In this post, we will learn how to carry out descriptive statistics in R. After we have learned how to do this, we will learn how to create a nice latex table and how to save the summary statistics to a .csv file. Note, in a recent post you learn how to quickly explore your data with one of Tukey’s exploratory data analysis methods:

Table of Contents

## Why Descriptive Statistics?

Carrying out descriptive statistics, also known as summary statistics, is a very good starting point for most statistical analyses. It is, furthermore, a very good way to summarize and communicate information about the data we have collected.

There are, of course, plenty of useful r-packages for data manipulation and summary statistics. In this post, we will mainly work with the base R functions, and the psych and Tidyverse packages. Tidyverse comes with a bunch of handy packages that you can use to, for example, add an empty column to the dataframe.

## Installing the R-packages

As mentioned in the previous section, we are, in this descriptive statistics with R post, going to work with some r-packages. If they’re not installed the following commands will install them.

```
list.of.packages <- c("tidyverse", "psych", "knitr", "kableExtra")
new.packages <- list.of.packages[!(list.of.packages %in% installed.packages()[,"Package"])]
if(length(new.packages)) install.packages(new.packages)
```

Code language: R (r)

In the code chunk above, we first created the vector with the packages we want to install. Second, we created a new vector carrying out value matching (with the %in% operator in R). Finally, we only installed the packages that were not installed already!

In this summary statistics in R tutorial, we will start by calculating descriptive statistics and some variance measures. After that, we continue with the most common ways to report the central tendency (i.e., the mean, the median). Finally, we will also calculate the harmonic, the geometric, and the trimmed mean.

## Descriptive statistics in R

In this section, we will start by calculating some demographic statistics for our data. Furthermore, we will calculate the number of missing values by group, the % of missing values by group, the mean age, age range, and such.

### Import Data

First, however, we are going to read an xlsx file using R (it can be downloaded here):

```
library(readxl)
play_df <- read_excel("../SimData/play_data.xlsx")
```

Code language: R (r)

Note, data can be stored in a range of different formats. For instance, we can also read a .dta (Stata) file, and a SPSS (.sav) with R.

Before calculating some summary statistics w can have a look at the first five rows of our data by typing `head(play_df)`

. Here’s how the data looks like:

Second, as we can see in the Gender column it is coded as 0 (and 1) and we are going to recode the values to “Male” and “Female”. We are going to use the recode function. If we want, or need to, we can also remove a column. Alternatively, when calculating the summary statistics, we can also select the columns we want to use.

```
library(tidyverse)
# Renaming variables:
play_df$Gender <- play_df$Gender %>%
recode("0" = "Male",
"1" = "Female")
```

Code language: R (r)

### Descriptive Statistics: e.g. mean age, range, and standard deviation

In this section, we are going to summarize the information about the participants of the study. That is, we are going to calculate the mean and standard deviation in terms of age, and the age range. Here, we use the Tidyverse package, again, and the summarise function:

```
require(tidyverse)
# Summarizing the dataframe:
play_df %>%
summarise(sd = sd(Age, na.rm = T),
mean = mean(Age, na.rm = T),
range = paste(min(Age, na.rm = T), "-", max(Age, na.rm = T)),
n = sum(!is.na(Age)))
```

Code language: R (r)

In the code chunk above, we calculated some summary statistics about the sample. Note, we used the na.rm = T because there might be missing values in the variable Age. To create the age range variable we take the min and the max of the variable Age. Notice that we used the paste function to create the range.

### Descriptive Statistics in R by Group: mean age, age range, standard deviation

Now, we are going to group the data and calculate the mean, standard deviation, age range, and how many there are in each group. In the code chunk below, all we have done is to add the group_by method and added “Gender” to that.

```
library(tidyverse)
# Summarizing by group:
play_df %>% group_by(Gender) %>%
summarise(sd = sd(Age, na.rm = T),
mean = mean(Age, na.rm = T),
range = paste(min(Age, na.rm = T), "-", max(Age, na.rm = T)),
n = sum(!is.na(Age)))
```

Code language: R (r)

## Summary statistics: Measures of Central Tendency in R

In this part of the R descriptive statistics tutorial, we will focus on the measures of central tendency. The central tendency is something we calculate because we often want to know about the “*average*” or “*middle*” of our data. The two most commonly used measures of central tendency can easily be obtained using R; the mean and the median.

