Use xlim() and ylim() functions

To change the range of a continuous axis, the functions xlim() and ylim() can be used as follow :

# x axis limits
sp + xlim(min, max)
# y axis limits
sp + ylim(min, max)

min and max are the minimum and the maximum values of each axis.

# Box plot : change y axis range
bp + ylim(0,50)
# scatter plots : change x and y limits
sp + xlim(5, 40)+ylim(0, 150)

Use expand_limts() function

# set the intercept of x and y axis at (0,0)
sp + expand_limits(x=0, y=0)
# change the axis limits
sp + expand_limits(x=c(0,30), y=c(0, 150))

Use scale_xx() functions

It is also possible to use the functions scale_x_continuous() and scale_y_continuous() to change x and y axis limits, respectively.

The simplified formats of the functions are :

scale_x_continuous(name, breaks, labels, limits, trans)
scale_y_continuous(name, breaks, labels, limits, trans)

The functions scale_x_continuous() and scale_y_continuous() can be used as follow :

# Change x and y axis labels, and limits
sp + scale_x_continuous(name="Speed of cars", limits=c(0, 30)) +
  scale_y_continuous(name="Stopping distance", limits=c(0, 150))

Log and sqrt transformations

Built in functions for axis transformations are :

• scale_x_log10(), scale_y_log10() : for log10 transformation
• scale_x_sqrt(), scale_y_sqrt() : for sqrt transformation
• scale_x_reverse(), scale_y_reverse() : to reverse coordinates
• coord_trans(x =“log10”, y=“log10”) : possible values for x and y are “log2”, “log10”, “sqrt”, …
• scale_x_continuous(trans=‘log2’), scale_y_continuous(trans=‘log2’) : another allowed value for the argument trans is ‘log10’

These functions can be used as follow :

# Default scatter plot
sp <- ggplot(cars, aes(x = speed, y = dist)) + geom_point()
sp
# Log transformation using scale_xx()
# possible values for trans : 'log2', 'log10','sqrt'
sp + scale_x_continuous(trans='log2') +
  scale_y_continuous(trans='log2')
# Sqrt transformation
sp + scale_y_sqrt()
# Reverse coordinates
sp + scale_y_reverse() 

The function coord_trans() can be used also for the axis transformation

# Possible values for x and y : "log2", "log10", "sqrt", ...
sp + coord_trans(x="log2", y="log2")

Format axis tick mark labels

Axis tick marks can be set to show exponents. The scales package is required to access break formatting functions.

# Log2 scaling of the y axis (with visually-equal spacing)
library(scales)
sp + scale_y_continuous(trans = log2_trans())
# show exponents
sp + scale_y_continuous(trans = log2_trans(),
    breaks = trans_breaks("log2", function(x) 2^x),
    labels = trans_format("log2", math_format(2^.x)))

Note that many transformation functions are available using the scales package : log10_trans(), sqrt_trans(), etc. Use help(trans_new) for a full list.

Format axis tick mark labels :

library(scales)
# Percent
sp + scale_y_continuous(labels = percent)
# dollar
sp + scale_y_continuous(labels = dollar)
# scientific
sp + scale_y_continuous(labels = scientific)

Display log tick marks

It is possible to add log tick marks using the function annotation_logticks().

Note that, these tick marks make sense only for base 10

The Animals data sets, from the package MASS, are used :

library(MASS)
head(Animals)

##                     body brain
## Mountain beaver     1.35   8.1
## Cow               465.00 423.0
## Grey wolf          36.33 119.5
## Goat               27.66 115.0
## Guinea pig          1.04   5.5
## Dipliodocus     11700.00  50.0

The function annotation_logticks() can be used as follow :

library(MASS) # to access Animals data sets
library(scales) # to access break formatting functions
# x and y axis are transformed and formatted
p2 <- ggplot(Animals, aes(x = body, y = brain)) + geom_point() +
     scale_x_log10(breaks = trans_breaks("log10", function(x) 10^x),
              labels = trans_format("log10", math_format(10^.x))) +
     scale_y_log10(breaks = trans_breaks("log10", function(x) 10^x),
              labels = trans_format("log10", math_format(10^.x))) +
     theme_bw()
# log-log plot without log tick marks
p2
# Show log tick marks
p2 + annotation_logticks()  

Note that, default log ticks are on bottom and left.

To specify the sides of the log ticks :

# Log ticks on left and right
p2 + annotation_logticks(sides="lr")
# All sides
p2+annotation_logticks(sides="trbl")

Allowed values for the argument sides are :

• t : for top
• r : for right
• b : for bottom
• l : for left
• the combination of t, r, b and l

Example of data

Create some time serie data

df <- data.frame(
  date = seq(Sys.Date(), len=100, by="1 day")[sample(100, 50)],
  price = runif(50)
)
df <- df[order(df$date), ]
head(df)

##          date      price
## 33 2016-09-21 0.07245190
## 3  2016-09-23 0.51772443
## 23 2016-09-25 0.05758921
## 43 2016-09-26 0.99389551
## 45 2016-09-27 0.94858770
## 29 2016-09-28 0.82420890

Plot with dates

# Plot with date
dp <- ggplot(data=df, aes(x=date, y=price)) + geom_line()
dp

Format axis tick mark labels

Load the package scales to access break formatting functions.

library(scales)
# Format : month/day
dp + scale_x_date(labels = date_format("%m/%d")) +
  theme(axis.text.x = element_text(angle=45))
# Format : Week
dp + scale_x_date(labels = date_format("%W"))
# Months only
dp + scale_x_date(breaks = date_breaks("months"),
  labels = date_format("%b"))

Note that, since ggplot2 v2.0.0, date and datetime scales now have date_breaks, date_minor_breaks and date_labels arguments so that you never need to use the long scales::date_breaks() or scales::date_format().

Date axis limits

US economic time series data sets (from ggplot2 package) are used :

head(economics)

##         date   pce    pop psavert uempmed unemploy
## 1 1967-07-01 507.4 198712    12.5     4.5     2944
## 2 1967-08-01 510.5 198911    12.5     4.7     2945
## 3 1967-09-01 516.3 199113    11.7     4.6     2958
## 4 1967-10-01 512.9 199311    12.5     4.9     3143
## 5 1967-11-01 518.1 199498    12.5     4.7     3066
## 6 1967-12-01 525.8 199657    12.1     4.8     3018

Create the plot of psavert by date :

• date : Month of data collection
• psavert : personal savings rate

# Plot with dates
dp <- ggplot(data=economics, aes(x=date, y=psavert)) + geom_line()
dp
# Axis limits c(min, max)
min <- as.Date("2002-1-1")
max <- max(economics$date)
dp+ scale_x_date(limits = c(min, max))

Generate some data

df <- data.frame(time=c("breakfeast", "Lunch", "Dinner"),
                bill=c(10, 30, 15))
head(df)

##         time bill
## 1 breakfeast   10
## 2      Lunch   30
## 3     Dinner   15

Create line plots and change line types

The argument linetype is used to change the line type :

library(ggplot2)
# Basic line plot with points
ggplot(data=df, aes(x=time, y=bill, group=1)) +
  geom_line()+
  geom_point()
# Change the line type
ggplot(data=df, aes(x=time, y=bill, group=1)) +
  geom_line(linetype = "dashed")+
  geom_point()

Create some data

df2 <- data.frame(sex = rep(c("Female", "Male"), each=3),
                  time=c("breakfeast", "Lunch", "Dinner"),
                  bill=c(10, 30, 15, 13, 40, 17) )
head(df2)

##      sex       time bill
## 1 Female breakfeast   10
## 2 Female      Lunch   30
## 3 Female     Dinner   15
## 4   Male breakfeast   13
## 5   Male      Lunch   40
## 6   Male     Dinner   17

Change globally the appearance of lines

In the graphs below, line types, colors and sizes are the same for the two groups :

library(ggplot2)
# Line plot with multiple groups
ggplot(data=df2, aes(x=time, y=bill, group=sex)) +
  geom_line()+
  geom_point()
# Change line types
ggplot(data=df2, aes(x=time, y=bill, group=sex)) +
  geom_line(linetype="dashed")+
  geom_point()
# Change line colors and sizes
ggplot(data=df2, aes(x=time, y=bill, group=sex)) +
  geom_line(linetype="dotted", color="red", size=2)+
  geom_point(color="blue", size=3)

Change automatically the line types by groups

In the graphs below, line types, colors and sizes are changed automatically by the levels of the variable sex :

# Change line types by groups (sex)
ggplot(df2, aes(x=time, y=bill, group=sex)) +
  geom_line(aes(linetype=sex))+
  geom_point()+
  theme(legend.position="top")
# Change line types + colors
ggplot(df2, aes(x=time, y=bill, group=sex)) +
  geom_line(aes(linetype=sex, color=sex))+
  geom_point(aes(color=sex))+
  theme(legend.position="top")

Change manually the appearance of lines

The functions below can be used :

• scale_linetype_manual() : to change line types
• scale_color_manual() : to change line colors
• scale_size_manual() : to change the size of lines

# Set line types manually
ggplot(df2, aes(x=time, y=bill, group=sex)) +
  geom_line(aes(linetype=sex))+
  geom_point()+
  scale_linetype_manual(values=c("twodash", "dotted"))+
  theme(legend.position="top")
# Change line colors and sizes
ggplot(df2, aes(x=time, y=bill, group=sex)) +
  geom_line(aes(linetype=sex, color=sex, size=sex))+
  geom_point()+
  scale_linetype_manual(values=c("twodash", "dotted"))+
  scale_color_manual(values=c('#999999','#E69F00'))+
  scale_size_manual(values=c(1, 1.5))+
  theme(legend.position="top")

Change the point shapes, colors and sizes automatically

In the R code below, point shapes, colors and sizes are controlled automatically by the variable cyl :

library(ggplot2)
# Scatter plot with multiple groups
# shape depends on cyl
ggplot(df, aes(x=wt, y=mpg, group=cyl)) +
  geom_point(aes(shape=cyl))
# Change point shapes and colors
ggplot(df, aes(x=wt, y=mpg, group=cyl)) +
  geom_point(aes(shape=cyl, color=cyl))
# change point shapes,  colors and sizes
ggplot(df, aes(x=wt, y=mpg, group=cyl)) +
  geom_point(aes(shape=cyl, color=cyl, size=cyl))

Change point shapes, colors and sizes manually :

The functions below can be used :

• scale_shape_manual() : to change point shapes
• scale_color_manual() : to change point colors
• scale_size_manual() : to change the size of points

# Change colors and shapes manually
ggplot(df, aes(x=wt, y=mpg, group=cyl)) +
  geom_point(aes(shape=cyl, color=cyl), size=2)+
  scale_shape_manual(values=c(3, 16, 17))+
  scale_color_manual(values=c('#999999','#E69F00', '#56B4E9'))+
  theme(legend.position="top")
# Change the point size manually
ggplot(df, aes(x=wt, y=mpg, group=cyl)) +
  geom_point(aes(shape=cyl, color=cyl, size=cyl))+
  scale_shape_manual(values=c(3, 16, 17))+
  scale_color_manual(values=c('#999999','#E69F00', '#56B4E9'))+
  scale_size_manual(values=c(2,3,4))+
  theme(legend.position="top")

Data

Data derived from ToothGrowth data sets are used. ToothGrowth describes the effect of Vitamin C on tooth growth in Guinea pigs.

df <- data.frame(dose=c("D0.5", "D1", "D2"),
                len=c(4.2, 10, 29.5))
head(df)

##   dose  len
## 1 D0.5  4.2
## 2   D1 10.0
## 3   D2 29.5

• len : Tooth length
• dose : Dose in milligrams (0.5, 1, 2)

Create line plots with points

library(ggplot2)
# Basic line plot with points
ggplot(data=df, aes(x=dose, y=len, group=1)) +
  geom_line()+
  geom_point()
# Change the line type
ggplot(data=df, aes(x=dose, y=len, group=1)) +
  geom_line(linetype = "dashed")+
  geom_point()
# Change the color
ggplot(data=df, aes(x=dose, y=len, group=1)) +
  geom_line(color="red")+
  geom_point()

Read more on line types : ggplot2 line types

You can add an arrow to the line using the grid package :

library(grid)
# Add an arrow
ggplot(data=df, aes(x=dose, y=len, group=1)) +
  geom_line(arrow = arrow())+
  geom_point()
# Add a closed arrow to the end of the line
myarrow=arrow(angle = 15, ends = "both", type = "closed")
ggplot(data=df, aes(x=dose, y=len, group=1)) +
  geom_line(arrow=myarrow)+
  geom_point()

Observations can be also connected using the functions geom_step() or geom_path() :

ggplot(data=df, aes(x=dose, y=len, group=1)) +
  geom_step()+
  geom_point()
ggplot(data=df, aes(x=dose, y=len, group=1)) +
  geom_path()+
  geom_point()

Data

Data derived from ToothGrowth data sets are used. ToothGrowth describes the effect of Vitamin C on tooth growth in Guinea pigs. Three dose levels of Vitamin C (0.5, 1, and 2 mg) with each of two delivery methods [orange juice (OJ) or ascorbic acid (VC)] are used :

df2 <- data.frame(supp=rep(c("VC", "OJ"), each=3),
                dose=rep(c("D0.5", "D1", "D2"),2),
                len=c(6.8, 15, 33, 4.2, 10, 29.5))
head(df2)

##   supp dose  len
## 1   VC D0.5  6.8
## 2   VC   D1 15.0
## 3   VC   D2 33.0
## 4   OJ D0.5  4.2
## 5   OJ   D1 10.0
## 6   OJ   D2 29.5

• len : Tooth length
• dose : Dose in milligrams (0.5, 1, 2)
• supp : Supplement type (VC or OJ)

Create line plots

In the graphs below, line types, colors and sizes are the same for the two groups :

# Line plot with multiple groups
ggplot(data=df2, aes(x=dose, y=len, group=supp)) +
  geom_line()+
  geom_point()
# Change line types
ggplot(data=df2, aes(x=dose, y=len, group=supp)) +
  geom_line(linetype="dashed", color="blue", size=1.2)+
  geom_point(color="red", size=3)

Change line types by groups

In the graphs below, line types and point shapes are controlled automatically by the levels of the variable supp :

# Change line types by groups (supp)
ggplot(df2, aes(x=dose, y=len, group=supp)) +
  geom_line(aes(linetype=supp))+
  geom_point()
# Change line types and point shapes
ggplot(df2, aes(x=dose, y=len, group=supp)) +
  geom_line(aes(linetype=supp))+
  geom_point(aes(shape=supp))

It is also possible to change manually the line types using the function scale_linetype_manual().

