Uncertainty in Scale Measurement

[tangodirt]

Having a bit of trouble estimating total scale uncertainty.

In this experiment, I used four precision weights (error << scale resolution). Each weight has a known mass and is weighted on a scale 20 different times. Therefore, for each weight, I have a mean scale measurement, a standard deviation, and the true value of the weight. Each weight measures a different range of the scale, for example, 250 g, 500 g, 750 g, 1000 g.

How can I go about estimating the total scale uncertainty? What I am looking for is a method to produce a total uncertainty for any given measurement. If I place an random object on the scale, say an apple that weighs 500 g, I can say that the scale is accurate to +/- ___ grams.

Any advice? I am running monte carlo simulations, but having a difficult time quantifying total error (not sure which method to use). I feel like there should be a method using fundamental statistics to determine this uncertainty.

 

[Dale]

You are probably going to want to do a regression ( hopefully linear is all you need) and then find a prediction interval. Here is a page that briefly discussed the difference between confidence intervals and prediction intervals.

https://www.ma.utexas.edu/users/mks/statmistakes/CIvsPI.html