Is it possible to validate the measurements of a precise scale with a scale wich is less precise?

Let's say I have a scale wich can display values down to 1g and another scale which can display the values down to 0.01g. I measure for example 100 pieces, which I know are about 1g, on the precise scale an save all the individual measurements. Then I measure the total weight of all pieces on the less precise scale and write this value down. If needed, I can make as many measurements as needed on the less precise scale and use all these measurements.

With the information gained, total weight and individual weights off the precise scale, what can I say about the accuracy of the precise scale?

  • $\begingroup$ Using the less-precise scale you have made just a single measurement? If so, your job of validation is going to be very difficult. $\endgroup$ – rolando2 Mar 19 '16 at 21:30
  • $\begingroup$ You can't say anything whatsoever about accuracy until you know the accuracies of the scale used for the measurements! $\endgroup$ – whuber Mar 20 '16 at 16:38
  • $\begingroup$ @rolando2 i can make as many measurements with the less precise scale as needed. I added this fact in to the question. $\endgroup$ – jrast Mar 20 '16 at 18:32
  • $\begingroup$ @whuber assume the accuracy is the same as the displayed value on the scale. $\endgroup$ – jrast Mar 20 '16 at 18:32

You can do this if you are sure that the measurement error for the coarse scale is low (that is, if you are sure that when your measure one hundred thousand 0.01 gram samples you will have a reading of 1000 gram +- some small error). In this case you will have a solid expected value for sums of fine-grained measurements and you will be able to see if these sums are well behaved (not biased towards lower or bigger values and have reasonable variance).

  • $\begingroup$ I understand the bias you mention in the answer. But can you add some more details about the variance? What can I say about the variance? $\endgroup$ – jrast Mar 20 '16 at 18:34
  • $\begingroup$ Actually, you don't need the coarse scale to estimate the variance. If you measure something 1000 times and add the results you will obtain a point sample from a population of sums of 1000 individual measurements. Since the measurements are independent from each other, you can sample in this manner several times, estimate the variance of this sample-of-sums and then simply divide by 1000: variance of a sum of i.i.d. variables equals the sum of their variances. You need the coarse-but-low-error measurement to check if fine-scaled measurements are biased. $\endgroup$ – macleginn Mar 23 '16 at 12:54

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