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I am an agronomist trying to estimate the average weight of fruit in a orchard. My first option is to grab 1000 fruit and get their weight mean. But as you can see, if i can get this with less fruits, I will save time (and fruits).

Is there any way to get a stopping rule based on the prior update (every time that I record a new single fruit weight)?

Thank you

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  • $\begingroup$ When exactly would you like to stop? $\endgroup$ – Tim Feb 1 '17 at 10:01
  • $\begingroup$ Well, I guess that's the question. I've read some text about the ROPE and HDI relation. Could it be one possible criteria? $\endgroup$ – Hugo Feb 1 '17 at 10:28
  • $\begingroup$ Hi Hugo. Chapter 13 of DBDA2E is all about "Goals, Power, and Sample Size." In particular, it discusses "optional stopping" using different goals. $\endgroup$ – John K. Kruschke Feb 1 '17 at 17:50
  • $\begingroup$ Thank you John K. Kruschke. I am reading your book but I am not finding out how to set a rule. I will work harder and get some more samples. $\endgroup$ – Hugo Feb 1 '17 at 18:17
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Short answer: No. A confidence interval, that you would use as a prior, provides no degree of belief.

The problem here is that you don't know which are the factors that makes your fruits have a different weight, thus you can't be sure to pick a significant samples of fruit.

Say for example that you have red and yellow fruits, and that they have a different weight (Red = 1kg, Yellow = 2kg). If you have the same amount of red and yellow fruits in your orchard then the average is 1.5kg. But if you pick only red fruits for your sample, then you will end up with an average of 1kg. Obviously you wouldn't use a sample of red fruits only because you know that the fruits have different colors, but what about their age ? position on the tree ? size ? size of the stone ? sun exposure ? etc...

Your problem is not to know when to stop adding fruits to your sample, but what fruits should you put in your sample. And this depends on agronomy criteria that you probably know much better than statisticians.

Now, if you come up with a perfectly homogeneous sample of fruits, the more you add, the more precise your mean estimate should be. When to stop depends on the precision you want to achieve (and you may want to have a look at that)

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