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I have some data that measures how a substance decays over time. At each time point I have 4 measurements. At time points where there is a lot of substance I use the standard error for error bars and this seems standard practice. However, when the amount of substance nears zero and I have a lot of variability in the measurement the standard error indicates that the lower error bars are values less than zero and this is physically impossible for this substance. When this is the case, how should I calculate where my error bars go? I suppose I'm assuming the underlying distribution of the data is gaussian when I use standard error, but clearly the data is not gaussian when it is near zero, because I can't have negative amounts of substance. Is there another distribution I should be using? Thanks.

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You should consider the log-normal distribution http://en.wikipedia.org/wiki/Log-normal_distribution which boils down to model the logarithm of the substance instead of the substance itself.

There also exists more complicated distributions that are suitable but the log-normal is often the default-choice when dealing with a positive and continuous random variable.

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