How can i calculate 95% confidence interval of geometric mean with SPPS? In some studies confidence intervals are given as range, [GM (x - y)], and in some others are given as a single value [GM (x)]. Which is the difference between them?
Bootstrapping is a possible but far too computer-intensive method. Much more elegant ist the straight-foreward analytical solution proposed by Washington.
To give a numerical example:
x = (2580,1279,490,1734,511)
x' = log(x)
mean(x') = 6.98
exp(6.98) = 1075 = geom.mean of x
CI(x') = [4.92...9.04] (calculated as usual using the t-distribution)
This interval on the log-scale is symmetric and could be represented as 6.98±2.06
exp(CI(x)) = [137...8434] = CI for the geom.mean of x.
This interval is not symmetric, using "±" is not possible, the limits must be stated explicitely. It may be presented as: "the geom.mean of x is 1075 (137...8434)". I prefer to use ellipses "..." instead of the minus "-" to indicate intervals to avoid a confusion with subtraction.
one option is to get the range using bootstrap resampling.
see an example...
is made to average more then just changing the geometric mean
http://statistics.about.com/od/Applications/a/Example-Of-Bootstrapping.htm
See link with question/answer in Cross Validated. The geometric mean (∏ni=1Xi)1/n is an arithmetic mean after taking logs 1/n∑ni=1logXi, so if you do know the CI for the arithmetic mean do the same for the logarithms of your data points and take exponents of the upper and lower bounds
http://stats.stackexchange.com/questions/8306/confidence-interval-for-geometric-mean
Bootstrapping is a possible but far too computer-intensive method. Much more elegant ist the straight-foreward analytical solution proposed by Washington.
To give a numerical example:
x = (2580,1279,490,1734,511)
x' = log(x)
mean(x') = 6.98
exp(6.98) = 1075 = geom.mean of x
CI(x') = [4.92...9.04] (calculated as usual using the t-distribution)
This interval on the log-scale is symmetric and could be represented as 6.98±2.06
exp(CI(x)) = [137...8434] = CI for the geom.mean of x.
This interval is not symmetric, using "±" is not possible, the limits must be stated explicitely. It may be presented as: "the geom.mean of x is 1075 (137...8434)". I prefer to use ellipses "..." instead of the minus "-" to indicate intervals to avoid a confusion with subtraction.
Hi, good afternoon,
Your question is interesting, How to calculate 95% confidence interval of geometric mean with SPSS.
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