Here is a recap of the occurrences by size:

table(dat$size)

## ## big small ## 77 73

We now create a contingency table of the two variables Species and size with the table() function:

table(dat$Species, dat$size)

## ## big small ## setosa 1 49 ## versicolor 29 21 ## virginica 47 3

or with the xtabs() function:

xtabs(~ dat$Species + dat$size)

## dat$size ## dat$Species big small ## setosa 1 49 ## versicolor 29 21 ## virginica 47 3

The contingency table gives the number of cases in each subgroup. For instance, there is only one big setosa flower, while there are 49 small setosa flowers in the dataset.

To go further, we can see from the table that setosa flowers seem to be larger in size than virginica flowers. In order to check whether size is significantly associated with species, we could perform a Chi-square test of independence since both variables are categorical variables. See how to do this test by hand and in R.

Note that Species are in rows and size in column because we specified Species and then size in table() . Change the order if you want to switch the two variables.

Instead of having the frequencies (i.e.. the number of cases) you can also have the relative frequencies (i.e., proportions) in each subgroup by adding the table() function inside the prop.table() function:

prop.table(table(dat$Species, dat$size))

## ## big small ## setosa 0.006666667 0.326666667 ## versicolor 0.193333333 0.140000000 ## virginica 0.313333333 0.020000000

Note that you can also compute the percentages by row or by column by adding a second argument to the prop.table() function: 1 for row, or 2 for column:

# percentages by row: round(prop.table(table(dat$Species, dat$size), 1), 2) # round to 2 digits with round()

## ## big small ## setosa 0.02 0.98 ## versicolor 0.58 0.42 ## virginica 0.94 0.06

# percentages by column: round(prop.table(table(dat$Species, dat$size), 2), 2) # round to 2 digits with round()

## ## big small ## setosa 0.01 0.67 ## versicolor 0.38 0.29 ## virginica 0.61 0.04

See the section on advanced descriptive statistics for more advanced contingency tables.

Mosaic plot

A mosaic plot allows to visualize a contingency table of two qualitative variables:

mosaicplot(table(dat$Species, dat$size), color = TRUE, xlab = "Species", # label for x-axis ylab = "Size" # label for y-axis )

The mosaic plot shows that, for our sample, the proportion of big and small flowers is clearly different between the three species. In particular, the virginica species is the biggest, and the setosa species is the smallest of the three species (in terms of sepal length since the variable size is based on the variable Sepal.Length ).

For your information, a mosaic plot can also be done via the mosaic() function from the package:

library(vcd) mosaic(~ Species + size, data = dat, direction = c("v", "h") )

Barplot

Barplots can only be done on qualitative variables (see the difference with a quantitative variable here). A barplot is a tool to visualize the distribution of a qualitative variable. We draw a barplot of the qualitative variable size :

barplot(table(dat$size)) # table() is mandatory

You can also draw a barplot of the relative frequencies instead of the frequencies by adding prop.table() as we did earlier:

barplot(prop.table(table(dat$size)))

library(ggplot2) # needed each time you open RStudio # The package ggplot2 must be installed first ggplot(dat) + aes(x = size) + geom_bar()

Histogram

A histogram gives an idea about the distribution of a quantitative variable. The idea is to break the range of values into intervals and count how many observations fall into each interval. Histograms are a bit similar to barplots, but histograms are used for quantitative variables whereas barplots are used for qualitative variables. To draw a histogram in R, use hist() :

hist(dat$Sepal.Length)

Add the arguments breaks = inside the hist() function if you want to change the number of bins. A rule of thumb (known as Sturges’ law) is that the number of bins should be the rounded value of the square root of the number of observations. The dataset includes 150 observations so in this case the number of bins can be set to 12.

ggplot(dat) + aes(x = Sepal.Length) + geom_histogram()

By default, the number of bins is 30. You can change this value with geom_histogram(bins = 12) for instance.

Boxplot

Boxplots are really useful in descriptive statistics and are often underused (mostly because it is not well understood by the public). A boxplot graphically represents the distribution of a quantitative variable by visually displaying five common location summary (minimum, median, first/third quartiles and maximum) and any observation that was classified as a suspected outlier using the interquartile range (IQR) criterion.