# Set line types manually
ggplot(df2, aes(x=dose, y=len, group=supp)) +
  geom_line(aes(linetype=supp))+
  geom_point()+
  scale_linetype_manual(values=c("twodash", "dotted"))

You can read more on line types here : ggplot2 line types

If you want to change also point shapes, read this article : ggplot2 point shapes

Change line colors by groups

Line colors are controlled automatically by the levels of the variable supp :

p<-ggplot(df2, aes(x=dose, y=len, group=supp)) +
  geom_line(aes(color=supp))+
  geom_point(aes(color=supp))
p

It is also possible to change manually line colors using the functions :

• scale_color_manual() : to use custom colors
• scale_color_brewer() : to use color palettes from RColorBrewer package
• scale_color_grey() : to use grey color palettes

# Use custom color palettes
p+scale_color_manual(values=c("#999999", "#E69F00", "#56B4E9"))
# Use brewer color palettes
p+scale_color_brewer(palette="Dark2")
# Use grey scale
p + scale_color_grey() + theme_classic()

Read more on ggplot2 colors here : ggplot2 colors

Change the colors of the plot panel background and the grid lines

1. The functions theme() and element_rect() are used for changing the plot panel background color :

p + theme(panel.background = element_rect(fill, colour, size, 
                                          linetype, color))

2. The appearance of grid lines can be changed using the function element_line() as follow :

# change major and minor grid lines
p + theme(
  panel.grid.major = element_line(colour, size, linetype,
                                   lineend, color),
  panel.grid.minor = element_line(colour, size, linetype,
                                   lineend, color)
  )

The R code below illustrates how to modify the appearance of the plot panel background and grid lines :

# Change the colors of plot panel background to lightblue
# and the color of grid lines to white
p + theme(
  panel.background = element_rect(fill = "lightblue",
                                colour = "lightblue",
                                size = 0.5, linetype = "solid"),
  panel.grid.major = element_line(size = 0.5, linetype = 'solid',
                                colour = "white"), 
  panel.grid.minor = element_line(size = 0.25, linetype = 'solid',
                                colour = "white")
  )

ggplot2 background color, grid lines, R programming

Remove plot panel borders and grid lines

It is possible to hide plot panel borders and grid lines with the function element_blank() as follow :

# Remove panel borders and grid lines
p + theme(panel.border = element_blank(),
          panel.grid.major = element_blank(),
          panel.grid.minor = element_blank())
# Hide panel borders and grid lines
# But change axis line
p + theme(panel.border = element_blank(),
          panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          axis.line = element_line(size = 0.5, linetype = "solid",
                                   colour = "black"))

ggplot2 background color, remove plot panel border, remove grid lines, R programming

Change the plot background color (not the panel)

p + theme(plot.background = element_rect(fill = "darkblue"))

ggplot2 background color, R programming

theme_tufte : a minimalist theme

# scatter plot
ggplot(mtcars, aes(wt, mpg)) +
  geom_point() + geom_rangeframe() + 
  theme_tufte()

ggplot2 theme_tufte, R statistical software

theme_economist : theme based on the plots in the economist magazine

p <- ggplot(iris, aes(Sepal.Length, Sepal.Width, colour = Species))+
  geom_point()
# Use economist color scales
p + theme_economist() + 
  scale_color_economist()+
  ggtitle("Iris data sets")

ggplot2 theme_economist, R statistical software

Note that, the function scale_fill_economist() are also available.

theme_stata: theme based on Stata graph schemes.

p + theme_stata() + scale_color_stata() +
  ggtitle("Iris data")

ggplot2 theme_stata, R statistical software

The stata theme color scales can be used as follow :

scale_fill_stata(scheme = "s2color", ...)
scale_color_stata(scheme = "s2color", ...)

The allowed values for the argument scheme are one of “s2color”, “s1rcolor”, “s1color”, or “mono”.

theme_wsj: theme based on plots in the Wall Street Journal

p + theme_wsj()+ scale_colour_wsj("colors6")+
  ggtitle("Iris data")

ggplot2 theme_wsj, R statistical software

The Wall Street Journal color and fill scales are :

scale_color_wsj(palette = "colors6", ...)
scale_fill_wsj(palette = "colors6", ...)

The color palette to use can be one of “rgby”, “red_green”, “black_green”, “dem_rep”, “colors6”.

theme_calc : theme based on LibreOffice Calc

These themes are based on the defaults in Google Docs and LibreOffice Calc, respectively.

p + theme_calc()+ scale_colour_calc()+
  ggtitle("Iris data")

ggplot2 theme_calc, R statistical software

theme_hc : theme based on Highcharts JS

p + theme_hc()+ scale_colour_hc()

ggplot2 theme_hc, R statistical software

Scatter plots

The R code below creates basic scatter plots using the argument geom = “point”. It’s also possible to combine different geoms (e.g.: geom = c(“point”, “smooth”)).

# Basic scatter plot
qplot(x = mpg, y = wt, data = df, geom = "point")
# Scatter plot with smoothed line
qplot(mpg, wt, data = df, 
      geom = c("point", "smooth"))

The following R code will change the color and the shape of points by groups. The column cyl will be used as grouping variable. In other words, the color and the shape of points will be changed by the levels of cyl.

qplot(mpg, wt, data = df, colour = cyl, shape = cyl)

Box plot, violin plot and dot plot

The R code below generates some data containing the weights by sex (M for male; F for female):

set.seed(1234)
wdata = data.frame(
        sex = factor(rep(c("F", "M"), each=200)),
        weight = c(rnorm(200, 55), rnorm(200, 58)))
head(wdata)

##   sex   weight
## 1   F 53.79293
## 2   F 55.27743
## 3   F 56.08444
## 4   F 52.65430
## 5   F 55.42912
## 6   F 55.50606

# Basic box plot from data frame
qplot(sex, weight, data = wdata, 
      geom= "boxplot", fill = sex)
# Violin plot
qplot(sex, weight, data = wdata, geom = "violin")
# Dot plot
qplot(sex, weight, data = wdata, geom = "dotplot",
      stackdir = "center", binaxis = "y", dotsize = 0.5)

Histogram and density plots

The histogram and density plots are used to display the distribution of data.

# Histogram  plot
# Change histogram fill color by group (sex)
qplot(weight, data = wdata, geom = "histogram",
      fill = sex)
# Density plot
# Change density plot line color by group (sex)
# change line type
qplot(weight, data = wdata, geom = "density",
    color = sex, linetype = sex)

One variable: Continuous

We’ll use weight data (wdata), generated in the previous sections.

head(wdata)

##   sex   weight
## 1   F 53.79293
## 2   F 55.27743
## 3   F 56.08444
## 4   F 52.65430
## 5   F 55.42912
## 6   F 55.50606

The following R code computes the mean value by sex:

library(plyr)
mu <- ddply(wdata, "sex", summarise, grp.mean=mean(weight))
head(mu)

##   sex grp.mean
## 1   F 54.94224
## 2   M 58.07325

We start by creating a plot, named a, that we’ll finish in the next section by adding a layer.

a <- ggplot(wdata, aes(x = weight))

# Basic plot
a + geom_area(stat = "bin")
# change fill colors by sex
a + geom_area(aes(fill = sex), stat ="bin", alpha=0.6) +
  theme_classic()

a + geom_area(aes(y = ..density..), stat ="bin")

a + stat_bin(geom = "area")

# Basic plot
a + geom_density()
# change line colors by sex
a + geom_density(aes(color = sex)) 
# Change fill color by sex
# Use semi-transparent fill: alpha = 0.4
a + geom_density(aes(fill = sex), alpha=0.4)
   
# Add mean line and Change color manually
a + geom_density(aes(color = sex)) +
  geom_vline(data=mu, aes(xintercept=grp.mean, color=sex),
             linetype="dashed") +
  scale_color_manual(values=c("#999999", "#E69F00"))

a + stat_density()

# Basic plot
a + geom_dotplot()
# change fill and color by sex
a + geom_dotplot(aes(fill = sex)) 
# Change fill color manually 
a + geom_dotplot(aes(fill = sex)) +
  scale_fill_manual(values=c("#999999", "#E69F00"))

# Basic plot
a + geom_freqpoly() 
# change y axis to density value
# and change theme
a + geom_freqpoly(aes(y = ..density..)) +
  theme_minimal()
# change color and linetype by sex
a + geom_freqpoly(aes(color = sex, linetype = sex)) +
  theme_minimal()

# Basic plot
a + geom_histogram()
# change line colors by sex
a + geom_histogram(aes(color = sex), fill = "white",
                   position = "dodge") 

a + geom_histogram(aes(y = ..density..))

a + stat_bin(geom = "histogram")

a + stat_ecdf()

ggplot(mtcars, aes(sample=mpg)) + stat_qq()

One variable: Discrete

The function geom_bar() can be used to visualize one discrete variable. In this case, the count of each level is plotted. We’ll use the mpg data set [in ggplot2 package]. The R code is as follow:

data(mpg)
b <- ggplot(mpg, aes(fl))
# Basic plot
b + geom_bar()
# Change fill color
b + geom_bar(fill = "steelblue", color ="steelblue") +
  theme_minimal()

To customize the plot, the following arguments can be used: alpha, color, fill, linetype and size. Learn more here: ggplot2 bar plot.

• Key function: geom_bar()
• Alternative function: stat_count()

b + stat_count()

Two variables: Continuous X, Continuous Y

We’ll use the mtcars data set. The variable cyl is used as grouping variable.

data(mtcars)
mtcars$cyl <- as.factor(mtcars$cyl)
head(mtcars[, c("wt", "mpg", "cyl")])

##                      wt  mpg cyl
## Mazda RX4         2.620 21.0   6
## Mazda RX4 Wag     2.875 21.0   6
## Datsun 710        2.320 22.8   4
## Hornet 4 Drive    3.215 21.4   6
## Hornet Sportabout 3.440 18.7   8
## Valiant           3.460 18.1   6

We start by creating a plot, named b, that we’ll finish in the next section by adding a layer.

b <- ggplot(mtcars, aes(x = wt, y = mpg))

# Basic plot
b + geom_point()
   
# change the color and the point 
# by the levels of cyl variable
b + geom_point(aes(color = cyl, shape = cyl)) 
# Change color manually
b + geom_point(aes(color = cyl, shape = cyl)) +
  scale_color_manual(values = c("#999999", "#E69F00", "#56B4E9"))+
  theme_minimal()

# Regression line only
b + geom_smooth(method = lm)
  
# Point + regression line
# Remove the confidence interval 
b + geom_point() + 
  geom_smooth(method = lm, se = FALSE)
# loess method: local regression fitting
b + geom_point() + geom_smooth()
# Change color and shape by groups (cyl)
b + geom_point(aes(color=cyl, shape=cyl)) + 
  geom_smooth(aes(color=cyl, shape=cyl), 
              method=lm, se=FALSE, fullrange=TRUE)

b + stat_smooth(method = "lm")

ggplot(mpg, aes(cty, hwy)) +
  geom_point() + geom_quantile() +
  theme_minimal()

ggplot(mpg, aes(cty, hwy)) +
  geom_point() + stat_quantile(quantiles = c(0.25, 0.5, 0.75))

# Add marginal rugs using faithful data
ggplot(faithful, aes(x=eruptions, y=waiting)) +
  geom_point() + geom_rug()

p <- ggplot(mpg, aes(displ, hwy))
# Default scatter plot
p + geom_point()
# Use jitter to reduce overplotting
p + geom_jitter(
    position = position_jitter(width = 0.5, height = 0.5))

b + geom_text(aes(label = rownames(mtcars)))

Two variables: Continuous bivariate distribution

We start by using the diamonds data set [in ggplot2].

data(diamonds)
head(diamonds[, c("carat", "price")])

##   carat price
## 1  0.23   326
## 2  0.21   326
## 3  0.23   327
## 4  0.29   334
## 5  0.31   335
## 6  0.24   336

We start by creating a plot, named c, that we’ll finish in the next section by adding a layer.

c <- ggplot(diamonds, aes(carat, price))

# Default plot 
c + geom_bin2d()
# Change the number of bins
c + geom_bin2d(bins = 15)

c + stat_bin_2d()
c + stat_summary_2d(aes(z = depth))

install.packages("hexbin")

require(hexbin)
# Default plot 
c + geom_hex()
# Change the number of bins
c + geom_hex(bins = 10)

c + stat_bin_hex()
c + stat_summary_hex(aes(z = depth))

# Scatter plot 
sp <- ggplot(faithful, aes(x=eruptions, y=waiting)) 

# Default plot
sp + geom_density_2d()
# Add points
sp + geom_point() + geom_density_2d()
# Use stat_density_2d with geom = "polygon"
sp + geom_point() + 
  stat_density_2d(aes(fill = ..level..), geom="polygon")

sp + stat_density_2d()

Two variables: Continuous function

In this section, we’ll see how to connect observations by line. The economics data set [in ggplot2] is used.

data(economics)
head(economics)

##         date   pce    pop psavert uempmed unemploy
## 1 1967-07-01 507.4 198712    12.5     4.5     2944
## 2 1967-08-01 510.5 198911    12.5     4.7     2945
## 3 1967-09-01 516.3 199113    11.7     4.6     2958
## 4 1967-10-01 512.9 199311    12.5     4.9     3143
## 5 1967-11-01 518.1 199498    12.5     4.7     3066
## 6 1967-12-01 525.8 199657    12.1     4.8     3018

We start by creating a plot, named d, that we’ll finish in the next section by adding a layer.

d <- ggplot(economics, aes(x = date, y = unemploy))

# Area plot
d + geom_area()
# Line plot: connecting observations, ordered by x
d + geom_line()
# Connecting observations by stairs
# a subset of economics data set is used
set.seed(1234)
ss <- economics[sample(1:nrow(economics), 20), ]
ggplot(ss, aes(x = date, y = unemploy)) + 
  geom_step()

To customize the plot, the following arguments can be used: alpha, color, linetype, size and fill (for geom_area only). Learn more here: ggplot2 line plot.

