# 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)

**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]**

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).

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

**Along Diagonal —**The histogram plots here belong to a particular single class.**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.