# Multimodal distribution

A multimodal distribution is a probability distribution with more than one peak. A distribution with one peak is called unimodal, while a distribution with two peaks is called bimodal. A bimodal distribution falls under the category of multimodal, since it also displays multiple peaks; among the multimodal distributions seen in statistical analysis, bimodal distributions are among the most common.

Galtung’s [2] classification system (AJUS) for distributions, introduced in 1969, was designed for eyeballing a distribution to categorize it for simplicity. This classification has since been modified to include a flat or no peak distribution [3]:

• A: unimodal distribution, peak in the middle
• J: unimodal, peak at either end
• U: bimodal, peak at both ends
• S: bimodal or multi-modal, multiple peaks
• F: flat, no peak

Under this classification bimodal distributions are classified as type S or U.

## Types of multimodal distribution

A comb distribution resembles the shape of a comb with alternating high and low peaks; it can be caused by rounded values. For instance, when measuring height to the nearest 100 cm with a class width of 50 cm for a histogram, the resulting distribution could display a comb shape.

An edge peak distribution is characterized by an outlier peak at the distribution edge, which may indicate incorrect plotting or a problem with data collection methods. Except in cases with an anticipated set of outliers, such as a few extreme responses in a survey, this type of distribution is usually considered erroneous.

A plateau distribution is a multimodal distribution with several peaks close together.

When there are two modes with different frequencies, the larger mode is called the major mode, while the smaller is the minor mode. The least occurring value between the modes is known as the antimode, and the difference between the major and minor modes is the amplitude. In time series, the major mode is called the acrophase, and the antimode is called the batiphase.

## Multimodal distribution causes and analysis

When a sample has a multimodal distribution, it generally suggests that the population distribution is not normal. It can also indicate the presence of diverse response patterns or extreme views, preferences, or attitudes in the sample.

To investigate the cause of multimodality, scrutinize your data closely. It’s possible that you may be inadvertently graphing two or more distributions in the same plot, as opposed to mapping a single multimodal distribution. For example, in the image below, two distinct groups of students are represented: one that studied (the peak on the left) and one that didn’t (the peak on the right).

Distributions are commonly described by the mean or median to determine the “center” of the distribution. However, this method becomes problematic for bimodal distributions. For instance, the mean exam score of 50 for students in the above example is misleading as few students scored near 50. In this case, a better approach would be to divide the data into two separate groups and analyze their location and spread individually. By doing this, we can identify the mean and standard deviation for “low scores” and “high scores” separately. It’s essential to visualize the distribution beforehand to ascertain whether it’s unimodal or multimodal. If it’s multimodal, using a single summary statistic like mean, median, or standard deviation is often misleading.

## References

[1] Image: Albinomonkey @ Wikimedia Commons.  Creative Commons Attribution-Share Alike 3.0 Unported

[2] Galtung, J. 1969. Theory and Methods of Social Research. Oslo: Universitetsforlaget.

[3] Rueding, D. Galtung’s AJUS System.

[4] Circadian Rhythms of Antioxidant Enzyme’s Activity in Young and Adult Rats under Light Deprivation Conditions – Scientific Figure on ResearchGate. Available from: https://www.researchgate.net/figure/Circadian-curve-with-the-period-of-24-h-and-terminology-52-Zenith-peak-is-a-maximal_fig1_326878588 [accessed 14 May, 2023]

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