• Key functions: geom_area(), geom_line(), geom_step()

Two variables: Discrete X, Continuous Y

The ToothGrowth data set we’ll be used to plot the continuous variable len (for tooth length) by the discrete variable dose. The following R code converts the variable dose from a numeric to a discrete factor variable.

data("ToothGrowth")
ToothGrowth$dose <- as.factor(ToothGrowth$dose)
head(ToothGrowth)

##    len supp dose
## 1  4.2   VC  0.5
## 2 11.5   VC  0.5
## 3  7.3   VC  0.5
## 4  5.8   VC  0.5
## 5  6.4   VC  0.5
## 6 10.0   VC  0.5

We start by creating a plot, named e, that we’ll finish in the next section by adding a layer.

e <- ggplot(ToothGrowth, aes(x = dose, y = len))

# Default plot
e + geom_boxplot()
# Notched box plot
e + geom_boxplot(notch = TRUE)
# Color by group (dose)
e + geom_boxplot(aes(color = dose))
# Change fill color by group (dose)
e + geom_boxplot(aes(fill = dose))

# Box plot with multiple groups
ggplot(ToothGrowth, aes(x=dose, y=len, fill=supp)) +
  geom_boxplot()

e + stat_boxplot(coeff = 1.5)

# Default plot
e + geom_violin(trim = FALSE)
# violin plot with mean points (+/- SD)
e + geom_violin(trim = FALSE) + 
  stat_summary(fun.data="mean_sdl",  fun.args = list(mult=1), 
               geom="pointrange", color = "red")
# Combine with box plot
e + geom_violin(trim = FALSE) + 
  geom_boxplot(width = 0.2)
# Color by group (dose) 
e + geom_violin(aes(color = dose), trim = FALSE)

e + stat_ydensity(trim = FALSE)

# Default plot
e + geom_dotplot(binaxis = "y", stackdir = "center")
# Dot plot with mean points (+/- SD)
e + geom_dotplot(binaxis = "y", stackdir = "center") + 
  stat_summary(fun.data="mean_sdl",  fun.args = list(mult=1), 
               geom="pointrange", color = "red")

# Combine with box plot
e + geom_boxplot() + 
  geom_dotplot(binaxis = "y", stackdir = "center") 
# Add violin plot
e + geom_violin(trim = FALSE) +
  geom_dotplot(binaxis='y', stackdir='center')
  
# Color and fill by group (dose) 
e + geom_dotplot(aes(color = dose, fill = dose), 
                 binaxis = "y", stackdir = "center")

# Default plot
e + geom_jitter(position=position_jitter(0.2))
# Strip charts with mean points (+/- SD)
e + geom_jitter(position=position_jitter(0.2)) + 
  stat_summary(fun.data="mean_sdl",  fun.args = list(mult=1), 
               geom="pointrange", color = "red")

# Combine with box plot
e + geom_jitter(position=position_jitter(0.2)) + 
  geom_dotplot(binaxis = "y", stackdir = "center") 
# Add violin plot
e + geom_violin(trim = FALSE) +
  geom_jitter(position=position_jitter(0.2))
  
# Change color and shape by group (dose) 
e +  geom_jitter(aes(color = dose, shape = dose),
                 position=position_jitter(0.2))

df <- data.frame(supp=rep(c("VC", "OJ"), each=3),
                dose=rep(c("D0.5", "D1", "D2"),2),
                len=c(6.8, 15, 33, 4.2, 10, 29.5))
head(df)

##   supp dose  len
## 1   VC D0.5  6.8
## 2   VC   D1 15.0
## 3   VC   D2 33.0
## 4   OJ D0.5  4.2
## 5   OJ   D1 10.0
## 6   OJ   D2 29.5

# Change line types by groups (supp)
ggplot(df, aes(x=dose, y=len, group=supp)) +
  geom_line(aes(linetype=supp))+
  geom_point()
# Change line types, point shapes and colors
ggplot(df, aes(x=dose, y=len, group=supp)) +
  geom_line(aes(linetype=supp, color = supp))+
  geom_point(aes(shape=supp, color = supp))

df <- data.frame(dose=c("D0.5", "D1", "D2"),
                len=c(4.2, 10, 29.5))
head(df)

##   dose  len
## 1 D0.5  4.2
## 2   D1 10.0
## 3   D2 29.5

df2 <- data.frame(supp=rep(c("VC", "OJ"), each=3),
                dose=rep(c("D0.5", "D1", "D2"),2),
                len=c(6.8, 15, 33, 4.2, 10, 29.5))
head(df2)

##   supp dose  len
## 1   VC D0.5  6.8
## 2   VC   D1 15.0
## 3   VC   D2 33.0
## 4   OJ D0.5  4.2
## 5   OJ   D1 10.0
## 6   OJ   D2 29.5

f <- ggplot(df, aes(x = dose, y = len))

# Basic bar plot
f + geom_bar(stat = "identity")
# Change fill color and add labels
f + geom_bar(stat="identity", fill="steelblue")+
  geom_text(aes(label=len), vjust=-0.3, size=3.5)+
  theme_minimal()
# Change bar plot line colors by groups
f + geom_bar(aes(color = dose),
             stat="identity", fill="white")
# Change bar plot fill colors by groups
f + geom_bar(aes(fill = dose), stat="identity")

g <- ggplot(data=df2, aes(x=dose, y=len, fill=supp)) 
# Stacked bar plot
g + geom_bar(stat = "identity")
# Use position=position_dodge()
g + geom_bar(stat="identity", position=position_dodge())

g + stat_identity(geom = "bar")
g + stat_identity(geom = "bar", position = "dodge")

Two variables: Discrete X, Discrete Y

The diamonds data set [in ggplot2] we’ll be used to plot the discrete variable color (for diamond colors) by the discrete variable cut (for diamond cut types). The plot is created using the function geom_jitter().

ggplot(diamonds, aes(cut, color)) +
  geom_jitter(aes(color = cut), size = 0.5)

To customize the plot, the following arguments can be used: alpha, color, fill, shape and size.

• Key function: geom_jitter()

Two variables: Visualizing error

The ToothGrowth data set we’ll be used. We start by creating a data set named df which holds ToothGrowth data.

# ToothGrowth data set
df <- ToothGrowth
df$dose <- as.factor(df$dose)
head(df)

##    len supp dose
## 1  4.2   VC  0.5
## 2 11.5   VC  0.5
## 3  7.3   VC  0.5
## 4  5.8   VC  0.5
## 5  6.4   VC  0.5
## 6 10.0   VC  0.5

The helper function below (data_summary()) will be used to calculate the mean and the standard deviation (used as error), for the variable of interest, in each group. The plyr package is required.

# Calculate the mean and the SD in each group
#+++++++++++++++++++++++++
# data : a data frame
# varname : the name of the variable to be summariezed
# grps : column names to be used as grouping variables
data_summary <- function(data, varname, grps){
  require(plyr)
  summary_func <- function(x, col){
    c(mean = mean(x[[col]], na.rm=TRUE),
      sd = sd(x[[col]], na.rm=TRUE))
  }
  data_sum<-ddply(data, grps, .fun=summary_func, varname)
  data_sum <- rename(data_sum, c("mean" = varname))
 return(data_sum)
}

Using the function data_summary(), the following R code creates a data set named df2 which holds the mean and the SD of tooth length (len) by groups (dose).

df2 <- data_summary(df, varname="len", grps= "dose")
# Convert dose to a factor variable
df2$dose=as.factor(df2$dose)
head(df2)

##   dose    len       sd
## 1  0.5 10.605 4.499763
## 2    1 19.735 4.415436
## 3    2 26.100 3.774150

We start by creating a plot, named f, that we’ll finish in the next section by adding a layer.

f <- ggplot(df2, aes(x = dose, y = len, 
                     ymin = len-sd, ymax = len+sd))

# Default plot
f + geom_crossbar()
# color by groups
f + geom_crossbar(aes(color = dose))
# Change color manually
f + geom_crossbar(aes(color = dose)) + 
  scale_color_manual(values = c("#999999", "#E69F00", "#56B4E9"))+
  theme_minimal()
# fill by groups and change color manually
f + geom_crossbar(aes(fill = dose)) + 
  scale_fill_manual(values = c("#999999", "#E69F00", "#56B4E9"))+
  theme_minimal()

df3 <- data_summary(df, varname="len", grps= c("supp", "dose"))
head(df3)

##   supp dose   len       sd
## 1   OJ  0.5 13.23 4.459709
## 2   OJ    1 22.70 3.910953
## 3   OJ    2 26.06 2.655058
## 4   VC  0.5  7.98 2.746634
## 5   VC    1 16.77 2.515309
## 6   VC    2 26.14 4.797731

f <- ggplot(df3, aes(x = dose, y = len, 
                     ymin = len-sd, ymax = len+sd))
# Default plot
f + geom_crossbar(aes(color = supp))
# Use position_dodge() to avoid overlap
f + geom_crossbar(aes(color = supp), 
                  position = position_dodge(1))

f <- ggplot(df, aes(x = dose, y = len, color = supp)) 
# Use geom_crossbar()
f + stat_summary(fun.data="mean_sdl", fun.args = list(mult=1), 
                 geom="crossbar", width = 0.6, 
                 position = position_dodge(0.8))

f <- ggplot(df2, aes(x = dose, y = len, 
                     ymin = len-sd, ymax = len+sd))

# Error bars colored by groups
f + geom_errorbar(aes(color = dose), width = 0.2)
# Combine with line plot
f + geom_line(aes(group = 1)) + 
  geom_errorbar(width = 0.2)
# Combine with bar plot, color by groups
f + geom_bar(aes(color = dose), stat = "identity", fill ="white") + 
  geom_errorbar(aes(color = dose), width = 0.2)

f <- ggplot(df3, aes(x = dose, y = len, 
                     ymin = len-sd, ymax = len+sd))
# Default plot
f + geom_bar(aes(fill = supp), stat = "identity",
             position = "dodge") + 
  geom_errorbar(aes(color = supp),  position = "dodge")

df2 <- data_summary(ToothGrowth, varname="len", grps = "dose")
head(df2)

##   dose    len       sd
## 1  0.5 10.605 4.499763
## 2    1 19.735 4.415436
## 3    2 26.100 3.774150

f <- ggplot(df2, aes(x = len, y = dose ,
                     xmin=len-sd, xmax=len+sd))

f <- ggplot(df2, aes(x = dose, y = len,
                     ymin=len-sd, ymax=len+sd))
# Line range
f + geom_linerange()
# Point range
f + geom_pointrange()

g <- ggplot(df, aes(x=dose, y=len)) + 
  geom_dotplot(binaxis='y', stackdir='center')

# use geom_crossbar()
g + stat_summary(fun.data="mean_sdl", fun.args = list(mult=1), 
                 geom="crossbar", width=0.5)
# Use geom_errorbar()
g + stat_summary(fun.data=mean_sdl, fun.args = list(mult=1), 
        geom="errorbar", color="red", width=0.2) +
  stat_summary(fun.y=mean, geom="point", color="red")
   
# Use geom_pointrange()
g + stat_summary(fun.data=mean_sdl, fun.args = list(mult=1), 
                 geom="pointrange", color="red")

Two variables: Maps

The function geom_map() can be used to create a map with ggplot2. The R package map is required. It contains geographical information useful for drawing easily maps in ggplot2.

Install map package (if you don’t have it):

install.packages("map")

In the following R code, we’ll create USA map and USArrests crime data to shade each region.

# Prepare the data
crimes <- data.frame(state = tolower(rownames(USArrests)), 
                     USArrests)
library(reshape2) # for melt
crimesm <- melt(crimes, id = 1)
# Get map data
require(maps) 
map_data <- map_data("state")
# Plot the map with Murder data
ggplot(crimes, aes(map_id = state)) + 
  geom_map(aes(fill = Murder), map = map_data) + 
  expand_limits(x = map_data$long, y = map_data$lat)

To customize the plot, the following arguments can be used: alpha, color, fill, linetype and size. Learn more here: ggplot2 map.

Key function: geom_map()

Three variables

The mtcars data set we’ll be used. We first compute a correlation matrix, which will be visualized using specific ggplot2 functions.

Prepare the data:

df <- mtcars[, c(1,3,4,5,6,7)]
# Correlation matrix
cormat <- round(cor(df),2)
# Melt the correlation matrix
require(reshape2)
cormat <- melt(cormat)
head(cormat)

##   Var1 Var2 value
## 1  mpg  mpg  1.00
## 2 disp  mpg -0.85
## 3   hp  mpg -0.78
## 4 drat  mpg  0.68
## 5   wt  mpg -0.87
## 6 qsec  mpg  0.42

We start by creating a plot, named g, that we’ll finish in the next section by adding a layer.

g <- ggplot(cormat, aes(x = Var1, y = Var2))

We’ll use the function geom_tile() to visualize a correlation matrix.

Compute and visualize correlation matrix:

# 1. Compute correlation
cormat <- round(cor(df),2)
# 2. Reorder the correlation matrix by 
# Hierarchical clustering
hc <- hclust(as.dist(1-cormat)/2)
cormat.ord <- cormat[hc$order, hc$order]
# 3. Get the upper triangle
cormat.ord[lower.tri(cormat.ord)]<- NA
# 4. Melt the correlation matrix
require(reshape2)
melted_cormat <- melt(cormat.ord, na.rm = TRUE)
# Create the heatmap
ggplot(melted_cormat, aes(Var2, Var1, fill = value))+
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", 
   midpoint = 0, limit = c(-1,1), space = "Lab",
   name="Pearson\nCorrelation") + # Change gradient color
  theme_minimal()+ # minimal theme
 theme(axis.text.x = element_text(angle = 45, vjust = 1, 
                                  size = 12, hjust = 1))+
 coord_fixed()

To customize the plot, the following arguments can be used: alpha, color, fill, linetype and size. Learn more here: ggplot2 correlation matrix heatmap.

• Key functions: geom_tile(), geom_raster()

Other types of graphs

• Pie chart: (click to read more)

• Survival curves: (click to read more)

Graphical primitives: polygon, path, ribbon, segment, rectangle

This section describes how to add graphical elements to a plot. The functions below we’ll be used:

1. The R code below draws France map using geom_polygon():

require(maps)
france = map_data('world', region = 'France')
ggplot(france, aes(x = long, y = lat, group = group)) +
  geom_polygon(fill = 'white', colour = 'black')

To customize the plot, the following arguments can be used: alpha, color, fill, linetype and size.

2. The following R code uses econimics data [in ggplot2] and produces path, ribbon and rectangles.

h <- ggplot(economics, aes(date, unemploy))
# Path
h + geom_path()
# Ribbon
h + geom_ribbon(aes(ymin = unemploy-900, ymax = unemploy+900),
                fill = "steelblue") +
  geom_path(size = 0.8)
# Rectangle
h + geom_rect(aes(xmin = as.Date('1980-01-01'), ymin = -Inf, 
                 xmax = as.Date('1985-01-01'), ymax = Inf),
             fill = "steelblue") +
  geom_path(size = 0.8) 

To customize the plot, the following arguments can be used: alpha, color, fill (for ribbon only), linetype and size.