The IQR criterion means that all observations above \(q_ + 1.5 \cdot IQR\) or below \(q_ - 1.5 \cdot IQR\) (where \(q_\) and \(q_\) correspond to first and third quartile respectively) are considered as potential outliers by R. The minimum and maximum in the boxplot are represented without these suspected outliers.

Seeing all these information on the same plot help to have a good first overview of the dispersion and the location of the data. Before drawing a boxplot of our data, see below a graph explaining the information present on a boxplot:

How to interpret a boxplot? Source: LFSAB1105

Now an example with our dataset:

boxplot(dat$Sepal.Length)

Boxplots are even more informative when presented side-by-side for comparing and contrasting distributions from two or more groups. For instance, we compare the length of the sepal across the different species:

boxplot(dat$Sepal.Length ~ dat$Species)

ggplot(dat) + aes(x = Species, y = Sepal.Length) + geom_boxplot()

Dotplot

A dotplot is more or less similar than a boxplot, except that:

• observations are represented as points
• it does not easily tell us about the median, first and third quartiles.

library(lattice) dotplot(dat$Sepal.Length ~ dat$Species)

ggplot(dat) + aes(x = Species, y = Sepal.Length) + geom_dotplot(binaxis = "y", stackdir = "center")

The advantage of using over for this plot is that we can easily see the mode.

Note that a dotplot is particularly useful when there are a limited number of observations, whereas a boxplot is more appropriate with large datasets.

Scatterplot

Scatterplots allow to check whether there is a potential link between two quantitative variables. For this reason, scatterplots are often used to visualize a potential correlation between two variables. For instance, when drawing a scatterplot of the length of the sepal and the length of the petal:

plot(dat$Sepal.Length, dat$Petal.Length)

There seems to be a positive association between the two variables.

ggplot(dat) + aes(x = Sepal.Length, y = Petal.Length) + geom_point()

Like boxplots, scatterplots are even more informative when differentiating the points according to a factor, in this case the species:

ggplot(dat) + aes(x = Sepal.Length, y = Petal.Length, colour = Species) + geom_point() + scale_color_hue()

Line plot

Line plots, particularly useful in time series or finance, can be created by adding the type = "l" argument in the plot() function:

plot(dat$Sepal.Length, type = "l" ) # "l" for line

QQ-plot

For a single variable

In order to check the normality assumption of a variable (normality means that the data follow a normal distribution, also known as a Gaussian distribution), we usually use histograms and/or QQ-plots. 1 See an article discussing about the normal distribution and how to evaluate the normality assumption in R if you need a refresh on that subject.

Histograms have been presented earlier, so here is how to draw a QQ-plot:

# Draw points on the qq-plot: qqnorm(dat$Sepal.Length) # Draw the reference line: qqline(dat$Sepal.Length)

Or a QQ-plot with confidence bands with the qqPlot() function from the package:

library(car) # package must be installed first qqPlot(dat$Sepal.Length)

## [1] 132 118

If points are close to the reference line (sometimes referred as Henry’s line) and within the confidence bands, the normality assumption can be considered as met. The bigger the deviation between the points and the reference line and the more they lie outside the confidence bands, the less likely that the normality condition is met. The variable Sepal.Length does not seem to follow a normal distribution because several points lie outside the confidence bands. When facing a non-normal distribution, the first step is usually to apply the logarithm transformation on the data and recheck to see whether the log-transformed data are normally distributed. Applying the logarithm transformation can be done with the log() function.

library(ggpubr) ggqqplot(dat$Sepal.Length)

By groups

For some statistical tests, the normality assumption is required in all groups. One solution is to draw a QQ-plot for each group by manually splitting the dataset into different groups and then draw a QQ-plot for each subset of the data (with the methods shown above). Another (easier) solution is to draw a QQ-plot for each group automatically with the argument groups = in the function qqPlot() from the package:

qqPlot(dat$Sepal.Length, groups = dat$size)

qplot( sample = Sepal.Length, data = dat, col = size, shape = size )

It is also possible to differentiate groups by only shape or color. For this, remove one of the argument col or shape in the qplot() function above.

