Understanding RMS Accuracy for Measurements

[BobbyBear]

Hello,

can someone please explain what exactly is meant when it is said that some measurement is accurate to some value RMS?

Eg, "suppose that we have a bucketful of nominally 100-ohm resistors, accurate to 1 percent RMS"

or,

"we shall use an ohmmeter with an accuracy of 3 ohms RMS random error on each reading"


I know what the rms value of a set of values is, I'm just not sure what is meant by these statements, can someone explain please?:p

thanks,
Bob

 

[SW VandeCarr]

Hello,

can someone please explain what exactly is meant when it is said that some measurement is accurate to some value RMS?

Eg, "suppose that we have a bucketful of nominally 100-ohm resistors, accurate to 1 percent RMS"

or,

"we shall use an ohmmeter with an accuracy of 3 ohms RMS random error on each reading"I know what the rms value of a set of values is, I'm just not sure what is meant by these statements, can someone explain please?:p

thanks,
Bob

I don't understand either. They are mixing terms. Accuracy is not about random error. Accuracy has to do with bias (or systematic error) and the root mean square error measures bias. So:

$$RMSE=\sqrt{E((\hat\theta-\theta)^2)}$$

RMS itself is the quadratic mean and is used to average out regular variations such as with sinusoidal wave patterns. It is not a measure of error.

Measures of random variation about a mean are different and are expressed as the variance or standard deviation of the mean.

http://en.wikipedia.org/wiki/Accuracy_and_precision