3. Add line segments between points (x1, y1) and (x2, y2):

# Create a scatter plot
i <- ggplot(mtcars, aes(wt, mpg)) + geom_point()
# Add segment
i + geom_segment(aes(x = 2, y = 15, xend = 3, yend = 15))
# Add arrow
require(grid)
i + geom_segment(aes(x = 5, y = 30, xend = 3.5, yend = 25),
                  arrow = arrow(length = unit(0.5, "cm")))

To customize the plot, the following arguments can be used: alpha, color, linetype and size. Learn more here: ggplot2 add line segment.

4. Add curves between points (x1, y1) and (x2, y2):

i + geom_curve(aes(x = 2, y = 15, xend = 3, yend = 15))

• Key functions: geom_path(), geom_ribbon(), geom_rect(), geom_segment()

Main title, axis labels and legend title

We start by creating a box plot using the data set ToothGrowth:

# Convert the variable dose from numeric to factor variable
ToothGrowth$dose <- as.factor(ToothGrowth$dose)
p <- ggplot(ToothGrowth, aes(x=dose, y=len)) + geom_boxplot()

The function below can be used for changing titles and labels:

The function labs() can be also used to change the legend title.

1. Change main title and axis labels

# Default plot
print(p)
# Change title and axis labels
p <- p +labs(title="Plot of length \n by dose",
        x ="Dose (mg)", y = "Teeth length")
p

Note that, \n is used to split long title into multiple lines.

2. Change the appearance of labels:

To change the appearance(color, size and face ) of labels, the functions theme() and element_text() can be used.

The function element_blank() hides the labels.

# Change the appearance of labels
p + theme(
plot.title = element_text(color="red", size=14, face="bold.italic"),
axis.title.x = element_text(color="blue", size=14, face="bold"),
axis.title.y = element_text(color="#993333", size=14, face="bold")
)
# Hide labels
p + theme(plot.title = element_blank(), 
          axis.title.x = element_blank(),
          axis.title.y = element_blank())

3. Change legend titles: Scale functions (fill, color, size, shape, …) are used to update legend titles.

# Default plot
p <- ggplot(ToothGrowth, aes(x=dose, y=len, fill=dose))+
  geom_boxplot()
p
# Modify legend titles
p + labs(fill = "Dose (mg)")

Learn more here: ggplot2 title: main, axis and legend titles.

Legend position and appearance

1. Create a box plot

# Convert the variable dose from numeric to factor variable
ToothGrowth$dose <- as.factor(ToothGrowth$dose)
p <- ggplot(ToothGrowth, aes(x=dose, y=len, fill=dose))+
  geom_boxplot()

2. Change legend position and appearance

# Change legend position: "left","top", "right", "bottom", "none"
p + theme(legend.position="top")
# Remove legends
p + theme(legend.position = "none")
# Change the appearance of legend title and labels
p + theme(legend.title = element_text(colour="blue"),
          legend.text = element_text(colour="red"))
# Change legend box background color
p + theme(legend.background = element_rect(fill="lightblue"))

3. Customize legends using scale functions
   • Change the order of legend items: scale_x_discrete()
   • Set legend title and labels: scale_fill_discrete()

# Change the order of legend items
p + scale_x_discrete(limits=c("2", "0.5", "1"))
# Set legend title and labels
p + scale_fill_discrete(name = "Dose", labels = c("A", "B", "C"))

Learn more here: ggplot2 legend position and appearance.

Change colors automatically and manually

ToothGrowth and mtcars data sets are used in the examples below.

# Convert dose and cyl columns from numeric to factor variables
ToothGrowth$dose <- as.factor(ToothGrowth$dose)
mtcars$cyl <- as.factor(mtcars$cyl)

We start by creating some plots which will be finished hereafter:

# Box plot
bp <- ggplot(ToothGrowth, aes(x=dose, y=len))
# Scatter plot
sp <- ggplot(mtcars, aes(x=wt, y=mpg))

1. Draw plots: change fill and outline colors

# box plot
bp + geom_boxplot(fill='steelblue', color="red")
# scatter plot
sp + geom_point(color='darkblue')

2. Change color by groups using the levels of dose variable

# Box plot
bp <- bp + geom_boxplot(aes(fill = dose))
bp
# Scatter plot
sp <- sp + geom_point(aes(color = cyl))
sp

3. Change colors manually:

• scale_fill_manual() for box plot, bar plot, violin plot, etc
• scale_color_manual() for lines and points

# Box plot
bp + scale_fill_manual(values=c("#999999", "#E69F00", "#56B4E9"))
# Scatter plot
sp + scale_color_manual(values=c("#999999", "#E69F00", "#56B4E9"))

4. Use RColorBrewer palettes: (Read more about RColorBrewer: color in R)

• scale_fill_brewer() for box plot, bar plot, violin plot, etc
• scale_color_brewer() for lines and points

# Box plot
bp + scale_fill_brewer(palette="Dark2")
# Scatter plot
sp + scale_color_brewer(palette="Dark2")

Available color palettes in the RColorBrewer package:

RColorBrewer palettes

5. Use gray colors:

• scale_fill_grey() for box plot, bar plot, violin plot, etc
• scale_colour_grey() for points, lines, etc

# Box plot
bp + scale_fill_grey() + theme_classic()
# Scatter plot
sp + scale_color_grey() + theme_classic()

6. Gradient or continuous colors:

Plots can be colored according to the values of a continuous variable using the functions :

• scale_color_gradient(), scale_fill_gradient() for sequential gradients between two colors
• scale_color_gradient2(), scale_fill_gradient2() for diverging gradients
• scale_color_gradientn(), scale_fill_gradientn() for gradient between n colors

Gradient colors for scatter plots: The graphs are colored using the qsec continuous variable :

# Color by qsec values
sp2<-ggplot(mtcars, aes(x=wt, y=mpg)) +
  geom_point(aes(color = qsec))
sp2
# Change the low and high colors
# Sequential color scheme
sp2+scale_color_gradient(low="blue", high="red")
# Diverging color scheme
mid<-mean(mtcars$qsec)
sp2+scale_color_gradient2(midpoint=mid, low="blue", mid="white",
                          high="red", space = "Lab" )

Learn more here: ggplot2 colors.

Point shapes, colors and size

The different points shapes commonly used in R are shown in the image below:

mtcars data is used in the following examples.

# Convert cyl as factor variable
mtcars$cyl <- as.factor(mtcars$cyl)

Create a scatter plot and change point shapes, colors and size:

# Basic scatter plot
ggplot(mtcars, aes(x=wt, y=mpg)) +
  geom_point(shape = 18, color = "steelblue", size = 4)
# Change point shapes and colors by groups
ggplot(mtcars, aes(x=wt, y=mpg)) +
  geom_point(aes(shape = cyl, color = cyl))

It’s also possible to manually change the appearance of points:

• scale_shape_manual() : to change point shapes
• scale_color_manual() : to change point colors
• scale_size_manual() : to change the size of points

# Change colors and shapes manually
ggplot(mtcars, aes(x=wt, y=mpg, group=cyl)) +
  geom_point(aes(shape=cyl, color=cyl), size=2)+
  scale_shape_manual(values=c(3, 16, 17))+
  scale_color_manual(values=c('#999999','#E69F00', '#56B4E9'))+
  theme(legend.position="top")

Learn more here: ggplot2 point shapes, colors and size.

Add text annotations to a graph

There are three important functions for adding texts to a plot:

• geom_text(): Textual annotations
• annotate(): Textual annotations
• annotation_custom(): Static annotations that are the same in every panel. These annotations are not affected by the plot scales.

A subset of mtcars data is used:

set.seed(1234)
df <- mtcars[sample(1:nrow(mtcars), 10), ]
df$cyl <- as.factor(df$cyl)

Scatter plots with textual annotations:

# Scatter plot
sp <- ggplot(df, aes(x=wt, y=mpg))+ geom_point() 
# Add text, change colors by groups
sp + geom_text(aes(label = rownames(df), color = cyl),
               size = 3, vjust = -1)
# Add text at a particular coordinate
sp + geom_text(x = 3, y = 30, label = "Scatter plot",
              color="red")

Learn more here: ggplot2 text: Add text annotations to a graph.

Line types

The different line types available in R software are : “blank”, “solid”, “dashed”, “dotted”, “dotdash”, “longdash”, “twodash”.

Note that, line types can be also specified using numbers : 0, 1, 2, 3, 4, 5, 6. 0 is for “blank”, 1 is for “solid”, 2 is for “dashed”, ….

A graph of the different line types is shown below :

1. Basic line plot

# Create some data
df <- data.frame(time=c("breakfeast", "Lunch", "Dinner"),
                bill=c(10, 30, 15))
head(df)

##         time bill
## 1 breakfeast   10
## 2      Lunch   30
## 3     Dinner   15

# Basic line plot with points
# Change the line type
ggplot(data=df, aes(x=time, y=bill, group=1)) +
  geom_line(linetype = "dashed")+
  geom_point()

2. Line plots with multiple groups

# Create some data
df2 <- data.frame(sex = rep(c("Female", "Male"), each=3),
                  time=c("breakfeast", "Lunch", "Dinner"),
                  bill=c(10, 30, 15, 13, 40, 17) )
head(df2)

##      sex       time bill
## 1 Female breakfeast   10
## 2 Female      Lunch   30
## 3 Female     Dinner   15
## 4   Male breakfeast   13
## 5   Male      Lunch   40
## 6   Male     Dinner   17

# Line plot with multiple groups
# Change line types and colors by groups (sex)
ggplot(df2, aes(x=time, y=bill, group=sex)) +
  geom_line(aes(linetype = sex, color = sex))+
  geom_point(aes(color=sex))+
  theme(legend.position="top")

The functions below can be used to change the appearance of line types manually:

• scale_linetype_manual() : to change line types
• scale_color_manual() : to change line colors
• scale_size_manual() : to change the size of lines

# Change line types, colors and sizes
ggplot(df2, aes(x=time, y=bill, group=sex)) +
  geom_line(aes(linetype=sex, color=sex, size=sex))+
  geom_point()+
  scale_linetype_manual(values=c("twodash", "dotted"))+
  scale_color_manual(values=c('#999999','#E69F00'))+
  scale_size_manual(values=c(1, 1.5))+
  theme(legend.position="top")

Learn more here: ggplot2 line types.

Themes and background colors

ToothGrowth data is used :

# Convert the column dose from numeric to factor variable
ToothGrowth$dose <- as.factor(ToothGrowth$dose)

1. Create a box plot

p <- ggplot(ToothGrowth, aes(x=dose, y=len)) + 
  geom_boxplot()

2. Change plot themes

Several functions are available in ggplot2 package for changing quickly the theme of plots :

• theme_gray(): gray background color and white grid lines
• theme_bw() : white background and gray grid lines

p + theme_gray(base_size = 14)
p + theme_bw()

ggplot2 background color, theme_gray and theme_bw, R programming

• theme_linedraw : black lines around the plot
• theme_light : light gray lines and axis (more attention towards the data)

p + theme_linedraw()
p + theme_light()

ggplot2 background color, theme_linedraw and theme_light, R programming

• theme_minimal: no background annotations
• theme_classic : theme with axis lines and no grid lines

p + theme_minimal()
p + theme_classic()

ggplot2 background color, theme_minimal and theme_classic, R programming

Learn more here: ggplot2 themes and background colors.

Axis limits: Minimum and Maximum values

Create a plot:

p <- ggplot(cars, aes(x = speed, y = dist)) + geom_point()

Different functions are available for setting axis limits:

# Default plot
print(p)
# Change axis limits using coord_cartesian()
p + coord_cartesian(xlim =c(5, 20), ylim = c(0, 50))
# Use xlim() and ylim()
p + xlim(5, 20) + ylim(0, 50)
# Expand limits
p + expand_limits(x = c(5, 50), y = c(0, 150))

Learn more here: ggplot2 axis limits.

Note that, date axis limits can be set using the functions scale_x_date() and scale_y_date(). Read more here: ggplot2 date axis.

Axis transformations: log and sqrt scales

1. Create a scatter plot:

p <- ggplot(cars, aes(x = speed, y = dist)) + geom_point()

2. ggplot2 functions for continuous axis transformations:

3. The R code below uses the function scale_xx_continuous() to transform axis scales:

# Default scatter plot
print(p)
# Log transformation using scale_xx()
# possible values for trans : 'log2', 'log10','sqrt'
p + scale_x_continuous(trans='log2') +
  scale_y_continuous(trans='log2')
# Format axis tick mark labels
require(scales)
p + scale_y_continuous(trans = log2_trans(),
    breaks = trans_breaks("log2", function(x) 2^x),
    labels = trans_format("log2", math_format(2^.x)))
# Reverse coordinates
p + scale_y_reverse() 

Learn more here: ggplot2 axis limits.

Axis ticks: customize tick marks and labels, reorder and select items

1. Functions for changing the style of axis tick mark labels:

2. Create a box plot:

p <- ggplot(ToothGrowth, aes(x=dose, y=len)) + geom_boxplot()
# print(p)

3. Change the style and the orientation angle of axis tick labels

# Change the style of axis tick labels
# face can be "plain", "italic", "bold" or "bold.italic"
p + theme(axis.text.x = element_text(face="bold", color="#993333", 
                           size=14, angle=45),
          axis.text.y = element_text(face="bold", color="blue", 
                           size=14, angle=45))
# Remove axis ticks and tick mark labels
p + theme(
  axis.text.x = element_blank(), # Remove x axis tick labels
  axis.text.y = element_blank(), # Remove y axis tick labels
  axis.ticks = element_blank()) # Remove ticks

4. Customize continuous and discrete axes:

• Discrete axes
  • scale_x_discrete(name, breaks, labels, limits): for X axis
  • scale_y_discrete(name, breaks, labels, limits): for y axis
• Continuous axes
  • scale_x_continuous(name, breaks, labels, limits, trans): for X axis
  • scale_y_continuous(name, breaks, labels, limits, trans): for y axis

Briefly, the meaning of the arguments are as follow:

scale_xx() functions can be used to change the following x or y axis parameters :

• axis titles
• axis limits (data range to display)
• choose where tick marks appear
• manually label tick marks

4.1. Discrete axes:

# Change x axis label and the order of items
p + scale_x_discrete(name ="Dose (mg)", 
                    limits=c("2","1","0.5"))
# Change tick mark labels
p + scale_x_discrete(breaks=c("0.5","1","2"),
        labels=c("Dose 0.5", "Dose 1", "Dose 2"))
# Choose which items to display
p + scale_x_discrete(limits=c("0.5", "2"))

4.2. Continuous axes:

# Default scatter plot
# +++++++++++++++++
sp <- ggplot(cars, aes(x = speed, y = dist)) + geom_point()
sp
# Customize the plot
#+++++++++++++++++++++
# 1. Change x and y axis labels, and limits
sp <- sp + scale_x_continuous(name="Speed of cars", limits=c(0, 30)) +
  scale_y_continuous(name="Stopping distance", limits=c(0, 150))
# 2. Set tick marks on y axis: a tick mark is shown on every 50
sp + scale_y_continuous(breaks=seq(0, 150, 50))
# Format the labels
# +++++++++++++++++
require(scales)
sp + scale_y_continuous(labels = percent) # labels as percents

Learn more here: ggplot2 Axis ticks: tick marks and labels.

