Is a confidence interval a random variable?
“A confidence interval is a random variable because x-bar (its center) is a random variable.” (In this case, it’s presumably an interval for the mean, but the reasoning carries over to other confidence intervals.) The sample mean is a statistic — a quantity you calculate from the sample.
How do you back log a confidence interval?
For the log transformation, you would back-transform by raising 10 to the power of your number. For example, the log transformed data above has a mean of 1.044 and a 95% confidence interval of ±0.344 log-transformed fish. The back-transformed mean would be 101.044=11.1 fish.
Which is an example of a confidence interval?
Statistics notes: Transformations, means, and confidence intervals. For example, the 95% confidence interval for the mean on the log scale is -0.35 to -0.31. 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.
Are there problems with back transformed confidence intervals?
This is fraught with problems. Consider the bind you’re in now, the two possible CI’s, one in transformed space where you do your analyses, and one back transformed, make very different statements about where the likely mu is in the other space. The recommended back transform creates more problems than it solves.
What is the 95% confidence interval for the geometric mean?
For example, the 95% confidence interval for the mean on the log scale is -0.35 to -0.31. 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.
Which is the easiest case for transformations of continuous random variables?
The easiest case for transformations of continuous random variables is the case of gone-to-one. We \\frst consider the case of gincreasing on the range of the random variable X. In this case, g1is also an increasing function. To compute the cumulative distribution of Y = g(X) in terms of the cumulative distribution of X, note that F