Suppose I'm planning an experiment where I drop ceramic tiles on a concrete floor and measure the masses of all the pieces after the tile shatters. I can't really measure dust particles, so there is a minimum size that I bother documenting.
I test each tile separately and note the collection of masses from each.
I want to eventually model a distribution of the masses you could expect from shattering a tile this way, but the tiles are expensive (or I'm cheap, whichever floats your boat). How do I quantify the added benefit of testing an additional tile so that I can decide how many to test?
It seems to me that the individual measurements of masses are dependent within a given sample. So I could fit masses from a single tile drop to a distribution and note the parameters that best fit. Data from another drop would result in different parameters. Each test would give me a random draw from the distribution of the parameters themselves. So if I drop 3 tiles, I really only have 3 points to define the distribution of the parameters, even though I might have hundreds of samples of tile masses.
Or maybe I can just throw all the data together and fit one distribution. Then the total number of pieces I measure is my sample size.