Add straight lines to a plot: horizontal, vertical and regression lines

The R function below can be used :

• geom_hline(yintercept, linetype, color, size): for horizontal lines
• geom_vline(xintercept, linetype, color, size): for vertical lines
• geom_abline(intercept, slope, linetype, color, size): for regression lines
• geom_segment() to add segments

1. Create a simple scatter plot

# Simple scatter plot
sp <- ggplot(data=mtcars, aes(x=wt, y=mpg)) + geom_point()

2. Add straight lines

# Add horizontal line at y = 2O; change line type and color
sp + geom_hline(yintercept=20, linetype="dashed", color = "red")
# Add vertical line at x = 3; change line type, color and size
sp + geom_vline(xintercept = 3, color = "blue", size=1.5)
# Add regression line
sp + geom_abline(intercept = 37, slope = -5, color="blue")+
  ggtitle("y = -5X + 37")
# Add horizontal line segment
sp + geom_segment(aes(x = 2, y = 15, xend = 3, yend = 15))

Learn more here: ggplot2 add straight lines to a plot.

Rotate a plot: flip and reverse

• coord_flip(): Create horizontal plots
• scale_x_reverse(), scale_y_reverse(): Reverse the axes

set.seed(1234)
# Basic histogram
hp <- qplot(x=rnorm(200), geom="histogram")
hp
# Horizontal histogram
hp + coord_flip()
# Y axis reversed
hp + scale_y_reverse()

Learn more here: ggplot2 rotate a graph.

Faceting: split a plot into a matrix of panels

Facets divide a plot into subplots based on the values of one or more categorical variables.

There are two main functions for faceting :

• facet_grid()
• facet_wrap()

Create a box plot filled by groups:

p <- ggplot(ToothGrowth, aes(x=dose, y=len, group=dose)) + 
  geom_boxplot(aes(fill=dose))
p

The following functions can be used for facets:

1. Facet with one discrete variable: Split by the levels of the group “supp”

# Split in vertical direction
p + facet_grid(supp ~ .)
# Split in horizontal direction
p + facet_grid(. ~ supp)

2. Facet with two discrete variables: Split by the levels of the groups “dose” and “supp”

# Facet by two variables: dose and supp.
# Rows are dose and columns are supp
p + facet_grid(dose ~ supp)
# Facet by two variables: reverse the order of the 2 variables
# Rows are supp and columns are dose
p + facet_grid(supp ~ dose)

By default, all the panels have the same scales (scales=“fixed”). They can be made independent, by setting scales to free, free_x, or free_y.

p + facet_grid(dose ~ supp, scales='free')

Learn more here: ggplot2 facet : split a plot into a matrix of panels.

Position adjustements

Position adjustments determine how to arrange geoms. The argument position is used to adjust geom positions:

p <- ggplot(mpg, aes(fl, fill = drv))
# Arrange elements side by side
p + geom_bar(position = "dodge")
# Stack objects on top of one another, 
# and normalize to have equal height
p + geom_bar(position = "fill")

# Stack elements on top of one another
p + geom_bar(position = "stack")
# Add random noise to X and Y position 
# of each element to avoid overplotting
ggplot(mpg, aes(cty, hwy)) + 
  geom_point(position = "jitter")

Note that, each of these position adjustments can be done using a function with manual width and height argument.

• position_dodge(width, height)
• position_fill(width, height)
• position_stack(width, height)
• position_jitter(width, height)

p + geom_bar(position = position_dodge(width = 1))

Learn more here: ggplot2 bar plots.

Coordinate systems

p <- ggplot(mpg, aes(fl)) + geom_bar()

The coordinate systems in ggplot2 are:

1. Arguments for coord_cartesian(), coord_fixed() and coord_flip()
   • xlim: limits for the x axis
   • ylim: limits for the y axis
   • ratio: aspect ratio, expressed as y/x
   • …: Other arguments passed onto coord_cartesian
2. Arguments for coord_polar()
   • theta: variable to map angle to (x or y)
   • start: offset of starting point from 12 o’clock in radians
   • direction: 1, clockwise; -1, anticlockwise
3. Arguments for coord_trans()
   • x, y: transformers for x and y axes
   • limx, limy: limits for x and y axes.

p + coord_cartesian(ylim = c(0, 200))
p + coord_fixed(ratio = 1/50)
p + coord_flip()

p + coord_polar(theta = "x", direction = 1)
p + coord_trans(y = "sqrt")

Books

• ggplot2: The Elements for Elegant Data Visualization in R

• Cookbook for R

Blog posts

• Build a plot layer by layer

Cheat Sheets

• Data Visualization with ggplot2, RStudio cheat sheet
• Beautiful plotting in R: A ggplot2 cheatsheet

Calculate the mean of each group :

library(plyr)
mu <- ddply(df, "sex", summarise, grp.mean=mean(weight))
head(mu)

##   sex grp.mean
## 1   F    54.70
## 2   M    65.36

Change line colors

Density plot line colors can be automatically controlled by the levels of sex :

# Change density plot line colors by groups
ggplot(df, aes(x=weight, color=sex)) +
  geom_density()
# Add mean lines
p<-ggplot(df, aes(x=weight, color=sex)) +
  geom_density()+
  geom_vline(data=mu, aes(xintercept=grp.mean, color=sex),
             linetype="dashed")
p

It is also possible to change manually density plot line colors using the functions :

• scale_color_manual() : to use custom colors
• scale_color_brewer() : to use color palettes from RColorBrewer package
• scale_color_grey() : to use grey color palettes

# Use custom color palettes
p+scale_color_manual(values=c("#999999", "#E69F00", "#56B4E9"))
# Use brewer color palettes
p+scale_color_brewer(palette="Dark2")
# Use grey scale
p + scale_color_grey() + theme_classic()

Read more on ggplot2 colors here : ggplot2 colors

Change fill colors

Density plot fill colors can be automatically controlled by the levels of sex :

# Change density plot fill colors by groups
ggplot(df, aes(x=weight, fill=sex)) +
  geom_density()
# Use semi-transparent fill
p<-ggplot(df, aes(x=weight, fill=sex)) +
  geom_density(alpha=0.4)
p
# Add mean lines
p+geom_vline(data=mu, aes(xintercept=grp.mean, color=sex),
             linetype="dashed")

It is also possible to change manually density plot fill colors using the functions :

• scale_fill_manual() : to use custom colors
• scale_fill_brewer() : to use color palettes from RColorBrewer package
• scale_fill_grey() : to use grey color palettes

# Use custom color palettes
p+scale_fill_manual(values=c("#999999", "#E69F00", "#56B4E9"))
# use brewer color palettes
p+scale_fill_brewer(palette="Dark2")
# Use grey scale
p + scale_fill_grey() + theme_classic()

Read more on ggplot2 colors here : ggplot2 colors

Scatter plots with text annotations

We start by creating a simple scatter plot using a subset of the mtcars data set containing 15 rows.

1. Prepare some data:

# Take a subset of 15 random points
set.seed(1234)
ss <- sample(1:32, 15)
df <- mtcars[ss, ]

2. Create a scatter plot:

p <- ggplot(df, aes(wt, mpg)) +
  geom_point(color = 'red') +
  theme_classic(base_size = 10)

3. Add text labels:

# Add text annotations using ggplot2::geom_text
p + geom_text(aes(label = rownames(df)),
              size = 3.5)

# Use ggrepel::geom_text_repel
require("ggrepel")
set.seed(42)
p + geom_text_repel(aes(label = rownames(df)),
                    size = 3.5) 

# Use ggrepel::geom_label_repel and 
# Change color by groups
set.seed(42)
p + geom_label_repel(aes(label = rownames(df),
                    fill = factor(cyl)), color = 'white',
                    size = 3.5) +
   theme(legend.position = "bottom")

Volcano plot

genes <- read.table("https://gist.githubusercontent.com/stephenturner/806e31fce55a8b7175af/raw/1a507c4c3f9f1baaa3a69187223ff3d3050628d4/results.txt", header = TRUE)
genes$Significant <- ifelse(genes$padj < 0.05, "FDR < 0.05", "Not Sig")
ggplot(genes, aes(x = log2FoldChange, y = -log10(pvalue))) +
  geom_point(aes(color = Significant)) +
  scale_color_manual(values = c("red", "grey")) +
  theme_bw(base_size = 12) + theme(legend.position = "bottom") +
  geom_text_repel(
    data = subset(genes, padj < 0.05),
    aes(label = Gene),
    size = 5,
    box.padding = unit(0.35, "lines"),
    point.padding = unit(0.3, "lines")
  )

source

Import your data into R

1. Prepare your data as specified here: Best practices for preparing your data set for R

2. Save your data in an external .txt tab or .csv files

3. Import your data into R as follow:

# If .txt tab file, use this
my_data <- read.delim(file.choose())
# Or, if .csv file, use this
my_data <- read.csv(file.choose())

Here, we’ll use the built-in R data set named PlantGrowth. It contains the weight of plants obtained under a control and two different treatment conditions.

my_data <- PlantGrowth

Check your data

To have an idea of what the data look like, we use the the function sample_n()[in dplyr package]. The sample_n() function randomly picks a few of the observations in the data frame to print out:

# Show a random sample
set.seed(1234)
dplyr::sample_n(my_data, 10)

   weight group
19   4.32  trt1
18   4.89  trt1
29   5.80  trt2
24   5.50  trt2
17   6.03  trt1
1    4.17  ctrl
6    4.61  ctrl
16   3.83  trt1
12   4.17  trt1
15   5.87  trt1

In R terminology, the column “group” is called factor and the different categories (“ctr”, “trt1”, “trt2”) are named factor levels. The levels are ordered alphabetically.

# Show the levels
levels(my_data$group)

[1] "ctrl" "trt1" "trt2"

If the levels are not automatically in the correct order, re-order them as follow:

my_data$group <- ordered(my_data$group,
                         levels = c("ctrl", "trt1", "trt2"))

It’s possible to compute summary statistics (mean and sd) by groups using the dplyr package.

• Compute summary statistics by groups - count, mean, sd:

library(dplyr)
group_by(my_data, group) %>%
  summarise(
    count = n(),
    mean = mean(weight, na.rm = TRUE),
    sd = sd(weight, na.rm = TRUE)
  )

Source: local data frame [3 x 4]
   group count  mean        sd
  (fctr) (int) (dbl)     (dbl)
1   ctrl    10 5.032 0.5830914
2   trt1    10 4.661 0.7936757
3   trt2    10 5.526 0.4425733

Visualize your data

• To use R base graphs read this: R base graphs. Here, we’ll use the ggpubr R package for an easy ggplot2-based data visualization.

• Install the latest version of ggpubr from GitHub as follow (recommended):

# Install
if(!require(devtools)) install.packages("devtools")
devtools::install_github("kassambara/ggpubr")

• Or, install from CRAN as follow:

install.packages("ggpubr")

• Visualize your data with ggpubr:

# Box plots
# ++++++++++++++++++++
# Plot weight by group and color by group
library("ggpubr")
ggboxplot(my_data, x = "group", y = "weight", 
          color = "group", palette = c("#00AFBB", "#E7B800", "#FC4E07"),
          order = c("ctrl", "trt1", "trt2"),
          ylab = "Weight", xlab = "Treatment")

One-way ANOVA Test in R

# Mean plots
# ++++++++++++++++++++
# Plot weight by group
# Add error bars: mean_se
# (other values include: mean_sd, mean_ci, median_iqr, ....)
library("ggpubr")
ggline(my_data, x = "group", y = "weight", 
       add = c("mean_se", "jitter"), 
       order = c("ctrl", "trt1", "trt2"),
       ylab = "Weight", xlab = "Treatment")

One-way ANOVA Test in R

If you still want to use R base graphs, type the following scripts:

# Box plot
boxplot(weight ~ group, data = my_data,
        xlab = "Treatment", ylab = "Weight",
        frame = FALSE, col = c("#00AFBB", "#E7B800", "#FC4E07"))
# plotmeans
library("gplots")
plotmeans(weight ~ group, data = my_data, frame = FALSE,
          xlab = "Treatment", ylab = "Weight",
          main="Mean Plot with 95% CI") 

Compute one-way ANOVA test

We want to know if there is any significant difference between the average weights of plants in the 3 experimental conditions.

The R function aov() can be used to answer to this question. The function summary.aov() is used to summarize the analysis of variance model.

# Compute the analysis of variance
res.aov <- aov(weight ~ group, data = my_data)
# Summary of the analysis
summary(res.aov)

            Df Sum Sq Mean Sq F value Pr(>F)  
group        2  3.766  1.8832   4.846 0.0159 *
Residuals   27 10.492  0.3886                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The output includes the columns F value and Pr(>F) corresponding to the p-value of the test.

Interpret the result of one-way ANOVA tests

As the p-value is less than the significance level 0.05, we can conclude that there are significant differences between the groups highlighted with “*" in the model summary.

Multiple pairwise-comparison between the means of groups

In one-way ANOVA test, a significant p-value indicates that some of the group means are different, but we don’t know which pairs of groups are different.

It’s possible to perform multiple pairwise-comparison, to determine if the mean difference between specific pairs of group are statistically significant.

TukeyHSD(res.aov)

  Tukey multiple comparisons of means
    95% family-wise confidence level
Fit: aov(formula = weight ~ group, data = my_data)
$group
            diff        lwr       upr     p adj
trt1-ctrl -0.371 -1.0622161 0.3202161 0.3908711
trt2-ctrl  0.494 -0.1972161 1.1852161 0.1979960
trt2-trt1  0.865  0.1737839 1.5562161 0.0120064

glht(model, lincft)

library(multcomp)
summary(glht(res.aov, linfct = mcp(group = "Tukey")))

     Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: Tukey Contrasts
Fit: aov(formula = weight ~ group, data = my_data)
Linear Hypotheses:
                 Estimate Std. Error t value Pr(>|t|)  
trt1 - ctrl == 0  -0.3710     0.2788  -1.331    0.391  
trt2 - ctrl == 0   0.4940     0.2788   1.772    0.198  
trt2 - trt1 == 0   0.8650     0.2788   3.103    0.012 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Adjusted p values reported -- single-step method)

pairwise.t.test(my_data$weight, my_data$group,
                 p.adjust.method = "BH")

    Pairwise comparisons using t tests with pooled SD 
data:  my_data$weight and my_data$group 
     ctrl  trt1 
trt1 0.194 -    
trt2 0.132 0.013
P value adjustment method: BH 

Check ANOVA assumptions: test validity?

