How to calculate % over-reported? 1,530 staff-reported beneficiaries

IJShoef

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This might seem elementary, but I have reasons for asking this. So if any one can please help me or point me to any reliable reference.

So here is the case-

In a data quality assessment I found that a staff has reported 1,530 beneficiary instead of 1,036 recorded in a register. Now what do I report?

A) 48% over-reporting found - taking 1,036 (the verified number) as the denominator
OR
B) 32% over-reporting found - taking 1,530 (the reported number) as the denominator
 
This might seem elementary, but I have reasons for asking this. So if any one can please help me or point me to any reliable reference.

So here is the case-

In a data quality assessment I found that a staff has reported 1,530 beneficiary instead of 1,036 recorded in a register. Now what do I report?

A) 48% over-reporting found - taking 1,036 (the verified number) as the denominator
OR
B) 32% over-reporting found - taking 1,530 (the reported number) as the denominator

Sometimes there can be some ambiguity in such a question, but typically you take a known correct value as the base, so your first answer would be correct. This is because you want to report how far a reported or estimated number is from the actual number, as a percentage of the latter.

Can you tell us why you are unsure?
 
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Sometimes there can be some ambiguity in such a question, but typically you take a known correct value as the base, so your first answer would be correct. This is because you want to report how far a reported or estimated number is from the actual number, as a percentage of the latter.

Can you tell us why you are unsure?

Thanks for your reply. I did report the first one(48%). But the program people are arguing that the second one (32%) is mathematically correct. They are Doctors and way senior to me. So I was checking before I meet with them again.

Btw, You said there can be some ambiguity...could you please tell me why?
 
Thanks for your reply. I did report the first one(48%). But the program people are arguing that the second one (32%) is mathematically correct. They are Doctors and way senior to me. So I was checking before I meet with them again.

Btw, You said there can be some ambiguity...could you please tell me why?

In some questions about percent errors, it is not clear which number, if any, can be trusted. Here, for example, they would be right if they think the reported amounts are correct and doubt the "register". (But then you wouldn't call it "over-reported", but maybe "under-recorded"!) It is possible that I am misunderstanding the context of your question, which is why I don't want to claim certainty. (I don't quite know what "register" you have, for example, or what "reported beneficiary" means; if I did, I could be more certain that it is considered the correct value.)

Also, terminology varies, and circumstances vary, so that what sounds like the same concept can be different. For example, if you were asked for the percent difference between two numbers, you would mean different things depending on whether one is taken to be the "correct" value, or not. In the latter case, you would commonly take the average of the two numbers as the base. This is mentioned in my discussion here. That's not relevant to your question, but is part of the ambiguity I had in mind.

Here are some references on various versions of percent error:

https://www.thoughtco.com/how-to-calculate-percent-error-609584 (experimental vs. theoretical/accepted/true/known value)
https://physics.appstate.edu/introd...icant-figures-and-error-analysis#percenterror (percent error vs. percent difference)
https://www.mathsisfun.com/data/percentage-difference-vs-error.html (percent change/error/difference)

But none of these is quite the same idea as your situation.
 
In some questions about percent errors, it is not clear which number, if any, can be trusted. Here, for example, they would be right if they think the reported amounts are correct and doubt the "register". (But then you wouldn't call it "over-reported", but maybe "under-recorded"!) It is possible that I am misunderstanding the context of your question, which is why I don't want to claim certainty. (I don't quite know what "register" you have, for example, or what "reported beneficiary" means; if I did, I could be more certain that it is considered the correct value.)

Also, terminology varies, and circumstances vary, so that what sounds like the same concept can be different. For example, if you were asked for the percent difference between two numbers, you would mean different things depending on whether one is taken to be the "correct" value, or not. In the latter case, you would commonly take the average of the two numbers as the base. This is mentioned in my discussion here. That's not relevant to your question, but is part of the ambiguity I had in mind.

Here are some references on various versions of percent error:

https://www.thoughtco.com/how-to-calculate-percent-error-609584 (experimental vs. theoretical/accepted/true/known value)
https://physics.appstate.edu/introd...icant-figures-and-error-analysis#percenterror (percent error vs. percent difference)
https://www.mathsisfun.com/data/percentage-difference-vs-error.html (percent change/error/difference)

But none of these is quite the same idea as your situation.

Thanks a lot for all you responses and for your time. Have a nice day.
 
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