```
set.seed(42)
library(qwraps2)
# define the markup language we are working in.
# options(qwraps2_markup = "latex") is also supported.
options(qwraps2_markup = "markdown")
```

It is common for a manuscript to require a data summary table. The table might include simple summary statistics for the whole sample and for subgroups. There are several tools available to build such tables. In my opinion, though, most of those tools have nuances imposed by the creators/authors such that other users need not only understand the tool, but also think like the authors. I wrote this package to be as flexible and general as possible. I hope you like these tools and will be able to use them in your work.

This vignette presents the use of the `summary_table`

,
`qsummary`

, and `qable`

functions for quickly
building data summary tables. We will be using summary statistic
functions, `mean_sd`

, `median_iqr`

,
`n_perc`

, and others, from *qwraps2* as
well.

We will use the data set `mtcars2`

for the examples
throughout this vignette data set for examples throughout this vignette.
`mtcars2`

is a modified and extended version of the base R
data set `mtcars`

. For details on the construction of the
`mtcars2`

data set please view the vignette:
`vignette("mtcars", package = "qwraps2")`

```
data(mtcars2)
str(mtcars2)
## 'data.frame': 32 obs. of 19 variables:
## $ make : chr "Mazda" "Mazda" "Datsun" "Hornet" ...
## $ model : chr "RX4" "RX4 Wag" "710" "4 Drive" ...
## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ disp : num 160 160 108 258 360 ...
## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...
## $ drat : num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...
## $ qsec : num 16.5 17 18.6 19.4 17 ...
## $ cyl : num 6 6 4 6 8 6 8 4 4 6 ...
## $ cyl_character: chr "6 cylinders" "6 cylinders" "4 cylinders" "6 cylinders" ...
## $ cyl_factor : Factor w/ 3 levels "6 cylinders",..: 1 1 2 1 3 1 3 2 2 1 ...
## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...
## $ engine : Factor w/ 2 levels "V-shaped","straight": 1 1 2 2 1 2 1 2 2 2 ...
## $ am : num 1 1 1 0 0 0 0 0 0 0 ...
## $ transmission : Factor w/ 2 levels "Automatic","Manual": 2 2 2 1 1 1 1 1 1 1 ...
## $ gear : num 4 4 4 3 3 3 3 4 4 4 ...
## $ gear_factor : Factor w/ 3 levels "3 forward gears",..: 2 2 2 1 1 1 1 2 2 2 ...
## $ carb : num 4 4 1 1 2 1 4 2 2 4 ...
## $ test_date : POSIXct, format: "1974-01-05" "1974-01-07" ...
```

`mean_sd`

returns the (arithmetic) mean and standard
deviation for numeric vector as a formatted character string. For
example, `mean_sd(mtcars2$mpg)`

returns the formatted string
20.09 ± 6.03. There are other options for formatting character
string:

If you need the mean and a confidence interval there is the function
`mean_ci`

. which returns a `qwraps2_mean_ci`

object which is a named vector with the mean, lower confidence limit,
and the upper confidence limit. The printing method for
`qwraps2_mean_ci`

objects is a call to the
`frmtci`

function. You an modify the formatting of printed
result by adjusting the arguments pasted to `frmtci`

.

Similar to the `mean_sd`

function, the
`median_iqr`

returns the median and the inner quartile range
(IQR) of a data vector.

The `n_perc`

function is the workhorse.
`n_perc0`

is also provided for ease of use in the same way
that base R has `paste`

and `paste0`

.
`n_perc`

returns the n (%) with the percentage sign in the
string, `n_perc0`

omits the percentage sign from the string.
The latter is good for tables, the former for in-line text.

```
n_perc(mtcars2$cyl == 4)
## [1] "11 (34.38%)"
n_perc0(mtcars2$cyl == 4)
## [1] "11 (34)"
n_perc(mtcars2$cyl_factor == 4) # this returns 0 (0.00%)
## [1] "0 (0.00%)"
n_perc(mtcars2$cyl_factor == "4 cylinders")
## [1] "11 (34.38%)"
n_perc(mtcars2$cyl_factor == levels(mtcars2$cyl_factor)[2])
## [1] "11 (34.38%)"
# The count and percentage of 4 or 6 cylinders vehicles in the data set is
n_perc(mtcars2$cyl %in% c(4, 6))
## [1] "18 (56.25%)"
```