The ANOVA test assumes that, the data are normally distributed and the variance across groups are homogeneous. We can check that with some diagnostic plots.

Check the homogeneity of variance assumption

The residuals versus fits plot can be used to check the homogeneity of variances.

In the plot below, there is no evident relationships between residuals and fitted values (the mean of each groups), which is good. So, we can assume the homogeneity of variances.

# 1. Homogeneity of variances
plot(res.aov, 1)

One-way ANOVA Test in R

Points 17, 15, 4 are detected as outliers, which can severely affect normality and homogeneity of variance. It can be useful to remove outliers to meet the test assumptions.

It’s also possible to use Bartlett’s test or Levene’s test to check the homogeneity of variances.

We recommend Levene’s test, which is less sensitive to departures from normal distribution. The function leveneTest() [in car package] will be used:

library(car)
leveneTest(weight ~ group, data = my_data)

Levene's Test for Homogeneity of Variance (center = median)
      Df F value Pr(>F)
group  2  1.1192 0.3412
      27               

From the output above we can see that the p-value is not less than the significance level of 0.05. This means that there is no evidence to suggest that the variance across groups is statistically significantly different. Therefore, we can assume the homogeneity of variances in the different treatment groups.

oneway.test(weight ~ group, data = my_data)

pairwise.t.test(my_data$weight, my_data$group,
                 p.adjust.method = "BH", pool.sd = FALSE)

Check the normality assumption

Normality plot of residuals. In the plot below, the quantiles of the residuals are plotted against the quantiles of the normal distribution. A 45-degree reference line is also plotted.

The normal probability plot of residuals is used to check the assumption that the residuals are normally distributed. It should approximately follow a straight line.

# 2. Normality
plot(res.aov, 2)

One-way ANOVA Test in R

As all the points fall approximately along this reference line, we can assume normality.

The conclusion above, is supported by the Shapiro-Wilk test on the ANOVA residuals (W = 0.96, p = 0.6) which finds no indication that normality is violated.

# Extract the residuals
aov_residuals <- residuals(object = res.aov )
# Run Shapiro-Wilk test
shapiro.test(x = aov_residuals )

    Shapiro-Wilk normality test
data:  aov_residuals
W = 0.96607, p-value = 0.4379

Non-parametric alternative to one-way ANOVA test

Note that, a non-parametric alternative to one-way ANOVA is Kruskal-Wallis rank sum test, which can be used when ANNOVA assumptions are not met.

kruskal.test(weight ~ group, data = my_data)

    Kruskal-Wallis rank sum test
data:  weight by group
Kruskal-Wallis chi-squared = 7.9882, df = 2, p-value = 0.01842

What is independent t-test ?

Independent (or unpaired two sample) t-test is used to compare the means of two unrelated groups of samples.

As an example, we have a cohort of 100 individuals (50 women and 50 men). The question is to test whether the average weight of women is significantly different from that of men?

In this case, we have two independents groups of samples and unpaired t-test can be used to test whether the means are different.

Independent t-test formula

• Let A and B represent the two groups to compare.
• Let \(m_A\) and \(m_B\) represent the means of groups A and B, respectively.
• Let \(n_A\) and \(n_B\) represent the sizes of group A and B, respectively.

The t test statistic value to test whether the means are different can be calculated as follow :

\[ t = \frac{m_A - m_B}{\sqrt{ \frac{S^2}{n_A} + \frac{S^2}{n_B} }} \]

\(S^2\) is an estimator of the common variance of the two samples. It can be calculated as follow :

\[ S^2 = \frac{\sum{(x-m_A)^2}+\sum{(x-m_B)^2}}{n_A+n_B-2} \]

Once t-test statistic value is determined, you have to read in t-test table the critical value of Student’s t distribution corresponding to the significance level alpha of your choice (5%). The degrees of freedom (df) used in this test are :

\[ df = n_A + n_B -2 \]

If the absolute value of the t-test statistics (|t|) is greater than the critical value, then the difference is significant. Otherwise it isn’t. The level of significance or (p-value) corresponds to the risk indicated by the t-test table for the calculated |t| value.

The test can be used only when the two groups of samples (A and B) being compared follow bivariate normal distribution with equal variances.

If the variances of the two groups being compared are different, the Welch t test can be used.

What is paired t-test ?

Paired Student’s t-test is used to compare the means of two related samples. That is when you have two values (pair of values) for the same samples.

For example, 20 mice received a treatment X for 3 months. The question is to test whether the treatment X has an impact on the weight of the mice at the end of the 3 months treatment. The weight of the 20 mice has been measured before and after the treatment. This gives us 20 sets of values before treatment and 20 sets of values after treatment from measuring twice the weight of the same mice.

In this case, paired t-test can be used as the two sets of values being compared are related. We have a pair of values for each mouse (one before and the other after treatment).

Paired t-test formula

To compare the means of the two paired sets of data, the differences between all pairs must be, first, calculated.

Let d represents the differences between all pairs. The average of the difference d is compared to 0. If there is any significant difference between the two pairs of samples, then the mean of d is expected to be far from 0.

t test statistisc value can be calculated as follow :

\[ t = \frac{m}{s/\sqrt{n}} \]

m and s are the mean and the standard deviation of the difference (d), respectively. n is the size of d.

Once t value is determined, you have to read in t-test table the critical value of Student’s t distribution corresponding to the significance level alpha of your choice (5%). The degrees of freedom (df) used in this test are :

\[ df = n - 1 \]

If the absolute value of the t-test statistics (|t|) is greater than the critical value, then the difference is significant. Otherwise it isn’t. The level of significance or (p-value) corresponds to the risk indicated by the t-test table for the calculated |t| value.

The test can be used only when the difference d is normally distributed.

Case of large sample sizes

If the sample size is large enough (n > 30), we can ignore the distribution of the data and use parametric tests.

The central limit theorem tells us that no matter what distribution things have, the sampling distribution tends to be normal if the sample is large enough (n > 30).

However, to be consistent, normality can be checked by visual inspection [normal plots (histogram), Q-Q plot (quantile-quantile plot)] or by significance tests].

Visual methods

Density plot and Q-Q plot can be used to check normality visually.

1. Density plot: the density plot provides a visual judgment about whether the distribution is bell shaped.

library("ggpubr")
ggdensity(my_data$len, 
          main = "Density plot of tooth length",
          xlab = "Tooth length")

2. Q-Q plot: Q-Q plot (or quantile-quantile plot) draws the correlation between a given sample and the normal distribution. A 45-degree reference line is also plotted.

library(ggpubr)
ggqqplot(my_data$len)

It’s also possible to use the function qqPlot() [in car package]:

library("car")
qqPlot(my_data$len)

As all the points fall approximately along this reference line, we can assume normality.

Normality test

Visual inspection, described in the previous section, is usually unreliable. It’s possible to use a significance test comparing the sample distribution to a normal one in order to ascertain whether data show or not a serious deviation from normality.

There are several methods for normality test such as Kolmogorov-Smirnov (K-S) normality test and Shapiro-Wilk’s test.

The null hypothesis of these tests is that “sample distribution is normal”. If the test is significant, the distribution is non-normal.

Shapiro-Wilk’s method is widely recommended for normality test and it provides better power than K-S. It is based on the correlation between the data and the corresponding normal scores.

Note that, normality test is sensitive to sample size. Small samples most often pass normality tests. Therefore, it’s important to combine visual inspection and significance test in order to take the right decision.

The R function shapiro.test() can be used to perform the Shapiro-Wilk test of normality for one variable (univariate):

shapiro.test(my_data$len)

    Shapiro-Wilk normality test
data:  my_data$len
W = 0.96743, p-value = 0.1091

From the output, the p-value > 0.05 implying that the distribution of the data are not significantly different from normal distribution. In other words, we can assume the normality.

Import your data into R

1. Prepare your data as specified here: Best practices for preparing your data set for R

2. Save your data in an external .txt tab or .csv files

3. Import your data into R as follow:

# If .txt tab file, use this
my_data <- read.delim(file.choose())
# Or, if .csv file, use this
my_data <- read.csv(file.choose())

Here, we’ll use the built-in R data set named ToothGrowth. It contains data from a study evaluating the effect of vitamin C on tooth growth in Guinea pigs. The experiment has been performed on 60 pigs, where each animal received one of three dose levels of vitamin C (0.5, 1, and 2 mg/day) by one of two delivery methods, (orange juice or ascorbic acid (a form of vitamin C and coded as VC). Tooth length was measured and a sample of the data is shown below.

# Store the data in the variable my_data
my_data <- ToothGrowth

Check your data

To get an idea of what the data look like, we display a random sample of the data using the function sample_n()[in dplyr package]. First, install dplyr if you don’t have it:

install.packages("dplyr")

# Show a random sample
set.seed(1234)
dplyr::sample_n(my_data, 10)

    len supp dose
38  9.4   OJ  0.5
36 10.0   OJ  0.5
37  8.2   OJ  0.5
50 27.3   OJ  1.0
59 29.4   OJ  2.0
1   4.2   VC  0.5
13 15.2   VC  1.0
56 30.9   OJ  2.0
27 26.7   VC  2.0
53 22.4   OJ  2.0

# Check the structure
str(my_data)

'data.frame':   60 obs. of  3 variables:
 $ len : num  4.2 11.5 7.3 5.8 6.4 10 11.2 11.2 5.2 7 ...
 $ supp: Factor w/ 2 levels "OJ","VC": 2 2 2 2 2 2 2 2 2 2 ...
 $ dose: num  0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ...

From the output above, R considers “dose” as a numeric variable. We’ll convert it as a factor variable (i.e., grouping variable) as follow.

# Convert dose as a factor and recode the levels
# as "D0.5", "D1", "D2"
my_data$dose <- factor(my_data$dose, 
                  levels = c(0.5, 1, 2),
                  labels = c("D0.5", "D1", "D2"))
head(my_data)

   len supp dose
1  4.2   VC D0.5
2 11.5   VC D0.5
3  7.3   VC D0.5
4  5.8   VC D0.5
5  6.4   VC D0.5
6 10.0   VC D0.5

Question: We want to know if tooth length depends on supp and dose.

• Generate frequency tables:

table(my_data$supp, my_data$dose)

    
     D0.5 D1 D2
  OJ   10 10 10
  VC   10 10 10

We have 2X3 design cells with the factors being supp and dose and 10 subjects in each cell. Here, we have a balanced design. In the next sections I’ll describe how to analyse data from balanced designs, since this is the simplest case.

Visualize your data

Box plots and line plots can be used to visualize group differences:

• Box plot to plot the data grouped by the combinations of the levels of the two factors.

• Two-way interaction plot, which plots the mean (or other summary) of the response for two-way combinations of factors, thereby illustrating possible interactions.

• To use R base graphs read this: R base graphs. Here, we’ll use the ggpubr R package for an easy ggplot2-based data visualization.

• Install the latest version of ggpubr from GitHub as follow (recommended):

# Install
if(!require(devtools)) install.packages("devtools")
devtools::install_github("kassambara/ggpubr")

• Or, install from CRAN as follow:

install.packages("ggpubr")

• Visualize your data with ggpubr:

# Box plot with multiple groups
# +++++++++++++++++++++
# Plot tooth length ("len") by groups ("dose")
# Color box plot by a second group: "supp"
library("ggpubr")
ggboxplot(my_data, x = "dose", y = "len", color = "supp",
          palette = c("#00AFBB", "#E7B800"))

Two-Way ANOVA Test in R

# Line plots with multiple groups
# +++++++++++++++++++++++
# Plot tooth length ("len") by groups ("dose")
# Color box plot by a second group: "supp"
# Add error bars: mean_se
# (other values include: mean_sd, mean_ci, median_iqr, ....)
library("ggpubr")
ggline(my_data, x = "dose", y = "len", color = "supp",
       add = c("mean_se", "dotplot"),
       palette = c("#00AFBB", "#E7B800"))

Two-Way ANOVA Test in R

If you still want to use R base graphs, type the following scripts:

# Box plot with two factor variables
boxplot(len ~ supp * dose, data=my_data, frame = FALSE, 
        col = c("#00AFBB", "#E7B800"), ylab="Tooth Length")
# Two-way interaction plot
interaction.plot(x.factor = my_data$dose, trace.factor = my_data$supp, 
                 response = my_data$len, fun = mean, 
                 type = "b", legend = TRUE, 
                 xlab = "Dose", ylab="Tooth Length",
                 pch=c(1,19), col = c("#00AFBB", "#E7B800"))

Arguments used for the function interaction.plot():

Compute two-way ANOVA test

We want to know if tooth length depends on supp and dose.

The R function aov() can be used to answer this question. The function summary.aov() is used to summarize the analysis of variance model.

res.aov2 <- aov(len ~ supp + dose, data = my_data)
summary(res.aov2)

            Df Sum Sq Mean Sq F value   Pr(>F)    
supp         1  205.4   205.4   14.02 0.000429 ***
dose         2 2426.4  1213.2   82.81  < 2e-16 ***
Residuals   56  820.4    14.7                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The output includes the columns F value and Pr(>F) corresponding to the p-value of the test.

From the ANOVA table we can conclude that both supp and dose are statistically significant. dose is the most significant factor variable. These results would lead us to believe that changing delivery methods (supp) or the dose of vitamin C, will impact significantly the mean tooth length.

Not the above fitted model is called additive model. It makes an assumption that the two factor variables are independent. If you think that these two variables might interact to create an synergistic effect, replace the plus symbol (+) by an asterisk (*), as follow.

# Two-way ANOVA with interaction effect
# These two calls are equivalent
res.aov3 <- aov(len ~ supp * dose, data = my_data)
res.aov3 <- aov(len ~ supp + dose + supp:dose, data = my_data)
summary(res.aov3)

            Df Sum Sq Mean Sq F value   Pr(>F)    
supp         1  205.4   205.4  15.572 0.000231 ***
dose         2 2426.4  1213.2  92.000  < 2e-16 ***
supp:dose    2  108.3    54.2   4.107 0.021860 *  
Residuals   54  712.1    13.2                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

It can be seen that the two main effects (supp and dose) are statistically significant, as well as their interaction.

