In a paper I came across 'non-parametric bootstrapping', which I hadn't heard of. It's used as a way to deal with small sample sizes. But my question is not yet about whether that is appropriate (cf. this question). I'm still trying to understand the basics. I read this, but am still confused!
example case: Suppose there is a population of worms and I want to know the average length. There are zillions of them. But I can only measure 100 individuals. I do so, and compute the mean. I wonder how much it really tells me about the wider population; so I follow the bootstrapping-with-resampling procedure and get a distribution for the means of the resamplings.
1) Why go through the resampling procedure to produce a distribution-of-means-of-length, rather than 'simply' use the original sample's distribution-of-length, as an indicator for the population length distribution?
2) Suppose the distribution-of-means-of-length turns out roughly Gaussian. So this certainly tells me something about the population, beyond what my sole sample mean tells me: for one thing, that there is some variability in lenghts (but as in point (1) above, would not my sample length distribution have told me that too). Now, AFAIU, this may further tell me something about the shape of the population distribution (as is the intention - right?) But then again, it may not! Perhaps the population length distribution is really bimodal with different-mean-length morphs in winter and summer, unbeknownst to me; and alas, I only measured in one season. So my sample of n=100 is unimodal and biased, but I don't know it. I don't see how the bootstrapping helps here. Resampling from that biased sample will never say anything about the 'missing mode'. But wasn't the goal of the bootstrapping precisely to let information in my sample enlighten me about the population distribution, or at least about how representative my sample is?
If I don't know whether the winter/summer scenario is the case, nothing about the bootstrapping seems to decide it for me. If I already knew about the winter/summer scenario, I would already know something about how my sample relates to the population, and would not have needed the bootstrapping (as much) to begin with? It's as if you want to know whether your sample is representative of the population; but the procedure circularly assumes that it is.
I must be missing the point... How?