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I want to determine the 95% confidence interval of a mean.

  1. I logged-transformed my data in order to achieve a normal distribution.

  2. Several observations contained 0, so I changed these to 1 so that they would be represented as 0 after the transformation.

  3. I then found the standard deviation of the log-transformed data.

  4. I computed the SE of the transformed data by the equation (SD/sqrt(n)*1.96),

  5. I back-transformed the SE with exp(SE) in order to get the SE on the scale of the original data.

  6. I then added and subtracted the back-transformed SE from the untransformed mean (calculated with the 0s) in order to find the lower and upper confidence limits of the mean.

I have a bad feeling my back-transformation (step 5) is either not done correctly, or in the wrong place. Could someone validate my method? Refute it maybe as well, with an explanation of any statistical rules I have violated with this method, and possible suggestions to solve the problem

Steve
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Reuben
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    You're right - you can't just back-transform the SE. Do you really want a CI for the mean, or something else? For example, if you back-transform the mean of $\log X$, you get the geometric mean of $X$, which isn't the same as the usual arithmetic mean, but still of interest. Also, I think you should transform everything the same way, e.g., use $\log(X+1)$ even when $X\ne0$. – Russ Lenth Aug 15 '14 at 19:13
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    See [this question](http://stats.stackexchange.com/questions/33382/how-do-i-calculate-a-confidence-interval-for-the-mean-of-a-log-normal-data-set) for solutions for standard errors/confidence intervals of the mean of lognormals. In addition to those, the CLT should also apply here as well, so transforming is not needed, and as Russ notes, back transforming will return the geometric mean of X, not the arithmetic. – Affine Aug 15 '14 at 20:27

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