Note that, in the situation where the interaction is not significant you should use the additive model.

Interpret the results

From the ANOVA results, you can conclude the following, based on the p-values and a significance level of 0.05:

• the p-value of supp is 0.000429 (significant), which indicates that the levels of supp are associated with significant different tooth length.
• the p-value of dose is < 2e-16 (significant), which indicates that the levels of dose are associated with significant different tooth length.
• the p-value for the interaction between supp*dose is 0.02 (significant), which indicates that the relationships between dose and tooth length depends on the supp method.

Compute some summary statistics

• Compute mean and SD by groups using dplyr R package:

require("dplyr")
group_by(my_data, supp, dose) %>%
  summarise(
    count = n(),
    mean = mean(len, na.rm = TRUE),
    sd = sd(len, na.rm = TRUE)
  )

Source: local data frame [6 x 5]
Groups: supp [?]
    supp   dose count  mean       sd
  (fctr) (fctr) (int) (dbl)    (dbl)
1     OJ   D0.5    10 13.23 4.459709
2     OJ     D1    10 22.70 3.910953
3     OJ     D2    10 26.06 2.655058
4     VC   D0.5    10  7.98 2.746634
5     VC     D1    10 16.77 2.515309
6     VC     D2    10 26.14 4.797731

• It’s also possible to use the function model.tables() as follow:

model.tables(res.aov3, type="means", se = TRUE)

Multiple pairwise-comparison between the means of groups

In ANOVA test, a significant p-value indicates that some of the group means are different, but we don’t know which pairs of groups are different.

It’s possible to perform multiple pairwise-comparison, to determine if the mean difference between specific pairs of group are statistically significant.

TukeyHSD(res.aov3, which = "dose")

  Tukey multiple comparisons of means
    95% family-wise confidence level
Fit: aov(formula = len ~ supp + dose + supp:dose, data = my_data)
$dose
          diff       lwr       upr   p adj
D1-D0.5  9.130  6.362488 11.897512 0.0e+00
D2-D0.5 15.495 12.727488 18.262512 0.0e+00
D2-D1    6.365  3.597488  9.132512 2.7e-06

glht(model, lincft)

library(multcomp)
summary(glht(res.aov2, linfct = mcp(dose = "Tukey")))

     Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: Tukey Contrasts
Fit: aov(formula = len ~ supp + dose, data = my_data)
Linear Hypotheses:
               Estimate Std. Error t value Pr(>|t|)    
D1 - D0.5 == 0    9.130      1.210   7.543   <1e-05 ***
D2 - D0.5 == 0   15.495      1.210  12.802   <1e-05 ***
D2 - D1 == 0      6.365      1.210   5.259   <1e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Adjusted p values reported -- single-step method)

pairwise.t.test(my_data$len, my_data$dose,
                p.adjust.method = "BH")

    Pairwise comparisons using t tests with pooled SD 
data:  my_data$len and my_data$dose 
   D0.5    D1     
D1 1.0e-08 -      
D2 4.4e-16 1.4e-05
P value adjustment method: BH 

Check ANOVA assumptions: test validity?

ANOVA assumes that the data are normally distributed and the variance across groups are homogeneous. We can check that with some diagnostic plots.

Check the homogeneity of variance assumption

The residuals versus fits plot is used to check the homogeneity of variances. In the plot below, there is no evident relationships between residuals and fitted values (the mean of each groups), which is good. So, we can assume the homogeneity of variances.

# 1. Homogeneity of variances
plot(res.aov3, 1)

Two-Way ANOVA Test in R

Points 32 and 23 are detected as outliers, which can severely affect normality and homogeneity of variance. It can be useful to remove outliers to meet the test assumptions.

Use the Levene’s test to check the homogeneity of variances. The function leveneTest() [in car package] will be used:

library(car)
leveneTest(len ~ supp*dose, data = my_data)

Levene's Test for Homogeneity of Variance (center = median)
      Df F value Pr(>F)
group  5  1.7086 0.1484
      54               

From the output above we can see that the p-value is not less than the significance level of 0.05. This means that there is no evidence to suggest that the variance across groups is statistically significantly different. Therefore, we can assume the homogeneity of variances in the different treatment groups.

Check the normality assumpttion

Normality plot of the residuals. In the plot below, the quantiles of the residuals are plotted against the quantiles of the normal distribution. A 45-degree reference line is also plotted.

The normal probability plot of residuals is used to verify the assumption that the residuals are normally distributed.

The normal probability plot of the residuals should approximately follow a straight line.

# 2. Normality
plot(res.aov3, 2)

Two-Way ANOVA Test in R

As all the points fall approximately along this reference line, we can assume normality.

The conclusion above, is supported by the Shapiro-Wilk test on the ANOVA residuals (W = 0.98, p = 0.5) which finds no indication that normality is violated.

# Extract the residuals
aov_residuals <- residuals(object = res.aov3)
# Run Shapiro-Wilk test
shapiro.test(x = aov_residuals )

    Shapiro-Wilk normality test
data:  aov_residuals
W = 0.98499, p-value = 0.6694

R function to compute paired t-test

To perform paired samples t-test comparing the means of two paired samples (x & y), the R function t.test() can be used as follow:

t.test(x, y, paired = TRUE, alternative = "two.sided")

Import your data into R

1. Prepare your data as specified here: Best practices for preparing your data set for R

2. Save your data in an external .txt tab or .csv files

3. Import your data into R as follow:

# If .txt tab file, use this
my_data <- read.delim(file.choose())
# Or, if .csv file, use this
my_data <- read.csv(file.choose())

Here, we’ll use an example data set, which contains the weight of 10 mice before and after the treatment.

# Data in two numeric vectors
# ++++++++++++++++++++++++++
# Weight of the mice before treatment
before <-c(200.1, 190.9, 192.7, 213, 241.4, 196.9, 172.2, 185.5, 205.2, 193.7)
# Weight of the mice after treatment
after <-c(392.9, 393.2, 345.1, 393, 434, 427.9, 422, 383.9, 392.3, 352.2)
# Create a data frame
my_data <- data.frame( 
                group = rep(c("before", "after"), each = 10),
                weight = c(before,  after)
                )

We want to know, if there is any significant difference in the mean weights after treatment?

Check your data

# Print all data
print(my_data)

    group weight
1  before  200.1
2  before  190.9
3  before  192.7
4  before  213.0
5  before  241.4
6  before  196.9
7  before  172.2
8  before  185.5
9  before  205.2
10 before  193.7
11  after  392.9
12  after  393.2
13  after  345.1
14  after  393.0
15  after  434.0
16  after  427.9
17  after  422.0
18  after  383.9
19  after  392.3
20  after  352.2

Compute summary statistics (mean and sd) by groups using the dplyr package.

• To install dplyr package, type this:

install.packages("dplyr")

• Compute summary statistics by groups:

library("dplyr")
group_by(my_data, group) %>%
  summarise(
    count = n(),
    mean = mean(weight, na.rm = TRUE),
    sd = sd(weight, na.rm = TRUE)
  )

Source: local data frame [2 x 4]
   group count   mean       sd
  (fctr) (int)  (dbl)    (dbl)
1  after    10 393.65 29.39801
2 before    10 199.16 18.47354

Visualize your data using box plots

To use R base graphs read this: R base graphs. Here, we’ll use the ggpubr R package for an easy ggplot2-based data visualization.

• Install the latest version of ggpubr from GitHub as follow (recommended):

# Install
if(!require(devtools)) install.packages("devtools")
devtools::install_github("kassambara/ggpubr")

• Or, install from CRAN as follow:

install.packages("ggpubr")

• Visualize your data:

# Plot weight by group and color by group
library("ggpubr")
ggboxplot(my_data, x = "group", y = "weight", 
          color = "group", palette = c("#00AFBB", "#E7B800"),
          order = c("before", "after"),
          ylab = "Weight", xlab = "Groups")

Paired Samples T-test in R

Box plots show you the increase, but lose the paired information. You can use the function plot.paired() [in pairedData package] to plot paired data (“before - after” plot).

• Install pairedData package:

install.packages("PairedData")

• Plot paired data:

# Subset weight data before treatment
before <- subset(my_data,  group == "before", weight,
                 drop = TRUE)
# subset weight data after treatment
after <- subset(my_data,  group == "after", weight,
                 drop = TRUE)
# Plot paired data
library(PairedData)
pd <- paired(before, after)
plot(pd, type = "profile") + theme_bw()

Paired Samples T-test in R

Preleminary test to check paired t-test assumptions

Assumption 1: Are the two samples paired?

Yes, since the data have been collected from measuring twice the weight of the same mice.

Assumption 2: Is this a large sample?

No, because n < 30. Since the sample size is not large enough (less than 30), we need to check whether the differences of the pairs follow a normal distribution.

How to check the normality?

Use Shapiro-Wilk normality test as described at: Normality Test in R.

• Null hypothesis: the data are normally distributed
• Alternative hypothesis: the data are not normally distributed

# compute the difference
d <- with(my_data, 
        weight[group == "before"] - weight[group == "after"])
# Shapiro-Wilk normality test for the differences
shapiro.test(d) # => p-value = 0.6141

From the output, the p-value is greater than the significance level 0.05 implying that the distribution of the differences (d) are not significantly different from normal distribution. In other words, we can assume the normality.

Note that, if the data are not normally distributed, it’s recommended to use the non parametric paired two-samples Wilcoxon test.

Compute paired samples t-test

Question : Is there any significant changes in the weights of mice after treatment?

1) Compute paired t-test - Method 1: The data are saved in two different numeric vectors.

# Compute t-test
res <- t.test(before, after, paired = TRUE)
res

    Paired t-test
data:  before and after
t = -20.883, df = 9, p-value = 6.2e-09
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -215.5581 -173.4219
sample estimates:
mean of the differences 
                -194.49 

2) Compute paired t-test - Method 2: The data are saved in a data frame.

# Compute t-test
res <- t.test(weight ~ group, data = my_data, paired = TRUE)
res

    Paired t-test
data:  weight by group
t = 20.883, df = 9, p-value = 6.2e-09
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 173.4219 215.5581
sample estimates:
mean of the differences 
                 194.49 

As you can see, the two methods give the same results.

t.test(weight ~ group, data = my_data, paired = TRUE,
        alternative = "less")

t.test(weight ~ group, data = my_data, paired = TRUE,
       alternative = "greater")

Interpretation of the result

The p-value of the test is 6.210^{-9}, which is less than the significance level alpha = 0.05. We can then reject null hypothesis and conclude that the average weight of the mice before treatment is significantly different from the average weight after treatment with a p-value = 6.210^{-9}.

Access to the values returned by t.test() function

The result of t.test() function is a list containing the following components:

The format of the R code to use for getting these values is as follow:

# printing the p-value
res$p.value

[1] 6.200298e-09

# printing the mean
res$estimate

mean of the differences 
                 194.49 

# printing the confidence interval
res$conf.int

[1] 173.4219 215.5581
attr(,"conf.level")
[1] 0.95

Install ggpubr R package for data visualization

You can draw R base graps as described at this link: R base graphs. Here, we’ll use the ggpubr R package for an easy ggplot2-based data visualization

• Install the latest version from GitHub as follow (recommended):

# Install
if(!require(devtools)) install.packages("devtools")
devtools::install_github("kassambara/ggpubr")

• Or, install from CRAN as follow:

install.packages("ggpubr")

R function to compute one-sample t-test

To perform one-sample t-test, the R function t.test() can be used as follow:

t.test(x, mu = 0, alternative = "two.sided")

Import your data into R

1. Prepare your data as specified here: Best practices for preparing your data set for R

2. Save your data in an external .txt tab or .csv files

3. Import your data into R as follow:

# If .txt tab file, use this
my_data <- read.delim(file.choose())
# Or, if .csv file, use this
my_data <- read.csv(file.choose())

Here, we’ll use an example data set containing the weight of 10 mice.

We want to know, if the average weight of the mice differs from 25g?

set.seed(1234)
my_data <- data.frame(
  name = paste0(rep("M_", 10), 1:10),
  weight = round(rnorm(10, 20, 2), 1)
)

Check your data

# Print the first 10 rows of the data
head(my_data, 10)

   name weight
1   M_1   17.6
2   M_2   20.6
3   M_3   22.2
4   M_4   15.3
5   M_5   20.9
6   M_6   21.0
7   M_7   18.9
8   M_8   18.9
9   M_9   18.9
10 M_10   18.2

# Statistical summaries of weight
summary(my_data$weight)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  15.30   18.38   18.90   19.25   20.82   22.20 

• Min.: the minimum value
• 1st Qu.: The first quartile. 25% of values are lower than this.
• Median: the median value. Half the values are lower; half are higher.
• 3rd Qu.: the third quartile. 75% of values are higher than this.
• Max.: the maximum value

Visualize your data using box plots

library(ggpubr)
ggboxplot(my_data$weight, 
          ylab = "Weight (g)", xlab = FALSE,
          ggtheme = theme_minimal())

One-Sample Student’s T-test in R

Preleminary test to check one-sample t-test assumptions

1. Is this a large sample? - No, because n < 30.
2. Since the sample size is not large enough (less than 30, central limit theorem), we need to check whether the data follow a normal distribution.

How to check the normality?

Read this article: Normality Test in R.

Briefly, it’s possible to use the Shapiro-Wilk normality test and to look at the normality plot.

1. Shapiro-Wilk test:
   • Null hypothesis: the data are normally distributed
   • Alternative hypothesis: the data are not normally distributed

shapiro.test(my_data$weight) # => p-value = 0.6993

From the output, the p-value is greater than the significance level 0.05 implying that the distribution of the data are not significantly different from normal distribtion. In other words, we can assume the normality.

• Visual inspection of the data normality using Q-Q plots (quantile-quantile plots). Q-Q plot draws the correlation between a given sample and the normal distribution.

library("ggpubr")
ggqqplot(my_data$weight, ylab = "Men's weight",
         ggtheme = theme_minimal())

One-Sample Student’s T-test in R

From the normality plots, we conclude that the data may come from normal distributions.

Note that, if the data are not normally distributed, it’s recommended to use the non parametric one-sample Wilcoxon rank test.

Compute one-sample t-test

We want to know, if the average weight of the mice differs from 25g (two-tailed test)?

