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Statistical Analysis over different samples - Prediction for the number of objects

Cross Validated Asked on December 8, 2021

This may be a really simple question but here’s my problem:

I have different boxes with soil (wet sandy kind) and big stones in it. Each box is around 10kg and I want to estimate the number of big stones in each box so what I do is:

  • Measuring the weight of the soil+stone of each box
  • Taking three smaller samples from each box, measuring their weights and counting the number of stones in those samples
  • With a cross product, I estimate the number of stones in the box (from the 3 samples independently) and then calculate an average and this is my estimation of the number of stones in the big box.

I want to do some statistics to see if I have significant differences in terms of number of stones between the 3 samples. I want to know if counting just one sample is enough or if I have to count 2, 3 or even more samples.
For now, I’ve just compared the estimation of the number of stones (product cross) for each sample. The problem is that this approach doesn’t take into account the size (i.e weight) of the samples (I guess that the heavier the sample is, the better it is for estimation).

How can I weight those samples, or is there a statistical method that fits my purpose?

Also, I don’t know if taking only the average between the estimates from the 3 samples is the right way to estimate the number of stones in those boxes…

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