Let \(\left\{x_1, x_2, x_3, \ldots, x_n \right\}\) be a sample of size \(n\) with \(x_i > 0\) for all \(i.\) Then the geometric mean, \(\mu_g,\) and geometric standard deviation are

\[ \begin{equation} \mu_g = \left( \prod_{i = 1}^{n} x_i \right)^{\frac{1}{n}} = b^{ \sum_{i = 1}^{n} \log_{b} x_i }, \end{equation} \] and \[ \begin{equation} \sigma_g = b ^ { \sqrt{ \frac{\sum_{i = 1}^{n} \left( \log_{b} \frac{x_i}{\mu_g} \right)^2}{n} } } \end{equation} \] or, for clarity, \[ \begin{equation} \log_{b} \sigma_g = \sqrt{ \frac{\sum_{i = 1}^{n} \left( \log_{b} \frac{x_i}{\mu_g} \right)^2}{n}} \end{equation} \]

When looking for the geometric standard deviation in R, the simple
`exp(sd(log(x)))`

is not exactly correct. The geometric
standard deviation uses \(n,\) the full
sample size, in the denominator, where as the `sd`

and
`var`

functions in R use the denominator \(n - 1.\) To get the geometric standard
deviation one should adjust the result by multiplying the variance by
\((n - 1) / n\) or the standard
deviation by \(\sqrt{(n - 1) / n}.\)
See the example below.

```
x <- runif(6, min = 4, max = 70)
# geometric mean
mu_g <- prod(x) ** (1 / length(x))
mu_g
## [1] 46.50714
exp(mean(log(x)))
## [1] 46.50714
1.2 ** mean(log(x, base = 1.2))
## [1] 46.50714
# geometric standard deviation
exp(sd(log(x))) ## This is wrong
## [1] 1.500247
# these equations are correct
sigma_g <- exp(sqrt(sum(log(x / mu_g) ** 2) / length(x)))
sigma_g
## [1] 1.448151
exp(sqrt((length(x) - 1) / length(x)) * sd(log(x)))
## [1] 1.448151
```

The functions `gmean`

, `gvar`

, and
`gsd`

provide the geometric mean, variance, and standard
deviation for a numeric vector.

```
gmean(x)
## [1] 46.50714
all.equal(gmean(x), mu_g)
## [1] TRUE
gvar(x)
## [1] 1.146958
all.equal(gvar(x), sigma_g^2) # This is supposed to be FALSE
## [1] "Mean relative difference: 0.8284385"
all.equal(gvar(x), exp(log(sigma_g)^2))
## [1] TRUE
gsd(x)
## [1] 1.448151
all.equal(gsd(x), sigma_g)
## [1] TRUE
```

`gmean_sd`

will provide a quick way for reporting the
geometric mean and geometric standard deviation in the same way that
`mean_sd`

does for the arithmetic mean and arithmetic
standard deviation:

The function `summary_table`

appears to be the most widely
used tool provided by the qwraps2 package. As such, that function has
earned its own vignette.

```
print(sessionInfo(), local = FALSE)
## R version 4.3.2 (2023-10-31)
## Platform: x86_64-apple-darwin20 (64-bit)
## Running under: macOS Monterey 12.6
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] qwraps2_0.6.0
##
## loaded via a namespace (and not attached):
## [1] digest_0.6.33 R6_2.5.1 fastmap_1.1.1 xfun_0.41
## [5] cachem_1.0.8 knitr_1.45 htmltools_0.5.7 rmarkdown_2.25
## [9] cli_3.6.1 sass_0.4.7 jquerylib_0.1.4 compiler_4.3.2
## [13] tools_4.3.2 evaluate_0.23 bslib_0.5.1 Rcpp_1.0.11
## [17] yaml_2.3.7 rlang_1.1.2 jsonlite_1.8.7
```