Dip Test

TL;DR

A statistical procedure (also called the duality of pattern test) for detecting multimodality in a distribution.
Combines a histogram-based visual check with the Hartigans’ dip test statistic to assess whether a distribution has multiple peaks.
The dip statistic is compared to a threshold to indicate multimodality or unimodality.

Definition

The DIP test, also known as the duality of pattern test, is a statistical method used to determine the presence of multimodality in a dataset. Multimodality refers to the presence of multiple modes, or peaks, in the distribution of data.

Explanation

The DIP test begins with a histogram of the data to visually inspect the frequency of data points across value ranges and to identify potential multiple peaks.
It then applies the Hartigans’ dip test, which yields a dip statistic intended to indicate multimodality.
According to the described procedure, if the dip statistic is less than a certain threshold, it suggests the presence of multimodality; if it is greater than the threshold, it suggests unimodality.

Examples

Example 1

Dataset of student grades with the following distribution:

60-70: 10 students
70-80: 15 students
80-90: 20 students
90-100: 5 students
A histogram shows a unimodal distribution with a single peak at the 80-90 range, suggesting most students scored between 80 and 90.
The Hartigans’ dip test dip statistic is described as the difference between the maximum and minimum values in the distribution: $\text{dip statistic} = 100 - 60 = 40$
Since this value is greater than the threshold, it suggests that the distribution is unimodal.

Example 2