Introduction to Bi-histograms

Histogram:

Histograms are like bar charts that display the frequency (count) of the data using bins. Below is an example of a Histogram plot [Fig 1], showing the count of employees with a monthly salary lying in a particular range. (or in a particular bin)

Fig 1: Histogram Plot

Bi-Histogram:

Bi-Histograms are essentially a bi (=2) histogram or a pair of histograms, one above the x-axis and one-below the x-axis, i.e. in opposite direction. [As shown in Fig 2]

Fig 2 : Bi-Histograms Plot

It is used to observe any changes occurring in the two subgroups of data in terms of:

• Location (observed when performing t-test)
• Variation (observed when performing f-test)
• Distribution (observed when performing Kolmogorov-Smirnov test)

Purpose of the adjoining histograms:

Bi-histograms serve as a great alternative to two-sample t-test as it is a graphical way of representing a variety of features of the subgroups simultaneously on a single plot such as:

• Skewness — shows how distorted the normal distribution of the two subgroups is.
• Location — shows at which point on the x-axis the data of the two subgroups is centred.
• Scale — shows if the plot of the two subgroups is stretched or squeezed.
• Outliers — shows the abnormalities lying in the two subgroups.

Working of Bi-Histograms:

There are two adjoining histograms present, one above and one below the x-axis.

• Above x-axis: Represents a plot of the variable for 1st condition/factor.
• Below x-axis: Represents a plot of the variable for 2nd condition/factor.

Interpreting a Bi-Histogram: 

Bi-Histogram graph tells if the histograms of the two sub-groups have significant overlap or not. In order to facilitate the comparison of multiple histograms, they are plotted in a matrix format. [As shown in Fig. 3] The rows and columns of this matrix define the variety of classes that gives a different insight into the data (subgroups).

Image Source: https://pubs.usgs.gov/of/2005/1231/InterpHist.htm

The following details can be observed in the image shown in Fig 3. In the matrix,

1. Along Diagonal — The histogram plots here belong to a particular single class.
2. Off Diagonal — The histogram here plots are bi-histogram plots

In the off-diagonal parts of the matrix,

• Red coloured histogram plots (above x-axis) — represents the row classes (factors or conditions) of the matrix.
• Green coloured histogram plots (below x-axis) — represents the column classes (factors or conditions) of the matrix.

Bi-Histogram is a powerful statistical tool that serves as a great alternative to a variety of statistical test. It gives a plethora of information related to the location, variation and distribution of the sub-groups, that to in a graphical manner, makes it easier to analyze and interpret. It can be built using Dataplot software.