### Calculate the Mean in R

In the previous section, we calculated summary statistics (e.g., mean, standard deviation, range) in one go. However, if we are only interested in one summary statistic, we can calculate them separately. First, if we only want to calculate the mean of one of our variables we can use the mean function. Note, here we are interested in calculating the summary statistics for the dependent variable “RT”:

```
# Calculating mean value:
mean(play_df$RT, na.rm = T)
# Output: [1] 0.4963685
```

Code language: R (r)

### Calculate the Mean by One Group

Second, when we use Tidyverse group_by and summarise functions, we just add the mean function. Note, this is very similar to what we did previously.

```
# Mean by Gender:
play_df %>% group_by(Gender) %>%
summarise(RT = mean(RT, na.rm = T))
```

Code language: R (r)

### Calculate the mean by Two Groups

Third, if we want to calculate the mean by two groups we add a group to the group_by function:

```
# Calculating mean by multiple (i.e, 2) groups:
play_df %>% group_by(Gender, Day) %>%
summarise(RT = mean(RT, na.rm = T))
```

Code language: R (r)

### Geometric, Harmonic, & Trimmed Mean in R

In this section, we are going to use the R-package psych to calculate the geometric, harmonic, and trimmed mean in R. Many times it may be better to calculate the geometric and harmonic mean when we are doing summary statistics. In R, these two descriptive statistics can be obtained using the summarise function together with the functions *geometric.mean* and *harmonic.mean *(from psych).

#### Geometric Mean in R

In this section, we, are going to calculate the geometric mean in R. One very nice thing, when working with summarise is that we can input any function, from another package, that we need to use. This, in the next code chunk we are going to use the geometric.mean function from the psych package to calculate the geometric mean.

```
# Calculating geometric mean by multiple groups:
play_df %>% group_by(Gender, Day) %>%
summarise("Geometric Mean" = psych::geometric.mean(RT, na.rm = T))
```

Code language: R (r)

#### Harmonic Mean in R

In this, R summary statistics example, we use summarise together with harmonic.mean to get the harmonic mean in R:

```
# Harmonic mean grouped by multiple groups
play_df %>% group_by(Gender, Day) %>%
summarise("Harmonic Mean" = psych::harmonic.mean(RT, na.rm = T))</code></pre>
```

Code language: R (r)

#### Trimmed Mean in R

In this section, we are going to calculate the trimmed mean. This can, actually, be done using the mean function. All we do is use the trim=.2:

```
play_df %>% group_by(Gender, Day) %>%
summarise("Harmonic Mean" = mean(RT, trim=0.2, na.rm = T))
```

Code language: R (r)

### Get the Median in R

In this section, we are going to calculate the median using R. It’s as easy as calculating the mean and just use the function called median.

`median(play_df$RT, na.rm = T)`

Code language: R (r)

### Median by Groups in R

Of course, we often want the median, as well, calculated by group (e.g. categorical variable) and if we want to calculate the median by group we just use group_by, again, and summarise:

```
play_df %>% group_by(Gender, Day) %>%
summarise(Mean = median(RT, na.rm = T))
```

Code language: R (r)

### Measures of Central Tendencies in One Tibble (Mean, Median, Harmonic, Geometric, and Trimmed)

Now, most of the time we want to get all the measures of central tendency (or all summary statistics we calculate in R) in the same output. We can, of course, get all the data in the same output using summarise. In the descriptive statistics in R example below, the standard deviation (*sd*), mean, median, harmonic mean, geometric mean, and trimmed mean are all in the same output.

```
play_df %>% group_by(Gender, Day) %>%
summarise(SD = sd(RT, na.rm = T),
Mean = mean(RT, na.rm = T),
Median = median(RT, na.rm = T),
"Trimmed Mean" = mean(RT, trim = 0.2, na.rm = T),
"Geometric Mean" = psych::geometric.mean(RT, na.rm = T),
"Harmonic Mean" = psych::harmonic.mean(RT, na.rm = T))
```

Code language: PHP (php)

## Descriptive Statistics: Measures of Variability in R

Central tendency (e.g., the mean & median) is not the only type of descriptive statistic that we want to calculate. Most of the time, we also want to have a look at a measure of the variability of our data.

### Standard deviation in R

In this section, we are going to calculate the standard deviation using R. We’ve, actually, already done this using the function sd.

