This function calculates a number of descriptive statistics for estimates with a given standard error (SE), most fundamentally using error-weighted approaches.

```
calc_Statistics(data, weight.calc = "square", digits = NULL,
n.MCM = NULL, na.rm = TRUE)
```

data

data.frame or '>RLum.Results object (**required**):
for data.frame two columns: De (`data[,1]`

) and De error (`data[,2]`

).
To plot several data sets in one plot the data sets must be provided
as `list`

, e.g. `list(data.1, data.2)`

.

weight.calc

character:
type of weight calculation. One out of `"reciprocal"`

(weight is 1/error),
`"square"`

(weight is 1/error^2). Default is `"square"`

.

digits

integer (*with default*):
round numbers to the specified digits.
If digits is set to `NULL`

nothing is rounded.

n.MCM

numeric (*with default*):
number of samples drawn for Monte Carlo-based statistics.
`NULL`

(the default) disables MC runs.

na.rm

logical (*with default*):
indicating whether `NA`

values should be stripped before the computation proceeds.

Returns a list with weighted and unweighted statistic measures.

0.1.7 (2018-01-21 17:22:38)

Dietze, M. (2018). calc_Statistics(): Function to calculate statistic measures. Function version 0.1.7. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J. (2018). Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.8.6. https://CRAN.R-project.org/package=Luminescence

The option to use Monte Carlo Methods (`n.MCM`

) allows calculating
all descriptive statistics based on random values. The distribution of these
random values is based on the Normal distribution with `De`

values as
means and `De_error`

values as one standard deviation. Increasing the
number of MCM-samples linearly increases computation time. On a Lenovo X230
machine evaluation of 25 Aliquots with n.MCM = 1000 takes 0.01 s, with
n = 100000, ca. 1.65 s. It might be useful to work with logarithms of these
values. See Dietze et al. (2016, Quaternary Geochronology) and the function
plot_AbanicoPlot for details.

# NOT RUN { ## load example data data(ExampleData.DeValues, envir = environment()) ## show a rough plot of the data to illustrate the non-normal distribution plot_KDE(ExampleData.DeValues$BT998) ## calculate statistics and show output str(calc_Statistics(ExampleData.DeValues$BT998)) # } # NOT RUN { ## now the same for 10000 normal distributed random numbers with equal errors x <- as.data.frame(cbind(rnorm(n = 10^5, mean = 0, sd = 1), rep(0.001, 10^5))) ## note the congruent results for weighted and unweighted measures str(calc_Statistics(x)) # } # NOT RUN { # }