Density plot

Density plot is a smoothed version of the histogram and is used in the same concept, that is, to represent the distribution of a numeric variable. The functions plot() and density() are used together to draw a density plot:

plot(density(dat$Sepal.Length))

ggplot(dat) + aes(x = Sepal.Length) + geom_density()

Correlation plot

The last type of descriptive plot is a correlation plot, also called a correlogram. This type of graph is more complex than the ones presented above, so it is detailed in a separate article. See how to draw a correlogram to highlight the most correlated variables in a dataset.

Advanced descriptive statistics

We covered the main functions to compute the most common and basic descriptive statistics. There are, however, many more functions and packages to perform more advanced descriptive statistics in R. In this section, I present some of them with applications to our dataset.

package

One package for descriptive statistics I often use for my projects in R is the package. The package is centered around 4 functions:

1. freq() for frequencies tables
2. ctable() for cross-tabulations
3. descr() for descriptive statistics
4. dfSummary() for dataframe summaries

A combination of these 4 functions is usually more than enough for most descriptive analyses. Moreover, the package has been built with R Markdown in mind, meaning that outputs render well in HTML reports. And for non-English speakers, built-in translations exist for French, Portuguese, Spanish, Russian and Turkish.

I illustrate each of the 4 functions in the following sections. Outputs that follow display much better in R Markdown reports, but in this article I limit myself to the raw outputs as the goal is to show how the functions work, not how to make them render well. See the setup settings in the vignette of the package if you want to print the outputs in a nice way in R Markdown. 2

Frequency tables with freq()

The freq() function produces frequency tables with frequencies, proportions, as well as missing data information.

library(summarytools) freq(dat$Species)

## Frequencies ## dat$Species ## Type: Factor ## ## Freq % Valid % Valid Cum. % Total % Total Cum. ## ---------------- ------ --------- -------------- --------- -------------- ## setosa 50 33.33 33.33 33.33 33.33 ## versicolor 50 33.33 66.67 33.33 66.67 ## virginica 50 33.33 100.00 33.33 100.00 ## 0 0.00 100.00 ## Total 150 100.00 100.00 100.00 100.00

If you do not need information about missing values, add the report.nas = FALSE argument:

freq(dat$Species, report.nas = FALSE # remove NA information )

## Frequencies ## dat$Species ## Type: Factor ## ## Freq % % Cum. ## ---------------- ------ -------- -------- ## setosa 50 33.33 33.33 ## versicolor 50 33.33 66.67 ## virginica 50 33.33 100.00 ## Total 150 100.00 100.00

And for a minimalist output with only counts and proportions:

freq(dat$Species, report.nas = FALSE, # remove NA information totals = FALSE, # remove totals cumul = FALSE, # remove cumuls headings = FALSE # remove headings )

## ## Freq % ## ---------------- ------ ------- ## setosa 50 33.33 ## versicolor 50 33.33 ## virginica 50 33.33

Cross-tabulations with ctable()

The ctable() function produces cross-tabulations (also known as contingency tables) for pairs of categorical variables. Using the two categorical variables in our dataset:

ctable( x = dat$Species, y = dat$size )

## Cross-Tabulation, Row Proportions ## Species * size ## Data Frame: dat ## ## ------------ ------ ------------ ------------ -------------- ## size big small Total ## Species ## setosa 1 ( 2.0%) 49 (98.0%) 50 (100.0%) ## versicolor 29 (58.0%) 21 (42.0%) 50 (100.0%) ## virginica 47 (94.0%) 3 ( 6.0%) 50 (100.0%) ## Total 77 (51.3%) 73 (48.7%) 150 (100.0%) ## ------------ ------ ------------ ------------ --------------

Row proportions are shown by default. To display column or total proportions, add the prop = "c" or prop = "t" arguments, respectively:

ctable( x = dat$Species, y = dat$size, prop = "t" # total proportions )

## Cross-Tabulation, Total Proportions ## Species * size ## Data Frame: dat ## ## ------------ ------ ------------ ------------ -------------- ## size big small Total ## Species ## setosa 1 ( 0.7%) 49 (32.7%) 50 ( 33.3%) ## versicolor 29 (19.3%) 21 (14.0%) 50 ( 33.3%) ## virginica 47 (31.3%) 3 ( 2.0%) 50 ( 33.3%) ## Total 77 (51.3%) 73 (48.7%) 150 (100.0%) ## ------------ ------ ------------ ------------ --------------

