# Gmean

##### Geometric Mean and Standard Deviation

Calculates the geometric mean, its confidence interval and the geometric standard deviation of a vector x.

- Keywords
- arith

##### Usage

```
Gmean(x, method = c("classic", "boot"), conf.level = NA, sides = c("two.sided","left","right"), na.rm = FALSE, ...)
Gsd(x, na.rm = FALSE)
```

##### Arguments

- x
- a positive numeric vector. An object which is not a vector is coerced (if possible) by as.vector.
- method
- a vector of character strings representing the type of intervals required. The value should be any subset of the values
`"classic"`

,`"boot"`

. See`boot.ci`

. - conf.level
- confidence level of the interval. Default is
`NA`

. - sides
- a character string specifying the side of the confidence interval, must be one of
`"two.sided"`

(default),`"left"`

or`"right"`

. You can specify just the initial letter.`"left"`

would be analogue to a hypothesis of`"greater"`

in a`t.test`

. - na.rm
- logical, indicating whether
`NA`

values should be stripped before the computation proceeds. Defaults to`FALSE`

. - ...
- further arguments are passed to the
`boot`

function. Supported arguments are`type`

(`"norm"`

,`"basic"`

,`"stud"`

,`"perc"`

,`"bca"`

),`parallel`

and the number of bootstrap replicates`R`

. If not defined those will be set to their defaults, being`"basic"`

for`type`

, option`"boot.parallel"`

(and if that is not set,`"no"`

) for`parallel`

and`999`

for`R`

.

##### Details

To compute the geometric mean, `log(x)`

is first calculated, before the arithmetic mean and its confidence interval are computed by `MeanCI`

.

So the geometric mean and geometric sd are restricted to positive inputs (because otherwise the answer can have an imaginary component). Hence if any argument is negative, the result will be `NA`

. If any argument is zero, then the geometric mean is zero.

The geometric mean is defined as $$\sqrt[n]{x_{1}\cdot x_{2}\cdot x_{3} \ldots \cdot x_{n}}$$

and its confidence interval is given as `exp(MeanCI(log(x)))`

.
Use `sapply`

to calculate the measures from data frame, resp. from a matrix.

##### Value

##### References

Snedecor, G. W., Cochran, W. G. Cochran (1989) Statistical Methods, 8th ed. Ames, *IA: Iowa State University Press *

##### See Also

##### Examples

```
x <- runif(5)
Gmean(x)
m <- matrix(runif(50), nrow = 10)
apply(m, 2, Gmean)
sapply(as.data.frame(m), Gmean)
```

*Documentation reproduced from package DescTools, version 0.99.19, License: GPL (>= 2)*