Contents
What is the confidence interval for geometric mean?
To get back to the original scale we antilog the confidence limits on the log scale to give a 95% confidence interval for the geometric mean on the natural scale (0.47) of 0.45 to 0.49 mmol/l. For comparison, the 95% confidence interval for the arithmetic mean using the raw, untransformed data is 0.48 to 0.54 mmol/l.
When to use confidence intervals for lognormal mean?
Generalized confidence intervals (Weerahandi, 1993) can be used for inference about parameters where the sampling distribution is complicated. As noted in equation (2), the lognormal mean is a function of , which can be assumed to be Normally distributed, and S2, which is a function of a variate.
When to use a logarithmic transformation in statistics?
A logarithmic transformation is often useful for data which have positive skewness like this, and here the approximation to a normal distribution is greatly improved. For the untransformed data the mean is 0.51 mmol/l and the standard deviation 0.22 mmol/l. The mean of the log10 transformed data is -0.33 and the standard deviation is 0.17.
What is the standard deviation of log10 transformed data?
For the untransformed data the mean is 0.51 mmol/l and the standard deviation 0.22 mmol/l. The mean of the log10 transformed data is -0.33 and the standard deviation is 0.17. If we take the mean on the transformed scale and back transform by taking the antilog, we get 10 -0.33 =0.47 mmol/l.
Can you transform the standard deviation back to the original scale?
As a result, we cannot transform the standard deviation back to the original scale. If we want to use the standard deviation or standard error it is easiest to do all calculations on the transformed scale and transform back, if necessary, at the end. For example, the 95% confidence interval for the mean on the log scale is -0.35 to -0.31.
How is the antilog of the log transformed data measured?
The antilog of the standard deviation, however, is not measured in mmol/l. Calculation of the standard deviation of the log transformed data requires taking the difference between each log observation and the log geometric mean.