# High/low accuracy

Usage of accuracy with values gives me always a headache when I try to think how can I write about higher/lower accuracy so that the reader understands correctly how it affects the values. This is especially problematic when dealing with non-physical unitless quantities. For example, there are N samples and we have a process that has an adjustable accuracy for selecting a sample, let's say the accuracy value is x samples. Then we need to increase that accuracy, i.e. use higher accuracy than x samples. Is it obvious to any human being that higher accuracy or increasing the accuracy means actually using a smaller value for the accuracy setting, or vice versa? Or is there a better way to express it?

I know that in some cases you could use a better term than accuracy; for example, if the question were about deviation, then it is clear that smaller deviation means smaller deviation value. But in some cases you just need to talk about accuracy, so I am not asking for an alternative term, but just a way to talk about higher/lower accuracy so that it becomes clear that it has an inverse effect on the accuracy value. I always end up explaining it explicitly so that the direction of the change cannot be misunderstood.

• I think your problem is that you are using the word ‘accuracy’ wrongly. Variation in the number of samples used for a test affects not the ACCURACY but the RELIABILITY of the result. The smaller the number samples, the greater the ‘margin for error’. But the ‘error’ is not a matter of accuracy but of how representative the sample is, or how reliable in terms of excluding the possibility that the results were affected by elements irrelevant to the theory. So the RELIABILITY of (say) tests carried out on a new medication increases in direct proportion to the number of samples tested. Jan 16, 2019 at 15:07
• Sorry but no, I am not using accuracy wrongly. Perhaps my example was not the best one but it could be valid though. By accuracy I meant a kind of resolution, or grid, that is used for selecting samples. I do not mean statistical variation! For example, let us have 1000 samples, and then I have a process that selects samples using a grid with intervals of 10 samples. So, the process itself is accurate and repeatable, but it can point only to samples 1, 11, 21, 31, etc. So, I could talk about accuracy of 10 samples, or +/- 5 samples. Jan 16, 2019 at 15:56

Your question is about an inverted numbering system, where something ‘higher’ is given a lower number.

This kind of numbering is often used in ranking systems. The Number 1 athlete has a higher rank than the Number 3 athlete. The Number 1 priority is the most important priority. The top student takes first place. You improve (increase) manufacturing yields if you reduce wastage.

Accuracy works the same way. The word “higher” in “higher accuracy” conveys the notion of “better”, rather than a numeric representation of the accuracy. To answer your question: yes, it is understood that higher accuracy corresponds to lower error.

Depending on the context, you can phrase this as:

• pick a tighter tolerance for greater accuracy; or
• pick a smaller range for higher resolution.
• Thanks! However, "tolerance" can be used only when the accuracy is about statistical variation. And in case of statistical variation I could speak exactly about variation or deviation instead of accuracy, and there is no problem with inverted numbering system. The usage of accuracy is needed when we are dealing with process that has a certain resolution, for example a grid with fixed intervals. There the question is not about tolerance but accuracy. So, I could say that "pick a smaller interval for the grid" when I mean higher accuracy. Jan 16, 2019 at 16:09
• Sorry Lawrence, I tried to vote your answer as useful but I do not have enough reputation... Jan 16, 2019 at 16:12
• @Malakias You're welcome, and thanks for your note. I hope this answers your question. Jan 17, 2019 at 4:15