In dcousin3/MeasurementPrecision: Measurement Precision Toolkit

Loading the library

The exact computations to round descriptive statistics are found in the main text under Table 1. The equations are all simple; however, there are a lot of formulas to remember. To assist in rounding descriptive statistics, I have designed a small R library called \texttt{MeasurementPrecision} (no space and two capital letters) which resides on GitHub. To upload it, first install the \texttt{devtools} library from CRAN (Wickham, Hester & Chang, 2019). Then prior to the first use, issue the commands

devtools::install_github("dcousin3/MeasurementPrecision")
library(MeasurementPrecision)

On subsequent sessions, you can only use

library(MeasurementPrecision)

A basic use

Let's assume the following two sets of observations

sample1 <- c(83, 58, 79, 50, 49, 53, 62, 79, 66)
sample2 <- c(71, 62, 83, 93, 56, 82, 66, 69, 82, 86, 74, 61, 59, 101, 94, 86, 75)

To get a rounded descriptive statistic, use a command named \texttt{roundMP.\textit{statistic}}. For example, to round the mean of the first sample, use:

roundMP.mean(fromData = sample1, deltax = 0.5)

where \texttt{deltax}, a mandatory argument, is the precision of the instrument. The command returns a one-line data frame with four columns:

roundMP.mean(fromData = sample1, deltax = 0.5)

where \texttt{machine.precision} is the unrounded result, \texttt{extrinsic} is the extrinsic precision-based rounding; \texttt{systematic} is the result assuming systematic measurement error and \texttt{non.systematic} is the result assuming non-systematic measurement error.

In any of the commands, you can use \texttt{fromData} if you want to specify raw data or \texttt{fromStatistics} to provide already-calculated descriptive statistics (provide them with all the precision you can). For example,

roundMP.mean(
    fromStatistics = list(mean = 64.333333, sd = 13.20982, n = 9), 
    deltax = 0.5
) 

returns the same results as above. If you issue this command with an empty list of statistics, an error message will let you know which statistics are required.

Getting rounded statistics beyond the mean

You can also round the standard deviation (\texttt{sd}), the standard error of the mean (\texttt{semean}) and the confidence interval of the mean (\texttt{cimean}):

roundMP.sd(fromData = sample1, deltax = 0.5)
roundMP.semean(fromData = sample1, deltax = 0.5)
roundMP.cimean(fromData = sample1, deltax = 0.5) 

In \texttt{roundMP.cimean}, add \texttt{gamma = } for a different coverage. For example, \texttt{gamma = 0.80} will round a 80% confidence interval of the mean.

A one-sample t-test requires the null hypothesis for the mean, provided with \texttt{mu0}, for example:

roundMP.t.test(fromData = sample2, mu0 = 65, deltax = 0.5)
````

where 65 kg is the average planetary body weight for humans.

For statistics on two independent samples, you can use

```r
roundMP.meandiff(fromData = list(sample2, sample1), deltax = 0.5)
roundMP.sdpool(fromData = list(sample2, sample1), deltax = 0.5)
roundMP.cohen.d(fromData = list(sample2, sample1), deltax = 0.5)

The argument \texttt{fromData} accepts vectors, matrices, data frames or a list of vectors (as illustrated here).

The non-systematic estimates are by default obtained from the simplifying assumptions described in Appendix B of the main paper. To use the full expression (non-parametric solution), add \texttt{assumptions = FALSE} to any of the commands, for example

roundMP.t.test(
    fromData = list(sample2, sample1), 
    deltax=0.5, assumptions = FALSE
)

Generally, there is not much differences whether the simplified or the full expression are used.

Specifying the desired scenario as default

By default, all the roundMP functions output 4 different results, following four approaches to rounding: "\texttt{machine.precision}", "\texttt{extrinsic}", "\texttt{systematic}", and "\texttt{non.systematic}". It is possible to select only one or a few scenarios among this list by setting the global option \texttt{roundMP.selectedScenario}. For example, the following will display results only for two scenario (rounding assuming extrinsic and on systematic measurement error):

options(roundMP.selectedScenario = c("extrinsic", "systematic"))
roundMP.mean(fromData = sample1, 0.5)

options(roundMP.selectedScenario = c("machine.precision", "extrinsic", "systematic", "non.systematic"))

Arguments \texttt{fromData}, \texttt{fromStatistics} and \texttt{fromObject}

Regarding \texttt{t.test}, it is also possible to get a rounded result from a \texttt{t.test} object directly using the argument \texttt{fromObject} instead (instead of \texttt{fromData} or \texttt{fromStatistics}). The input has to contain a t-test, not a Welch test (so use var.equal = TRUE for two-samples):

res <- t.test(sample1, sample2, var.equal = TRUE)
roundMP.t.test(fromObject = res, deltax = 0.5)

Note that the library \texttt{MeasurementPrecision} must be loaded prior to use the \texttt{t.test} function as the t.test function is redefined by \texttt{MeasurementPrecision}.

Detailed output

Finally, to obtain more details on the computations, and see the exact precision, you can add the option \texttt{verbose = TRUE} to any command. For example,

roundMP.mean(fromData = list(sample1), deltax = 0.5, verbose = TRUE)

The results of the last line are identical to the solution provided earlier, but detailed information preceeds the results, showing the exact precision for each scenario, whether a simplifying assumption was used, and the resulting rounded result.

dcousin3/MeasurementPrecision documentation built on April 26, 2020, 4:59 p.m.