`sd(play_df$RT, na.rm = T)`

Code language: R (r)

If we want to calculate the standard deviation by groups this is, again, doable using the group_by and summarise functions.

```
play_df %>% group_by(Gender, Day) %>%
summarise("SD" = sd(RT, na.rm = T))
```

Code language: R (r)

### Interquartile Range in R

In this descriptive statistics in R example, we will use *IQR* to calculate the interquartile range in R.

`IQR(play_df$RT, na.rm = T)`

Code language: R (r)

### Quantiles in R

We can also calculate quantiles. Here, we only do this by groups and we have to create a custom function (see this post for the original code adapted in the example below) to do this together with summarise_at.

```
p <- c(0.25, 0.5, 0.75)
p_funs <- map(p, ~partial(quantile, probs = .x, na.rm = TRUE)) %>%
set_names(nm = p)
play_df %>% group_by(Gender, Day) %>%
summarise_at(vars(RT), lst(!!!p_funs))
```

Code language: R (r)

### Calculate Variance in R

In this last section, of this descriptive statistics in R tutorial, we are going to calculate the variance. Furthermore, In R, the variance is easy to calculate using R. In the summary statistics in R example below, we will use the *var* function.

`var(play_df$RT, na.rm = T)`

Code language: R (r)

Now, we are going to calculate the descriptive statistic variance by groups.

```
play_df %>% group_by(Gender, Day) %>%
summarise(Variance = var(RT, na.rm = T))
```

Code language: R (r)

After we have calculated the descriptive statistics we can visualize the data as well. Another step, int the data analysis pipeline, may be dummy coding. In a more recent post, it is covered how to create dummy variables in R.

## Summary Statistics in R using psych

In this section, we will use the r-package psych to calculate most of the descriptive statistics we calculated above. Here, we will use the function describeBy to calculate the standard deviation, median, mean, interquartile range, trimmed mean range, skewness, kurtosis, standard error, and quantiles.

```
library(psych)
with(play_df, describeBy(RT, group = list(Gender, Day),
IQR = T, quant = c(0.25, 0.50, 0.75)))
```

Code language: R (r)

## Descriptive Statistics in R with dplyr

In this section, we are going to calculate the summary statistics above, using dplyr, group_by, and summarise. Furthermore, we are saving this table and we are going to create a latex table using the kable function from the knitr package.

```
tbl <- play_df %>% group_by(Gender, Day) %>%
summarise(SD = sd(RT, na.rm = T),
Mean = mean(RT, na.rm = T),
Median = median(RT, na.rm = T),
"Trimmed Mean" = mean(RT, trim = 0.2, na.rm = T),
"Geometric Mean" = psych::geometric.mean(RT, na.rm = T),
"Harmonic Mean" = psych::harmonic.mean(RT, na.rm = T),
IQR = IQR(RT, na.rm = T),
"%25 Q" = quantile(RT, .25, na.rm = T),
"%50 Q" = quantile(RT, .5, na.rm = T),
"%75 Q" = quantile(RT, .75, na.rm = T))
```

Code language: PHP (php)

## LaTeX Table with Descriptive Statistics

Now, we are ready to use kable to create a latex table. In the code chunk below, we load kableExtra and knitr. Kable is used to creating the latex table and kable_styling to scale the table down so it fits a PDF created with RMarkdown.

```
library(kableExtra)
library(knitr)
kable(tbl, format = "latex",
digits=2, booktabs = TRUE) %>%
kable_styling(latex_options = "scale_down")
```

Code language: R (r)

## Saving Descriptive Statistics to a CSV File

If we want to save our descriptive statistics, calculated in R, we can use the Tidyverse write_excel_csv function. In the example below, we are saving the R tibble *tbl* created earlier to a .csv file:

`write_excel_csv(tbl, "descriptive_stats.csv")`

Code language: R (r)

The next step in the data analysis pipeline would be to visualize the data to further explore any possible relationships. See the scatter plot in R with ggplot2 tutorial for more information on data visualization in R.

## Conclusion: Descriptive Statistics in R

In this post, we have learned how to describe our data. More specifically, we have learned how to calculate measures of central tendency (mean, median, etc), variability (standard deviation), and more. Furthermore, we have calculated summary statistics using R and saved it as a latex table and a CSV file.