, though they can keep the one they started eating, thanks very much. -- Colin°^Talk 19:12, 15 January 2023 (UTC)

I think it's the same person eating all the cookies, in all the sections. (I hope they'll save some for tomorrow.) WhatamIdoing (talk) 21:07, 19 February 2024 (UTC)

Lesson

The article title and intro use "times" but the body text uses percentages. Why? Both can be confusing wrt "as many" or "more than", but percentages are harder again.

Perhaps as well as giving a lesson on understanding percentages and relative comparisons, the essay could include advice to writers. The first being perhaps to avoid percentages, as people don't understand them. On a photo website recently, they commented on a new "6K" monitor for creatives to use. They said "the 6K display delivers 150 percent more pixels than a 4K display". This not only contains the "percent more than" issue that requires thinking carefully, but also is commenting on two numbers (6K and 4K) that approximate to the horizontal resolution of the screen and a third (pixels) that is the product of the horizontal and vertical resolution. Here, I don't think it was necessary to use relative maths (percent more, or x times as many) when they could have just given the absolute numbers. The 6K display has about 21 million pixels, compared to the 8 million pixels of a 4K display, and readers could choose to imagine the two numbers relativity in any way they find best.

Using the relative maths is essential if you are dealing with a change in a variable, such as "Wonderpam is 200% more effective than existing treatments of scaryitis", or you want to emphasise the transformation rather than just convey the actual amounts involved. So for example, saying "Joe has one cookie and Jill has three" is far simpler than "Joe has one cookie and Jill has [checks essay] 200% more cookies than Joe" or even "Joe has one cookie and Jill has three times as many". However, if you wanted to emphasise how much better off Jill was then of course "Jill has three times as many" conveys that much better than just giving two numbers. And I'd argue, a lot lot better than using percentages.

Is there anything published that could be linked to. Has anyone done a study to compare

• has trebled
• has three times as many
• is two times more again
• is 300% as much
• is 200% more than

Is there any difference between growing (200%) and shrinking (50%) in terms of people getting it right? Thinking about the above list, in the opposite direction, we don't even have a word (thirded isn't a word). But we do have

• has a third as many
• is two thirds less than
• is 33% of
• is 66% less than

One difference that I can think of is Jack, who has no cookies at all. He has 100% fewer cookies than Joe and also 100% fewer cookies than Jill. But there's no way to express, relatively, how much more cookied Joe and Jill are than Jack. Which reminds me of a family joke. Trivial little competitions (like guessing how long the walk back home will take) are rewarded with "the usual prize", which is nothing at all. Well, I am a Scot. And being the one who got it right is its own reward. Sometimes, the conversation goes "So, are we playing for the usual prize?" and I can respond "Oh, I'm feeling generous today. Let's double it". -- Colin°^Talk 19:12, 15 January 2023 (UTC)

@Colin, Jill and Joe have infinitely more cookies than Jack.

I think (but have not looked for research around) that people are equally likely to get it wrong in both directions. The reason I think this is largely because comparing 4 to 5 is consistently difficult. Five is 25% more than four. Four is 20% less than five. You have to know which one is being used as the denominator to get it right. Also, about 30% of US adults can't handle math (when the test is given in English) that's more complex than figuring out the sale price when an item is 50% off.[1] WhatamIdoing (talk) 18:01, 2 August 2024 (UTC)

It is interesting that the 100% fewer than and infinitely more than both tell you Jack has no cookies but neither tell you how many cookies Jill and Joe have. Nearly 100% of US adults can't spell maths, so you've got that problem to deal with first. -- Colin°^Talk 12:20, 3 August 2024 (UTC)

That's why Number needed to treat is popular with public health educators, and relative risk is popular with marketing departments. They don't want you to know that their product reduces your risk from "already very small" to "even smaller"; they want you to think that it is a 99% reduction. WhatamIdoing (talk) 16:46, 3 August 2024 (UTC)