To remove proportions altogether, add the argument prop = "n" . Furthermore, to display only the bare minimum, add the totals = FALSE and headings = FALSE arguments:

ctable( x = dat$Species, y = dat$size, prop = "n", # remove proportions totals = FALSE, # remove totals headings = FALSE # remove headings )

## ## ------------ ------ ----- ------- ## size big small ## Species ## setosa 1 49 ## versicolor 29 21 ## virginica 47 3 ## ------------ ------ ----- -------

This is equivalent than table(dat$Species, dat$size) and xtabs(~ dat$Species + dat$size) performed in the section on contingency tables.

To display results of the Chi-square test of independence, add the chisq = TRUE argument: 3

ctable( x = dat$Species, y = dat$size, chisq = TRUE, # display results of Chi-square test of independence headings = FALSE # remove headings )

## ## ------------ ------ ------------ ------------ -------------- ## size big small Total ## Species ## setosa 1 ( 2.0%) 49 (98.0%) 50 (100.0%) ## versicolor 29 (58.0%) 21 (42.0%) 50 (100.0%) ## virginica 47 (94.0%) 3 ( 6.0%) 50 (100.0%) ## Total 77 (51.3%) 73 (48.7%) 150 (100.0%) ## ------------ ------ ------------ ------------ -------------- ## ## ---------------------------- ## Chi.squared df p.value ## ------------- ---- --------- ## 86.0345 2 0 ## ----------------------------

The p-value is close to 0 so we reject the null hypothesis of independence between the two variables. In our context, this indicates that species and size are dependent and that there is a significant relationship between the two variables.

It is also possible to create a contingency table for each level of a third categorical variable thanks to the combination of the stby() and ctable() functions. There are only 2 categorical variables in our dataset, so let’s use the tabacco dataset which has 4 categorical variables (i.e., gender, age group, smoker, diseased). For this example, we would like to create a contingency table of the variables smoker and diseased , and this for each gender :

stby( list( x = tobacco$smoker, # smoker and diseased y = tobacco$diseased ), INDICES = tobacco$gender, # for each gender FUN = ctable # ctable for cross-tabulation )

## Cross-Tabulation, Row Proportions ## smoker * diseased ## Data Frame: tobacco ## Group: gender = F ## ## -------- ---------- ------------- ------------- -------------- ## diseased Yes No Total ## smoker ## Yes 62 (42.2%) 85 (57.8%) 147 (100.0%) ## No 49 (14.3%) 293 (85.7%) 342 (100.0%) ## Total 111 (22.7%) 378 (77.3%) 489 (100.0%) ## -------- ---------- ------------- ------------- -------------- ## ## Group: gender = M ## ## -------- ---------- ------------- ------------- -------------- ## diseased Yes No Total ## smoker ## Yes 63 (44.1%) 80 (55.9%) 143 (100.0%) ## No 47 (13.6%) 299 (86.4%) 346 (100.0%) ## Total 110 (22.5%) 379 (77.5%) 489 (100.0%) ## -------- ---------- ------------- ------------- --------------

Descriptive statistics with descr()

The descr() function produces descriptive (univariate) statistics with common central tendency statistics and measures of dispersion. (See the difference between a measure of central tendency and dispersion if you need a reminder.)

A major advantage of this function is that it accepts single vectors as well as data frames. If a data frame is provided, all non-numerical columns are ignored so you do not have to remove them yourself before running the function.

