Statistics How To

J Shaped Distribution

Probability Distributions >

A J shaped distribution is a probability distribution in the rough shape of the letter J placed on its side, or its mirror image. These distributions tend to have some observations at one end, very few in the middle, and a large number at the other end.
j shaped distribution

J Shaped Distribution Example

Product reviews are an example of a J Shaped distribution: the distribution of product reviews (e.g. on Amazon) frequently shows many ratings are 5-star, a few are 1-star (or vice-versa), and a handful are in between— (Hu & Zhang, 2009).

Terminology Problems with “J shape”

L to R: Arial, Verdana, Times New Roman.

The term “J-Shaped” is an informal description of what some distributions look like. Part of the reason its informal, and hasn’t been committed to the annals of statistical history, is that the letter J has different looks; If you’re a little confused about the shape of the distribution, it could be because you’re looking at the “J” in the wrong font. The J-distribution takes its name from fonts like Verdana, which has a half arm on top. An “arm” is the part of a letter (“glyph”) that’s the horizontal stroke on top. Some fonts have a full arm (e.g. Times New Roman), or none at all (e.g. Arial), which causes the confusion.


Statistical Problems

Aside from font problems, Hu & Zhang note that the J-shaped distribution “…creates some fundamental statistical problems.” The mean, a common statistic used for calculating future sales, product quality, consumer satisfaction and other metrics only works for unimodal distributions (distributions with one “hump”). The J-shaped distribution is bimodal (two humps); when a mean is calculated from a bimodal distribution, it essentially becomes meaningless. For example, a collection of 1 and 5 star ratings gives a mean of 3 stars— which is not a good reflection of reality.

References

Hu & Zhang, (2009). Overcoming the J-shaped distribution of product reviews. Communications of the ACM – A View of Parallel Computing CACM Homepage archive. Volume 52 Issue 10, October. Pages 144-147. Retrieved December 8, 2017 from: https://dl.acm.org/citation.cfm?id=1562800
Wikipedia (2017). Typeface anatomy. Retrieved December 8, 2017 from: https://en.wikipedia.org/wiki/Typeface_anatomy

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