Probability & Statistics/More rabbits
QUESTION: Hello Clyde,
I hope you are not fed up yet with my rabbit questions. I would like to ask a last one. I was searching in statistics and sampling books however I can't find a straight answer. Perhaps the question is too particular.
It is basically the same setup however this time I have several plots of land that are slightly different because they are in separate parts of the country, however the rabbit species is the same. So the wild rabbits freely come in an out of the corresponding plot, we assume that at measurement times we can capture all the rabbits within a plot and weight them in order to estimate the mean and variance of the weight of a rabbit, at such plot and collection round. Again, The populations are assumed 'stable' over time, plots are independent from each other (because they are far from each other), collection rounds are assumed independent of each other and the weight of one rabbit is assumed independent of the weight of another one. Last time you showed me how to estimate the mean and variance of a set of collection rounds in a single plot of land. This time I have the problem of estimating a mean and variance of the weight of a rabbit across plots of land, during say a single collection round. It is necessary that the two samples (that in general would have different numbers of individuals) contribute the same to the mean and variance across plots because plots have slightly different conditions, although the rabbit species is the same. The hope is that somehow these estimates are still more reliable than those of single plots (although the variance may grow a bit due to the slight differences between plots). If we want every plot to contribute equally then the estimator of the mean would be the mean of means of individual plots right? what would then be the estimator of the variance of the weight of a rabbit across plots if every plot contributes equally?
Many thanks in advance again...
ANSWER: "If we want every plot to contribute equally then the estimator of the mean would be the mean of means of individual plots right?"
Based on what you are describing, yes. I cannot say whether this is ecologically/biologically accurate or valid, but if you want to assume each plot contributes equally to the overall stats, you just take the average of the averages.
---------- FOLLOW-UP ----------
QUESTION: So this would be using a pooled mean and the correct corresponding variance would be a pooled variance (http://en.wikipedia.org/wiki/Pooled_variance
) right? :)
Many thanks again,
Right -- I forgot the name of this, but that's exactly what we talked about in the first answer to the question. It is (importantly) not
the actual variance, but it is the best way we can think of to compute a "weighted variance" using only the variance from each group (i.e. not using all of the original data points).