Box Plot

Box Plot

Box Plot

• This is a Plot that can be useful for Exploratory Data Analysis
• This plot is a visualization of Summary Statistics
• it’s “a convenient way of graphically depicting groups of numerical data through their quartiles”

General idea:

• What is Distribution of data?
  • is it compact? symmetric?
• Are there Outliers?

• IQR = Q3 - Q1 - the length of the box
• whiskers (fences) capture data outside of the box

boxplot(..., range=0, ...)
boxplot(..., horizontal=T, ...) // horizontal boxplot

range=0 means that it will show usual box plot.

Modified Box Plot

Modified box plot can be used to show Outliers

• IQR (Inter Quartile Range) - difference between 3rd and 1st quartile
• Inner fences - the values that are 1.5 times the IQR beyond the 1st and 3rd quartile
• Lower inner fence = 1st quartile - (1.5 x IQR)
• Upper inner fence = 3rd quartile + (1.5 x IQR)
• observations beyond the whiskers (fences) are outliers and marked with dots

In R

• by default boxplot shows modified box plot
• IQR(data) shows the IQR

Bivariate Analysis

We can calculate all 5 number values for all quantitative variables associated with a specific category.

• And for each category get a box plot
• With box plots, we also can see how two values interact
• 

R

boxplot(d$a ~ as.factor(d$f))

• it will show separate boxplot of values in $a$ for each values of $f$
• 

boxplot(d$a ~ as.factor(d$f), col=c("blue","orange"), names=c("yes","no"), varwidth=T)

• if we want to show how much data is there for each factor,
• we can make the with of the boxes proportional to the volume of data
• using varwidth=T
• 

Box Plot with Other Plots

Box plots are nice to combine with other plots

• for example, with a Scatter Plot
• link
• This is the R snipped to produce this figure

See Also

• R Visualization Snippets

Sources

• Statistics: Making Sense of Data (coursera)
• Data Analysis (coursera)
• http://en.wikipedia.org/wiki/Box_plot