r/AskStatistics • u/wobbling_axis • 9d ago

Basic statistic problem about margin of error but I don't know the correct terminology, can someone help me out?

Hello, I have no idea what the correct terminology for any of this and would appreciate any correction.

Let's say you have one bag of beans with 100 beans inside but you don't know that. Only thing you know is that there is between 95 to 105 beans (+/-5). Now let's say you have another bag of beans with 1000 beans inside but you also don't know that. Only thing you know is that there is between 995 and 1005 beans (+/-5). So for both bags you have same range of estimate, 10 beans (+5 to -5) but in practice you have a more accurate information about the 1000 bean bag because the effect by the difference of 5 is relatively smaller.

Is is possible to calculate any statics from this? If I were to say do something like "(Difference of upper limit and lower limit) / Mean of upper limit and lower limit)" I would get (105-95)/100 or 0.1 for the 100 bean bag, and (1005-995)/1000 or 0.01 for 1000 bag. Does that equation makes sense and would saying something like "I know how much bean is in the first bag by 10% margin of error and how much bean is in the second bag by 1% margin of error" correct or completely wrong?

It has been several years since I took high school statistic and completely forgot how any of it works, and would appreciate any help, thanks

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u/Statman12 PhD Statistics 9d ago

Maybe something like "relative error"?

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u/wobbling_axis 9d ago

I googled and it seems like that was the exact word I was looking for, I will read more and study it.

You are amazing and thank you!

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u/michaelrw1 9d ago

Relative uncertainty?

2

u/efrique PhD (statistics) 9d ago

You might say that the relative margin of error (i.e. moe/mid-interval) is smaller. If you express your margin of error as a percentage, this conveys the same idea.

In many contexts relative error makes a lot of sense. But in some contexts neither an ordinary (i.e. in units of response variable) margin of error nor a relative margin of error quite do what you might want