The descr() function allows to display:

• only a selection of descriptive statistics of your choice, with the stats = c("mean", "sd") argument for mean and standard deviation for example
• the minimum, first quartile, median, third quartile and maximum with stats = "fivenum"
• the most common descriptive statistics (mean, standard deviation, minimum, median, maximum, number and percentage of valid observations), with stats = "common" :

descr(dat, headings = FALSE, # remove headings stats = "common" # most common descriptive statistics )

## ## Petal.Length Petal.Width Sepal.Length Sepal.Width ## --------------- -------------- ------------- -------------- ------------- ## Mean 3.76 1.20 5.84 3.06 ## Std.Dev 1.77 0.76 0.83 0.44 ## Min 1.00 0.10 4.30 2.00 ## Median 4.35 1.30 5.80 3.00 ## Max 6.90 2.50 7.90 4.40 ## N.Valid 150.00 150.00 150.00 150.00 ## Pct.Valid 100.00 100.00 100.00 100.00

Tip: if you have a large number of variables, add the transpose = TRUE argument for a better display.

In order to compute these descriptive statistics by group (e.g., Species in our dataset), use the descr() function in combination with the stby() function:

stby( data = dat, INDICES = dat$Species, # by Species FUN = descr, # descriptive statistics stats = "common" # most common descr. stats )

## Descriptive Statistics ## dat ## Group: Species = setosa ## N: 50 ## ## Petal.Length Petal.Width Sepal.Length Sepal.Width ## --------------- -------------- ------------- -------------- ------------- ## Mean 1.46 0.25 5.01 3.43 ## Std.Dev 0.17 0.11 0.35 0.38 ## Min 1.00 0.10 4.30 2.30 ## Median 1.50 0.20 5.00 3.40 ## Max 1.90 0.60 5.80 4.40 ## N.Valid 50.00 50.00 50.00 50.00 ## Pct.Valid 100.00 100.00 100.00 100.00 ## ## Group: Species = versicolor ## N: 50 ## ## Petal.Length Petal.Width Sepal.Length Sepal.Width ## --------------- -------------- ------------- -------------- ------------- ## Mean 4.26 1.33 5.94 2.77 ## Std.Dev 0.47 0.20 0.52 0.31 ## Min 3.00 1.00 4.90 2.00 ## Median 4.35 1.30 5.90 2.80 ## Max 5.10 1.80 7.00 3.40 ## N.Valid 50.00 50.00 50.00 50.00 ## Pct.Valid 100.00 100.00 100.00 100.00 ## ## Group: Species = virginica ## N: 50 ## ## Petal.Length Petal.Width Sepal.Length Sepal.Width ## --------------- -------------- ------------- -------------- ------------- ## Mean 5.55 2.03 6.59 2.97 ## Std.Dev 0.55 0.27 0.64 0.32 ## Min 4.50 1.40 4.90 2.20 ## Median 5.55 2.00 6.50 3.00 ## Max 6.90 2.50 7.90 3.80 ## N.Valid 50.00 50.00 50.00 50.00 ## Pct.Valid 100.00 100.00 100.00 100.00

Data frame summaries with dfSummary()

The dfSummary() function generates a summary table with statistics, frequencies and graphs for all variables in a dataset. The information shown depends on the type of the variables (character, factor, numeric, date) and also varies according to the number of distinct values.

dfSummary(dat)

## Data Frame Summary ## dat ## Dimensions: 150 x 6 ## Duplicates: 1 ## ## ----------------------------------------------------------------------------------------------------------- ## No Variable Stats / Values Freqs (% of Valid) Graph Valid Missing ## ---- -------------- ----------------------- -------------------- --------------------- ---------- --------- ## 1 Sepal.Length Mean (sd) : 5.8 (0.8) 35 distinct values . . : : 150 0 ## [numeric] min < med < max: : : : : (100.0%) (0.0%) ## 4.3 < 5.8 < 7.9 : : : : : ## IQR (CV) : 1.3 (0.1) : : : : : ## : : : : : : : : ## ## 2 Sepal.Width Mean (sd) : 3.1 (0.4) 23 distinct values : 150 0 ## [numeric] min < med < max: : (100.0%) (0.0%) ## 2 < 3 < 4.4 . : ## IQR (CV) : 0.5 (0.1) : : : : ## . . : : : : : : ## ## 3 Petal.Length Mean (sd) : 3.8 (1.8) 43 distinct values : 150 0 ## [numeric] min < med < max: : . : (100.0%) (0.0%) ## 1 < 4.3 < 6.9 : : : . ## IQR (CV) : 3.5 (0.5) : : : : : . ## : : . : : : : : . ## ## 4 Petal.Width Mean (sd) : 1.2 (0.8) 22 distinct values : 150 0 ## [numeric] min < med < max: : (100.0%) (0.0%) ## 0.1 < 1.3 < 2.5 : . . : ## IQR (CV) : 1.5 (0.6) : : : : . ## : : : : : . : : : ## ## 5 Species 1. setosa 50 (33.3%) IIIIII 150 0 ## [factor] 2. versicolor 50 (33.3%) IIIIII (100.0%) (0.0%) ## 3. virginica 50 (33.3%) IIIIII ## ## 6 size 1. big 77 (51.3%) IIIIIIIIII 150 0 ## [character] 2. small 73 (48.7%) IIIIIIIII (100.0%) (0.0%) ## -----------------------------------------------------------------------------------------------------------

