ScottKnott-package: The ScottKnott Clustering Algorithm

In ScottKnott: The ScottKnott Clustering Algorithm

The ScottKnott Clustering Algorithm

Description

The Scott & Knott clustering algorithm is a widely used multiple comparison method in the Analysis of Variance context (Gates and Bilbro, 1978; Bony et al., 2001; Dilson et al., 2002; Jyotsna et al., 2003).

Proposed by Scott and Knott (1974), the method overcomes the overlapping problem common to other procedures such as the t-test, Tukey, Duncan, and Newman-Keuls tests. Overlapping occurs when one or more treatments are simultaneously assigned to more than one group; as the number of treatments grows to twenty or more, this ambiguity can make it virtually impossible for the experimenter to distinguish the true group structure. The Scott & Knott method does not have this problem, which is widely regarded as one of its main advantages.

The method uses a cluster analysis algorithm that, starting from the complete set of observed treatment means, recursively partitions them so that any two resulting groups are disjoint.

In their own words: “we study the consequences of using a well-known method of cluster analysis to partition the sample treatment means in a balanced design and show how a corresponding likelihood ratio test gives a method of judging the significance of difference among groups obtained”.

Monte Carlo studies suggest that the Scott & Knott method has high power and type I error rates that closely follow the nominal levels. The ScottKnott package applies this algorithm to objects of class formula, aov, aovlist, lm, and lmerMod from a prior analysis of variance, and presents results both numerically and graphically.

As of version 1.2-8, the package handles unbalanced designs using adjusted means, as described in Conrado et al. (2017).

Author(s)

Faria, J. C. ([e-mail])
Jelihovschi, E. G. ([e-mail])
Allaman, I. B. ([e-mail])

References

Bony S., Pichon N., Ravel C., Durix A., Balfourier F., Guillaumin J.J. 2001. The Relationship between Mycotoxin Synthesis and Isolate Morphology in Fungal Endophytes of Lolium perenne. New Phytologist, 1521, 125-137.

Borges L.C., FERREIRA D.F. 2003. Poder e taxas de erro tipo I dos testes Scott-Knott, Tukey e Student-Newman-Keuls sob distribuicoes normal e nao normais dos residuos. Power and type I errors rate of Scott-Knott, Tukey and Student-Newman-Keuls tests under normal and non-normal distributions of the residues. Rev. Mat. Estat., Sao Paulo, 211: 67-83.

Calinski T., Corsten L.C.A. 1985. Clustering Means in ANOVA by Simultaneous Testing. Bio-metrics, 411, 39-48.

Da Silva E.C, Ferreira D.F, Bearzoti E. 1999. Evaluation of power and type I error rates of Scott-Knotts test by the method of Monte Carlo. Cienc. agrotec., Lavras, 23, 687-696.

Dilson A.B, David S.D., Kazimierz J., William W.K. 2002. Half-sib progeny evaluation and selection of potatoes resistant to the US8 genotype of Phytophthora infestans from crosses between resistant and susceptible parents. Euphytica, 125, 129-138.

Gates C.E., Bilbro J.D. 1978. Illustration of a Cluster Analysis Method for Mean Separation. Agron J, 70, 462-465.

Wilkinson, G.N, Rogers, C.E. 1973. Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 3, pp. 392-399.

Jyotsna S., Zettler L.W., van Sambeek J.W., Ellersieck M.R., Starbuck C.J. 2003. Symbiotic Seed Germination and Mycorrhizae of Federally Threatened Platanthera PraeclaraOrchidaceae. American Midland Naturalist, 1491, 104-120.

Ramalho M.A.P., Ferreira DF, Oliveira AC 2000. Experimentacao em Genetica e Melhoramento de Plantas. Editora UFLA.

Scott R.J., Knott M. 1974. A cluster analysis method for grouping means in the analysis of variance. Biometrics, 30, 507-512.

Conrado, T. V., Ferreira, D. F., Scapim, C. A., and Maluf, W. R. "Adjusting the Scott-Knott cluster analyses for unbalanced designs." Crop Breeding and Applied Biotechnology 17.1 (2017): 1-9.

ScottKnott documentation built on May 24, 2026, 5:06 p.m.