Chris wrote:
>
> I know how to construct a confidence interval for a percentage when
> there is a binomial (# of good units / # of total units) distribution.
> How is the C.I. constructed if I have data such as the % of a liquid
> evaporated for each of a number of batches and I want to know let's
> say the limits of 99% of the population of the batches? Each batch
> has a %, say x kg out of y kg. I don't think a kg can be considered a
> "unit" (or can it?)
The fact that the data involve "percentages" here is a red herring. A
kilogram cannot be considered a unit in your sense, as its size is just
a convention; and moreover, liquids do not evaporate by a
Poisson/binomial process in which each individual gallon/kilo/firkin has
a certain chance of evaporating *pop!* in one go, independent of the
rest.
For large samples (number of batches) a normal model with t test/CI
would probably be appropriate. How large "large" is depends on the
distribution.
For small samples detailed mathematical models of evaporation might be
needed - is the randomness due to temperature fluctuations? purity
fluctuations? cross section of the tank as a function of depth?
windspeed? somebody leaving the top off sometimes? Depending on all
that, you might be able to get away with a normal model; or you might
need to transform or use a nonparametric method or something. Indeed, it
is possible that a CI for percent evaporation might not even be a good
summary of the observations in some of these cases - say that the
evaporation is either 0.05% if the lid is left on or 4% per day if it's
left off. You'd have a mixed model with a large spike near 0 and along
tail; "average percent loss" would be a bad description of reality.
-Robert Dawson
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