describeBy() from the package

The describeBy() function from the package allows to report several summary statistics (i.e., number of valid cases, mean, standard deviation, median, trimmed mean, mad: median absolute deviation (from the median), minimum, maximum, range, skewness and kurtosis) by a grouping variable.

library(psych) describeBy( dat, dat$Species # grouping variable )

## ## Descriptive statistics by group ## group: setosa ## vars n mean sd median trimmed mad min max range skew kurtosis ## Sepal.Length 1 50 5.01 0.35 5.0 5.00 0.30 4.3 5.8 1.5 0.11 -0.45 ## Sepal.Width 2 50 3.43 0.38 3.4 3.42 0.37 2.3 4.4 2.1 0.04 0.60 ## Petal.Length 3 50 1.46 0.17 1.5 1.46 0.15 1.0 1.9 0.9 0.10 0.65 ## Petal.Width 4 50 0.25 0.11 0.2 0.24 0.00 0.1 0.6 0.5 1.18 1.26 ## Species* 5 50 1.00 0.00 1.0 1.00 0.00 1.0 1.0 0.0 NaN NaN ## size* 6 50 1.98 0.14 2.0 2.00 0.00 1.0 2.0 1.0 -6.65 43.12 ## se ## Sepal.Length 0.05 ## Sepal.Width 0.05 ## Petal.Length 0.02 ## Petal.Width 0.01 ## Species* 0.00 ## size* 0.02 ## ------------------------------------------------------------ ## group: versicolor ## vars n mean sd median trimmed mad min max range skew kurtosis ## Sepal.Length 1 50 5.94 0.52 5.90 5.94 0.52 4.9 7.0 2.1 0.10 -0.69 ## Sepal.Width 2 50 2.77 0.31 2.80 2.78 0.30 2.0 3.4 1.4 -0.34 -0.55 ## Petal.Length 3 50 4.26 0.47 4.35 4.29 0.52 3.0 5.1 2.1 -0.57 -0.19 ## Petal.Width 4 50 1.33 0.20 1.30 1.32 0.22 1.0 1.8 0.8 -0.03 -0.59 ## Species* 5 50 2.00 0.00 2.00 2.00 0.00 2.0 2.0 0.0 NaN NaN ## size* 6 50 1.42 0.50 1.00 1.40 0.00 1.0 2.0 1.0 0.31 -1.94 ## se ## Sepal.Length 0.07 ## Sepal.Width 0.04 ## Petal.Length 0.07 ## Petal.Width 0.03 ## Species* 0.00 ## size* 0.07 ## ------------------------------------------------------------ ## group: virginica ## vars n mean sd median trimmed mad min max range skew kurtosis ## Sepal.Length 1 50 6.59 0.64 6.50 6.57 0.59 4.9 7.9 3.0 0.11 -0.20 ## Sepal.Width 2 50 2.97 0.32 3.00 2.96 0.30 2.2 3.8 1.6 0.34 0.38 ## Petal.Length 3 50 5.55 0.55 5.55 5.51 0.67 4.5 6.9 2.4 0.52 -0.37 ## Petal.Width 4 50 2.03 0.27 2.00 2.03 0.30 1.4 2.5 1.1 -0.12 -0.75 ## Species* 5 50 3.00 0.00 3.00 3.00 0.00 3.0 3.0 0.0 NaN NaN ## size* 6 50 1.06 0.24 1.00 1.00 0.00 1.0 2.0 1.0 3.59 11.15 ## se ## Sepal.Length 0.09 ## Sepal.Width 0.05 ## Petal.Length 0.08 ## Petal.Width 0.04 ## Species* 0.00 ## size* 0.03

aggregate() function

The aggregate() function allows to split the data into subsets and then to compute summary statistics for each. For instance, if we want to compute the mean for the variables Sepal.Length and Sepal.Width by Species and Size :

aggregate(cbind(Sepal.Length, Sepal.Width) ~ Species + size, data = dat, mean )