# One-sample t-test
res <- t.test(my_data$weight, mu = 25)
# Printing the results
res 

    One Sample t-test
data:  my_data$weight
t = -9.0783, df = 9, p-value = 7.953e-06
alternative hypothesis: true mean is not equal to 25
95 percent confidence interval:
 17.8172 20.6828
sample estimates:
mean of x 
    19.25 

t.test(my_data$weight, mu = 25,
              alternative = "less")

t.test(my_data$weight, mu = 25,
              alternative = "greater")

Interpretation of the result

The p-value of the test is 7.95310^{-6}, which is less than the significance level alpha = 0.05. We can conclude that the mean weight of the mice is significantly different from 25g with a p-value = 7.95310^{-6}.

Access to the values returned by t.test() function

The result of t.test() function is a list containing the following components:

The format of the R code to use for getting these values is as follow:

# printing the p-value
res$p.value

[1] 7.953383e-06

# printing the mean
res$estimate

mean of x 
    19.25 

# printing the confidence interval
res$conf.int

[1] 17.8172 20.6828
attr(,"conf.level")
[1] 0.95

Install ggpubr R package for data visualization

You can draw R base graphs as described at this link: R base graphs. Here, we’ll use the ggpubr R package for an easy ggplot2-based data visualization

• Install the latest version from GitHub as follow (recommended):

# Install
if(!require(devtools)) install.packages("devtools")
devtools::install_github("kassambara/ggpubr")

• Or, install from CRAN as follow:

install.packages("ggpubr")

R function to compute one-sample Wilcoxon test

To perform one-sample Wilcoxon-test, the R function wilcox.test() can be used as follow:

wilcox.test(x, mu = 0, alternative = "two.sided")

Import your data into R

1. Prepare your data as specified here: Best practices for preparing your data set for R

2. Save your data in an external .txt tab or .csv files

3. Import your data into R as follow:

# If .txt tab file, use this
my_data <- read.delim(file.choose())
# Or, if .csv file, use this
my_data <- read.csv(file.choose())

Here, we’ll use an example data set containing the weight of 10 mice.

We want to know, if the median weight of the mice differs from 25g?

set.seed(1234)
my_data <- data.frame(
  name = paste0(rep("M_", 10), 1:10),
  weight = round(rnorm(10, 20, 2), 1)
)

Check your data

# Print the first 10 rows of the data
head(my_data, 10)

   name weight
1   M_1   17.6
2   M_2   20.6
3   M_3   22.2
4   M_4   15.3
5   M_5   20.9
6   M_6   21.0
7   M_7   18.9
8   M_8   18.9
9   M_9   18.9
10 M_10   18.2

# Statistical summaries of weight
summary(my_data$weight)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  15.30   18.38   18.90   19.25   20.82   22.20 

• Min.: the minimum value
• 1st Qu.: The first quartile. 25% of values are lower than this.
• Median: the median value. Half the values are lower; half are higher.
• 3rd Qu.: the third quartile. 75% of values are higher than this.
• Max.: the maximum value

Visualize your data using box plots

library(ggpubr)
ggboxplot(my_data$weight, 
          ylab = "Weight (g)", xlab = FALSE,
          ggtheme = theme_minimal())

One-Sample Wilcoxon Signed Rank Test in R

Compute one-sample Wilcoxon test

We want to know, if the average weight of the mice differs from 25g (two-tailed test)?

# One-sample wilcoxon test
res <- wilcox.test(my_data$weight, mu = 25)
# Printing the results
res 

    Wilcoxon signed rank test with continuity correction
data:  my_data$weight
V = 0, p-value = 0.005793
alternative hypothesis: true location is not equal to 25

# print only the p-value
res$p.value

[1] 0.005793045

The p-value of the test is 0.005793, which is less than the significance level alpha = 0.05. We can reject the null hypothesis and conclude that the average weight of the mice is significantly different from 25g with a p-value = 0.005793.

wilcox.test(my_data$weight, mu = 25,
              alternative = "less")

wilcox.test(my_data$weight, mu = 25,
              alternative = "greater")

Install ggpubr R package for data visualization

You can draw R base graphs as described at this link: R base graphs. Here, we’ll use the ggpubr R package for an easy ggplot2-based data visualization

• Install the latest version from GitHub as follow (recommended):

# Install
if(!require(devtools)) install.packages("devtools")
devtools::install_github("kassambara/ggpubr")

• Or, install from CRAN as follow:

install.packages("ggpubr")

R function to compute unpaired two-samples t-test

To perform two-samples t-test comparing the means of two independent samples (x & y), the R function t.test() can be used as follow:

t.test(x, y, alternative = "two.sided", var.equal = FALSE)

Import your data into R

1. Prepare your data as specified here: Best practices for preparing your data set for R

2. Save your data in an external .txt tab or .csv files

3. Import your data into R as follow:

# If .txt tab file, use this
my_data <- read.delim(file.choose())
# Or, if .csv file, use this
my_data <- read.csv(file.choose())

Here, we’ll use an example data set, which contains the weight of 18 individuals (9 women and 9 men):

# Data in two numeric vectors
women_weight <- c(38.9, 61.2, 73.3, 21.8, 63.4, 64.6, 48.4, 48.8, 48.5)
men_weight <- c(67.8, 60, 63.4, 76, 89.4, 73.3, 67.3, 61.3, 62.4) 
# Create a data frame
my_data <- data.frame( 
                group = rep(c("Woman", "Man"), each = 9),
                weight = c(women_weight,  men_weight)
                )

We want to know, if the average women’s weight differs from the average men’s weight?

Check your data

# Print all data
print(my_data)

   group weight
1  Woman   38.9
2  Woman   61.2
3  Woman   73.3
4  Woman   21.8
5  Woman   63.4
6  Woman   64.6
7  Woman   48.4
8  Woman   48.8
9  Woman   48.5
10   Man   67.8
11   Man   60.0
12   Man   63.4
13   Man   76.0
14   Man   89.4
15   Man   73.3
16   Man   67.3
17   Man   61.3
18   Man   62.4

It’s possible to compute summary statistics (mean and sd) by groups. The dplyr package can be used.

• To install dplyr package, type this:

install.packages("dplyr")

• Compute summary statistics by groups:

library(dplyr)
group_by(my_data, group) %>%
  summarise(
    count = n(),
    mean = mean(weight, na.rm = TRUE),
    sd = sd(weight, na.rm = TRUE)
  )

Source: local data frame [2 x 4]
   group count     mean        sd
  (fctr) (int)    (dbl)     (dbl)
1    Man     9 68.98889  9.375426
2  Woman     9 52.10000 15.596714

Visualize your data using box plots

# Plot weight by group and color by group
library("ggpubr")
ggboxplot(my_data, x = "group", y = "weight", 
          color = "group", palette = c("#00AFBB", "#E7B800"),
        ylab = "Weight", xlab = "Groups")

Unpaired Two-Samples Student’s T-test in R

Preleminary test to check independent t-test assumptions

Assumption 1: Are the two samples independents?

Yes, since the samples from men and women are not related.

Assumtion 2: Are the data from each of the 2 groups follow a normal distribution?

Use Shapiro-Wilk normality test as described at: Normality Test in R. - Null hypothesis: the data are normally distributed - Alternative hypothesis: the data are not normally distributed

We’ll use the functions with() and shapiro.test() to compute Shapiro-Wilk test for each group of samples.

# Shapiro-Wilk normality test for Men's weights
with(my_data, shapiro.test(weight[group == "Man"]))# p = 0.1
# Shapiro-Wilk normality test for Women's weights
with(my_data, shapiro.test(weight[group == "Woman"])) # p = 0.6

From the output, the two p-values are greater than the significance level 0.05 implying that the distribution of the data are not significantly different from the normal distribution. In other words, we can assume the normality.

Note that, if the data are not normally distributed, it’s recommended to use the non parametric two-samples Wilcoxon rank test.

Assumption 3. Do the two populations have the same variances?

We’ll use F-test to test for homogeneity in variances. This can be performed with the function var.test() as follow:

res.ftest <- var.test(weight ~ group, data = my_data)
res.ftest

    F test to compare two variances
data:  weight by group
F = 0.36134, num df = 8, denom df = 8, p-value = 0.1714
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.08150656 1.60191315
sample estimates:
ratio of variances 
         0.3613398 

The p-value of F-test is p = 0.1713596. It’s greater than the significance level alpha = 0.05. In conclusion, there is no significant difference between the variances of the two sets of data. Therefore, we can use the classic t-test witch assume equality of the two variances.

Compute unpaired two-samples t-test

Question : Is there any significant difference between women and men weights?

1) Compute independent t-test - Method 1: The data are saved in two different numeric vectors.

# Compute t-test
res <- t.test(women_weight, men_weight, var.equal = TRUE)
res

    Two Sample t-test
data:  women_weight and men_weight
t = -2.7842, df = 16, p-value = 0.01327
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -29.748019  -4.029759
sample estimates:
mean of x mean of y 
 52.10000  68.98889 

2) Compute independent t-test - Method 2: The data are saved in a data frame.

# Compute t-test
res <- t.test(weight ~ group, data = my_data, var.equal = TRUE)
res

    Two Sample t-test
data:  weight by group
t = 2.7842, df = 16, p-value = 0.01327
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
  4.029759 29.748019
sample estimates:
  mean in group Man mean in group Woman 
           68.98889            52.10000 

As you can see, the two methods give the same results.

t.test(weight ~ group, data = my_data,
        var.equal = TRUE, alternative = "less")

t.test(weight ~ group, data = my_data,
        var.equal = TRUE, alternative = "greater")

Interpretation of the result

The p-value of the test is 0.01327, which is less than the significance level alpha = 0.05. We can conclude that men’s average weight is significantly different from women’s average weight with a p-value = 0.01327.

Access to the values returned by t.test() function

The result of t.test() function is a list containing the following components:

The format of the R code to use for getting these values is as follow:

# printing the p-value
res$p.value

[1] 0.0132656

# printing the mean
res$estimate

  mean in group Man mean in group Woman 
           68.98889            52.10000 

# printing the confidence interval
res$conf.int

[1]  4.029759 29.748019
attr(,"conf.level")
[1] 0.95

R function to compute Wilcoxon test

To perform two-samples Wilcoxon test comparing the means of two independent samples (x & y), the R function wilcox.test() can be used as follow:

wilcox.test(x, y, alternative = "two.sided")

Import your data into R

1. Prepare your data as specified here: Best practices for preparing your data set for R

2. Save your data in an external .txt tab or .csv files

3. Import your data into R as follow:

# If .txt tab file, use this
my_data <- read.delim(file.choose())
# Or, if .csv file, use this
my_data <- read.csv(file.choose())

Here, we’ll use an example data set, which contains the weight of 18 individuals (9 women and 9 men):

# Data in two numeric vectors
women_weight <- c(38.9, 61.2, 73.3, 21.8, 63.4, 64.6, 48.4, 48.8, 48.5)
men_weight <- c(67.8, 60, 63.4, 76, 89.4, 73.3, 67.3, 61.3, 62.4) 
# Create a data frame
my_data <- data.frame( 
                group = rep(c("Woman", "Man"), each = 9),
                weight = c(women_weight,  men_weight)
                )

We want to know, if the median women’s weight differs from the median men’s weight?

Check your data

print(my_data)

   group weight
1  Woman   38.9
2  Woman   61.2
3  Woman   73.3
4  Woman   21.8
5  Woman   63.4
6  Woman   64.6
7  Woman   48.4
8  Woman   48.8
9  Woman   48.5
10   Man   67.8
11   Man   60.0
12   Man   63.4
13   Man   76.0
14   Man   89.4
15   Man   73.3
16   Man   67.3
17   Man   61.3
18   Man   62.4

It’s possible to compute summary statistics (median and interquartile range (IQR)) by groups. The dplyr package can be used.

• To install dplyr package, type this:

install.packages("dplyr")

• Compute summary statistics by groups:

library(dplyr)
group_by(my_data, group) %>%
  summarise(
    count = n(),
    median = median(weight, na.rm = TRUE),
    IQR = IQR(weight, na.rm = TRUE)
  )

Source: local data frame [2 x 4]
   group count median   IQR
  (fctr) (int)  (dbl) (dbl)
1    Man     9   67.3  10.9
2  Woman     9   48.8  15.0

Visualize your data using box plots

You can draw R base graphs as described at this link: R base graphs. Here, we’ll use the ggpubr R package for an easy ggplot2-based data visualization

• Install the latest version of ggpubr from GitHub as follow (recommended):

# Install
if(!require(devtools)) install.packages("devtools")
devtools::install_github("kassambara/ggpubr")

• Or, install from CRAN as follow:

install.packages("ggpubr")

• Visualize your data:

# Plot weight by group and color by group
library("ggpubr")
ggboxplot(my_data, x = "group", y = "weight", 
          color = "group", palette = c("#00AFBB", "#E7B800"),
          ylab = "Weight", xlab = "Groups")

Unpaired Two-Samples Wilcoxon Test in R

Compute unpaired two-samples Wilcoxon test

Question : Is there any significant difference between women and men weights?

1) Compute two-samples Wilcoxon test - Method 1: The data are saved in two different numeric vectors.

res <- wilcox.test(women_weight, men_weight)
res

    Wilcoxon rank sum test with continuity correction
data:  women_weight and men_weight
W = 15, p-value = 0.02712
alternative hypothesis: true location shift is not equal to 0

It will give a warning message, saying that “cannot compute exact p-value with tie”. It comes from the assumption of a Wilcoxon test that the responses are continuous. You can suppress this message by adding another argument exact = FALSE, but the result will be the same.

2) Compute two-samples Wilcoxon test - Method 2: The data are saved in a data frame.

res <- wilcox.test(weight ~ group, data = my_data,
                   exact = FALSE)
res

    Wilcoxon rank sum test with continuity correction
data:  weight by group
W = 66, p-value = 0.02712
alternative hypothesis: true location shift is not equal to 0

# Print the p-value only
res$p.value

[1] 0.02711657

As you can see, the two methods give the same results.

The p-value of the test is 0.02712, which is less than the significance level alpha = 0.05. We can conclude that men’s median weight is significantly different from women’s median weight with a p-value = 0.02712.

wilcox.test(weight ~ group, data = my_data, 
        exact = FALSE, alternative = "less")

wilcox.test(weight ~ group, data = my_data,
        exact = FALSE, alternative = "greater")

R function

The R function wilcox.test() can be used as follow:

wilcox.test(x, y, paired = TRUE, alternative = "two.sided")

Import your data into R

1. Prepare your data as specified here: Best practices for preparing your data set for R

2. Save your data in an external .txt tab or .csv files

3. Import your data into R as follow:

# If .txt tab file, use this
my_data <- read.delim(file.choose())
# Or, if .csv file, use this
my_data <- read.csv(file.choose())

Here, we’ll use an example data set, which contains the weight of 10 mice before and after the treatment.