# Scree plot

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Diagnostic plot in multivariate statistics

A sample scree plot produced in [R](/source/R_(programming_language)). The [Kaiser criterion](/source/Kaiser_criterion) is shown in red.

In [multivariate statistics](/source/Multivariate_statistics), a **scree plot** is a line plot of the [eigenvalues](/source/Eigenvalue) of [factors](/source/Factor_analysis) or [principal components](/source/Principal_component) in an analysis.[1] The scree plot is used to determine the number of factors to retain in an [exploratory factor analysis](/source/Exploratory_factor_analysis) (FA) or principal components to keep in a [principal component analysis](/source/Principal_component_analysis) (PCA). The procedure of finding statistically significant factors or components using a scree plot is also known as a **scree test**. [Raymond B. Cattell](/source/Raymond_B._Cattell) introduced the scree plot in 1966.[2]

A scree plot always displays the eigenvalues in a downward curve, ordering the eigenvalues from largest to smallest. According to the scree test, the ["elbow" of the graph](/source/Elbow_of_a_curve) where the eigenvalues seem to level off is found, and factors or components to the left of this point should be retained as significant.[3]

As the "elbow" point has been defined as point of maximum curvature, this property has led to the creation of the [Kneedle algorithm](https://en.wikipedia.org/w/index.php?title=Kneedle_algorithm&action=edit&redlink=1).[4]

## Etymology

A scree at [Mount Yamnuska](/source/Mount_Yamnuska), [Alberta](/source/Alberta), [Canada](/source/Canada)

The scree plot is named after the elbow's resemblance to a [scree](/source/Scree) in nature.

## Criticism

This test is sometimes criticized for its subjectivity. Scree plots can have multiple "elbows" that make it difficult to know the correct number of factors or components to retain, making the test [unreliable](/source/Reliability_(statistics)). There is also no standard for the scaling of the x and y axes, which means that different statistical programs can produce different plots from the same data.[5]

The test has also been criticized for producing too few factors or components for factor retention.[*[clarification needed](https://en.wikipedia.org/wiki/Wikipedia:Please_clarify)*][1]

## See also

Wikimedia Commons has media related to [Scree plot](https://commons.wikimedia.org/wiki/Category:Scree_plot).

- [Biplot](/source/Biplot)

- [Parallel analysis](/source/Parallel_analysis)

- [Elbow method](/source/Elbow_method_(clustering))

- [Determining the number of clusters in a data set](/source/Determining_the_number_of_clusters_in_a_data_set)

## References

1. ^ [***a***](#cite_ref-LewithJonas2010_1-0) [***b***](#cite_ref-LewithJonas2010_1-1) George Thomas Lewith; Wayne B. Jonas; Harald Walach (23 November 2010). [*Clinical Research in Complementary Therapies: Principles, Problems and Solutions*](https://books.google.com/books?id=CSNw-spnFdkC&pg=PA354). Elsevier Health Sciences. p. 354. [ISBN](/source/ISBN_(identifier)) [978-0-7020-4916-3](https://en.wikipedia.org/wiki/Special:BookSources/978-0-7020-4916-3).

1. **[^](#cite_ref-2)** Cattell, Raymond B. (1966). "The Scree Test For The Number Of Factors". *Multivariate Behavioral Research*. **1** (2): 245–276. [doi](/source/Doi_(identifier)):[10.1207/s15327906mbr0102_10](https://doi.org/10.1207%2Fs15327906mbr0102_10). [PMID](/source/PMID_(identifier)) [26828106](https://pubmed.ncbi.nlm.nih.gov/26828106).

1. **[^](#cite_ref-DmitrienkoChuang-Stein2007_3-0)** Alex Dmitrienko; [Christy Chuang-Stein](/source/Christy_Chuang-Stein); [Ralph B. D'Agostino](/source/Ralph_B._D'Agostino) (2007). [*Pharmaceutical Statistics Using SAS: A Practical Guide*](https://books.google.com/books?id=FlXwIvSHND8C&pg=PA380). SAS Institute. p. 380. [ISBN](/source/ISBN_(identifier)) [978-1-59994-357-2](https://en.wikipedia.org/wiki/Special:BookSources/978-1-59994-357-2).

1. **[^](#cite_ref-4)** Satopaa, Ville; Albrecht, Jeannie; Irwin, David; Raghavan, Barath (2011-06-20). *Finding a "kneedle" in a haystack: Detecting knee points in system behavior*. 2011 / 31st International Conference on Distributed Computing Systems. IEEE Workshops. [Institute of Electrical and Electronics Engineers](/source/Institute_of_Electrical_and_Electronics_Engineers). pp. 166–171. [doi](/source/Doi_(identifier)):[10.1109/ICDCSW.2011.20](https://doi.org/10.1109%2FICDCSW.2011.20).

1. **[^](#cite_ref-NormanStreiner2007_5-0)** Norman, Geoffrey R.; Streiner, David L. (15 September 2007). [*Biostatistics: The bare essentials*](https://books.google.com/books?id=8rkqWafdpuoC&pg=PA201). PMPH-USA. p. 201. [ISBN](/source/ISBN_(identifier)) [978-1-55009-400-8](https://en.wikipedia.org/wiki/Special:BookSources/978-1-55009-400-8) – via Google Books.

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Adapted from the Wikipedia article [Scree plot](https://en.wikipedia.org/wiki/Scree_plot) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Scree_plot?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.