## Species size Sepal.Length Sepal.Width ## 1 setosa big 5.800000 4.000000 ## 2 versicolor big 6.282759 2.868966 ## 3 virginica big 6.663830 2.997872 ## 4 setosa small 4.989796 3.416327 ## 5 versicolor small 5.457143 2.633333 ## 6 virginica small 5.400000 2.600000

An alternative is the summaryBy() function from the package:

# summary statistics by group library(doBy) summaryBy(Sepal.Length + Sepal.Width ~ Species, data = dat, FUN = summary )

## Species Sepal.Length.Min. Sepal.Length.1st Qu. Sepal.Length.Median ## 1 setosa 4.3 4.800 5.0 ## 2 versicolor 4.9 5.600 5.9 ## 3 virginica 4.9 6.225 6.5 ## Sepal.Length.Mean Sepal.Length.3rd Qu. Sepal.Length.Max. Sepal.Width.Min. ## 1 5.006 5.2 5.8 2.3 ## 2 5.936 6.3 7.0 2.0 ## 3 6.588 6.9 7.9 2.2 ## Sepal.Width.1st Qu. Sepal.Width.Median Sepal.Width.Mean Sepal.Width.3rd Qu. ## 1 3.200 3.4 3.428 3.675 ## 2 2.525 2.8 2.770 3.000 ## 3 2.800 3.0 2.974 3.175 ## Sepal.Width.Max. ## 1 4.4 ## 2 3.4 ## 3 3.8

If you are interested in some specific descriptive statistics, you can easily specify them via the FUN argument:

summaryBy(Sepal.Length + Sepal.Width ~ Species, data = dat, FUN = c(mean, var) )

## Species Sepal.Length.mean Sepal.Width.mean Sepal.Length.var ## 1 setosa 5.006 3.428 0.1242490 ## 2 versicolor 5.936 2.770 0.2664327 ## 3 virginica 6.588 2.974 0.4043429 ## Sepal.Width.var ## 1 0.14368980 ## 2 0.09846939 ## 3 0.10400408

Another alternative is with the summarise() and group_by() functions from the package:

library(dplyr) group_by(dat, Species) %>% summarise( mean = mean(Sepal.Length, na.rm = TRUE), sd = sd(Sepal.Length, na.rm = TRUE) )

## # A tibble: 3 × 3 ## Species mean sd ##   ## 1 setosa 5.01 0.352 ## 2 versicolor 5.94 0.516 ## 3 virginica 6.59 0.636

Conclusion

Thanks for reading.

I hope this article helped you to do descriptive statistics in R. If you would like to do the same by hand or understand what these statistics represent, I invite you to read the article “Descriptive statistics by hand”.

As always, if you have a question or a suggestion related to the topic covered in this article, please add it as a comment so other readers can benefit from the discussion.

(Note that this article is available for download on my Gumroad page.)

1. Normality tests such as Shapiro-Wilk or Kolmogorov-Smirnov tests can also be used to test whether the data follow a normal distribution or not. However, in practice, normality tests are often considered as too conservative in the sense that for large sample size, a small deviation from the normality may cause the normality condition to be violated. For this reason, it is often the case that the normality condition is verified based on a combination of visual inspections (with histograms and QQ-plots) and formal test (Shapiro-Wilk test for instance).↩︎
2. Note that the plain.ascii and style arguments are needed for this package. In our examples, these arguments are added in the settings of each chunk so they are not visible.↩︎
3. Note that it is also possible to compute odds ratio and risk ratio. See the vignette of the package for more information on this matter as these ratios are beyond the scope of this article.↩︎

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