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Regards,

I've seen a few sensors which its datasheet claims to have a better resolution than the mean accuracy. I understand resolution as the lower identifiable value of the measurement; and, as so, half of it is the lower movement that you can see.

For example, the ds18b20 1-wire temperature sensor:

its 12bits AD resolution are analog to a 0.0625V value, and the typical error is given by:

ds18b20 typical error curve

so, suppose that I need to monitor a liquid that is between 30 and 70ºC; that fantastic resolution a third than the mean error for that gap.

I tend to think that I could extrapolate the mean curve and, in function of the current point, adjust the resolution.

But, in other example, this is the specification values for the BME280 (t/p/h) temperature sensor:

bme280 temperature characteristics

In this case I have a 0.01ºC resolution with a 0.5ºC accuracy (at best); but no error distribution chart.

So.. What it is for!??

Thanks in advance.

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    \$\begingroup\$ A watch has a resolution of 1 second, but it may be 1 hour slow. \$\endgroup\$
    – Chu
    Feb 27 '17 at 20:02
  • \$\begingroup\$ What does note 9 say? We can't see it because you forgot to link to the datasheet you're referring to. \$\endgroup\$ Feb 27 '17 at 20:24
  • \$\begingroup\$ @Chu That's actually representative of the difference between accuracy and precision more than accuracy and resolution. \$\endgroup\$
    – Hari Ganti
    Feb 27 '17 at 20:24
  • \$\begingroup\$ I don't think you can truly extrapolate the mean error for a set of samples the way it seems you're describing it (it's actually hard to interpret what you mean), but you can calibrate your sensor with a more precise sensor. If you know the temperature of a sample, and you measure it with a new sensor, you can make an error correction map. That said, there's no guarantee the correction map is repeatable, which is why the error bound exists. Theoretically, you can't know the value any more accurately without additional information. \$\endgroup\$
    – Hari Ganti
    Feb 27 '17 at 20:34
  • \$\begingroup\$ @Hari Ganti, does 'accuracy' have a quantitative definition these days? \$\endgroup\$
    – Chu
    Feb 27 '17 at 20:39
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Generally, resolution and accuracy refer to two separate phenomena when taking samples:

Accuracy

This one is easier to understand. If the actual value of some measurable quantity is 5, then the accuracy of the measuring tool is based on how close to 5 is gets. If the tool is specified with a ±10% accuracy bound, then we could have a measurement anywhere from 4.5 to 5.5. If it is specified with a ±.10 error bound, then we could get a measurement of 4.9 to 5.1. In any case, the accuracy relates to a tool's ability to ascertain the correct value for a measurement.

Resolution

For analog equipment, the resolution is easy to understand. As you said, it's generally taken as half the smallest readable value. On digital electronics, however, things can get more interesting (and even on analog ones, given the next few examples). Let's say that you have a piece of silicon that produces a voltage in response to incident light (a photocell or, perhaps, a CCD). The resolution is 1V per 1W/m^2, or for an irradiance of 1W/m^2, the cell produces 1V.

As we know from photography, the ISO value is typically representative of the resolution. Increasing the ISO gets us closer to the minimum resolution, while lower ISO values allow us to set an artificial threshold higher than the minimum.

In this example, we know that photocells and CCDs respond to more than light; they also respond to heat and random quantum fluctuations. As a result, we may have a device capable of producing large voltages in response to tiny fluctuations, but because of noise inherent to the sensor design, we can't distinguish between samples within that noise band.

You can even see this with analog sensors. Sometimes, the sensor is so sensitive (some pressure gauges, as an example) that they fluctuate with system vibrations.

Combining the Two

Going back to the light sensor, if the baseline noise value is ±5V, then we couldn't discern differences in light for ±5W/m^2 because they could all have the same reading (within the same ±5V range). Thus, the accuracy of such a device is now ±5V/(W/m^2) while the resolution is still 1V/(W/m^2).

Ultimately, the resolution simply tells you the sensitivity of a measuring tool while the accuracy tells you the threshold for identifying unique samples.

Bonus Section: Precision

If you're really lucky, you'll get a datasheet including long-term performance, to show drift characteristics, or error bounds for multiple samples of the same quantity, to show you absolute precision. Just because a sensor can read to the ppm (parts per million), and just because it is accurate (for a single measurement) to the ppt (parts per thousand), that doesn't mean you can ever get meaningful data if the precision is limited to the ppp (parts per part).

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  • \$\begingroup\$ The official terminology to use is "uncertainty of measurement" or UOM and that will take you into the statistics. \$\endgroup\$
    – skvery
    Feb 27 '17 at 21:25
  • \$\begingroup\$ It depends very much on the field you're in. As I pointed out, my fields have typically considered all three measurements separately. It provides the most information, allowing for the best data analysis. When I've heard "uncertainty," it has always been in the context of Gaussian fits to datasets, in which the mean-value theorem then applies. \$\endgroup\$
    – Hari Ganti
    Feb 27 '17 at 21:40
  • \$\begingroup\$ Thanks for the detailed explanation. I understand the concepts. But i cannot help remember my electric measurements assignature teacher hiting us with a stick if we express the value of a meassurement with more digits than the accuracy. As you said, without 'lucky' complete and detailed datasheets, I dont see the utility of such resolutions. \$\endgroup\$
    – Ste Ak
    Feb 28 '17 at 14:30
  • \$\begingroup\$ I actually explained something like this to a friend of mine who is a teacher since he wondered the same thing. It all depends on the field. Practically, digits beyond our certainty are useless, but they provide insight into the processes. If our resolution far exceeds the accuracy, it can tell us that the measurement techniques may have contributed to (or done little to mitigate) errors. It can also tell us how things like thermal noise conflate with photocell activity or other correlational data. \$\endgroup\$
    – Hari Ganti
    Feb 28 '17 at 19:22
  • \$\begingroup\$ Collecting data is often quite easy. The real challenge is in data analysis and statistics. \$\endgroup\$
    – Hari Ganti
    Feb 28 '17 at 19:22

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