So I was reading through this survey and noticed that for some of the questions, some of the responses had a 0%, which I assume means that nobody responded with that option. However, sometimes, one of the responses has a -1%. In all cases where one of the potential responses is -1%, the remaining responses total 101%, which does give a total of 100%.
Example:
Question 1:
34% - Response A
32% - Response B
15% - Response C
12% - Response D
8% - Response E
-1% - Response F
At first I thought this was just a typo, but out of 64 questions, three of them have an answer with a -1%. Any idea why this might be? Is this an actual thing in statistics that represents a choice of responses that I don’t understand?
Is the negatively scored answer a real possible answer? It’s looks to me like it’s a correction for rounding of the other numbers so that the total of answers is 100%.
Not sure why they would feel the need to be that precise rather than just put in a disclaimer about totals being over 100% due to rounding though.
It’s likely just a mathematical error that arose when manipulating the data. I imagine that if all of the responses are both whole percentages and neatly add up to 100%, they must have been doing something to that effect.
Here’s one way I could imagine that they would just sum round everything and subtract from a value if it added up to more than 100%. If that process somehow selected the lowest value when it’s 0%, it could change that to -1%. I could see that getting by if someone simply expected every value to have at least some response, and so they didn’t have a case for it, and no one looked at it too closely before it got published.
A rounding issue! It’s so simple! I must be really tired or something because I didn’t even consider that they might be rounding from fractions. And the numbers were probably entered automatically by a program so a human didn’t catch it.
There’s no reasonable rounding method that would round a nonnegative number to something negative. That doesn’t mean that they didn’t manage to do it, but somebody’s doing something goofy.
In fact, I’m having an awfully hard time coming up with any unreasonable rounding method that would result in that. All I can come up with is multiple iterations of biased rounding methods combined with fudge factors.
My best guess would be that they have some statistical model which says that people will overreport something by X%, and so they’re “correcting” by subtracting off that amount.
Is it always the last number? Maybe they use F=100-(A+B+C+D+E) to get always a sum of 100; if too many others are rounded up, the final answer (is that your final answer?) will be negative. Do you occasionally see -2?
Are all three questions with a negative for the last choice?
A method of rounding the first four and subtracting them from 100 to get the final would have the total always be 100 but would have this quirk. That is, an unreasonable rounding process.
md2000, that’s exactly what I did do, didn’t I? You noticed that “-1” was coming up very often, and you wondered if occasionally the result might be “-2”, and I gave you an example of how that could happen. Did I misunderstand the question you asked that I quoted?
I don’t think md2000 was wondering if the result might be -2, I think he was asking the OP is the result was sometimes -2 which would validate his speculation.
Some individuals answered the polls more than once, with different answers, but the individuals were counted only once, resulting in more responses than respondents.
Some individuals made more than one choice per question, but the individuals were counted only once, resulting in more responses than respondents.
Some questions weren’t answered, and the polls handled “no answer” in unconventional way (most would say "incorrect, but I’m not so judgmental).
I’m not sure how, but it seems a disparity like one of these could result in negative sums or averages.
Most likely:
The poll includes the option to change your answer.
And the simplest way to code that to keep all the totals correct is to subtract 1 from the total whenever someone changes their answer away from this choice, and add 1 to the new answer they choose.
But if they happened to be the only person to choose that answer, and then they change it, the total will be left with a -1 answer. The total of all percentages will be correct, it will still sum to 100%.
If 2 or 3 people did this (and nobody actually stayed with that answer) , you could end up with -2 or -3 as a result. But all the totals together would still total 100%.
Which after you recalculate the percentages goes to 40/60/0%.
I don’t see how subtracting and adding will ever give you a negative percent, unless you allow users to change (i.e. “unselect”) answers they never picked in the first place, which would probably be harder to implement than the more logical solution.
Yeah, I’m inclined to think that something like this happened. There’s never a -2, only -1’s. Yes, it’s always the last number in the list, and all results are in whole numbers, which means there was some definite rounding going on (though I’m not sure the exact method).
Yes, sorry, this. Does the OP’s examples (or similar distributions from the same source) also occasionally include -2? It would be rarer but not impossible, and show that rounding and subtracting was the process.
(I once worked with an old COBOL budget program that did something similar. It printed the results in thousands of dollars, and so sometimes the columns did not add up due to rounding. The accountants had a choice - live with the rounding errors, or fiddle with the column of numbers to ensure the totals matched. In that case, they chose to live with “does not add up”.)
I was a programmer in a BASIC shop (mid-1980s) and we discovered that the invoicing program was calculating the tax on each line item, and then totalled them up on the bottom. The bottom-line tax was (if I remember correctly) about eight cents off from what it should have been, i.e., calculated on the total goods. Rounding!