Type: Package
Title: Efficient Implementation of Kendall's Correlation Coefficient Computation
Version: 0.7.0
Imports: stats
Suggests: knitr, rmarkdown, spelling, testthat (≥ 3.0.0)
Depends: R(≥ 3.5.0)
Description: The computational complexity of the implemented algorithm for Kendall's correlation is O(n log(n)), which is faster than the base R implementation with a computational complexity of O(n^2). For small vectors (i.e., less than 100 observations), the time difference is negligible. However, for larger vectors, the speed difference can be substantial and the numerical difference is minimal. The references are Knight (1966) <doi:10.2307/2282833>, Abrevaya (1999) <doi:10.1016/S0165-1765(98)00255-9>, Christensen (2005) <doi:10.1007/BF02736122> and Emara (2024) https://learningcpp.org/. This implementation is described in Vargas Sepulveda (2024) <doi:10.48550/arXiv.2408.09618>.
License: Apache License (≥ 2)
BugReports: https://github.com/pachadotdev/kendallknight/issues
URL: https://pacha.dev/kendallknight/, https://github.com/pachadotdev/kendallknight
RoxygenNote: 7.3.2
Encoding: UTF-8
NeedsCompilation: yes
LinkingTo: cpp11
VignetteBuilder: knitr
Config/testthat/edition: 3
Language: en-US
LazyData: true
Packaged: 2025-05-16 13:01:31 UTC; pacha
Author: Mauricio Vargas Sepulveda ORCID iD [aut, cre], Loader Catherine [ctb] (original stirlerr implementations in C (2000)), Ross Ihaka [ctb] (original chebyshev_eval, gammafn and lgammacor implementations in C (1998)), Statistics Canada [dtc] (manufactured goods dataset)
Maintainer: Mauricio Vargas Sepulveda <m.sepulveda@mail.utoronto.ca>
Repository: CRAN
Date/Publication: 2025-05-16 13:20:01 UTC

kendallknight: Efficient Implementation of Kendall's Correlation Coefficient Computation

Description

The computational complexity of the implemented algorithm for Kendall's correlation is O(n log(n)), which is faster than the base R implementation with a computational complexity of O(n^2). For small vectors (i.e., less than 100 observations), the time difference is negligible. However, for larger vectors, the speed difference can be substantial and the numerical difference is minimal. The references are Knight (1966) doi:10.2307/2282833, Abrevaya (1999) doi:10.1016/S0165-1765(98)00255-9, Christensen (2005) doi:10.1007/BF02736122 and Emara (2024) https://learningcpp.org/. This implementation is described in Vargas Sepulveda (2024) doi:10.48550/arXiv.2408.09618.

Author(s)

Maintainer: Mauricio Vargas Sepulveda m.sepulveda@mail.utoronto.ca (ORCID)

Other contributors:

See Also

Useful links:

Number of doctorates versus arcade revenue in the United States

Description

A dataset containing the yearly number of doctorates awarded in computer science and the total revenue generated by arcades in the United States for the period 2000-2009.

Usage

arcade

Format

A data frame with 10 rows and 3 variables:

year

Year of the observation.

doctorates

Number of doctorates awarded in computer science.

revenue

Total revenue generated by arcades (in billions of dollars).

Source

Spurious Correlations (Vigen 2015)

Examples

arcade

Kendall Correlation

Description

kendall_cor() calculates the Kendall correlation coefficient between two numeric vectors. It uses the algorithm described in Knight (1966), which is based on the number of concordant and discordant pairs. The computational complexity of the algorithm is O(n \log(n)), which is faster than the base R implementation in stats::cor(..., method = "kendall") that has a computational complexity of O(n^2). For small vectors (i.e., less than 100 observations), the time difference is negligible. However, for larger vectors, the difference can be substantial.

By construction, the implementation drops missing values on a pairwise basis. This is the same as using stats::cor(..., use = "pairwise.complete.obs").

Usage

kendall_cor(x, y = NULL)

Arguments

x

a numeric vector or matrix.

y

an optional numeric vector.

Value

A numeric value between -1 and 1.

References

Knight, W. R. (1966). "A Computer Method for Calculating Kendall's Tau with Ungrouped Data". Journal of the American Statistical Association, 61(314), 436–439.

Abrevaya J. (1999). Computation of the Maximum Rank Correlation Estimator. Economic Letters 62, 279-285.

Christensen D. (2005). Fast algorithms for the calculation of Kendall's Tau. Journal of Computational Statistics 20, 51-62.

Emara (2024). Khufu: Object-Oriented Programming using C++

Examples

# input vectors -> scalar output
x <- c(1, 0, 2)
y <- c(5, 3, 4)
kendall_cor(x, y)

# input matrix -> matrix output
x <- mtcars[, c("mpg", "cyl")]
kendall_cor(x)

Kendall Correlation Test

Description

kendall_cor_test() calculates p-value for the the Kendall correlation using the exact values when the number of observations is less than 50. For larger samples, it uses an approximation as in base R.

Usage

kendall_cor_test(
  x,
  y,
  alternative = c("two.sided", "greater", "less"),
  conf.level = 0.95
)

Arguments

x

a numeric vector.

y

a numeric vector.

alternative

a character string specifying the alternative hypothesis. The possible values are "two.sided", "greater", and "less".

conf.level

confidence level for the returned confidence interval. Must be a single number between 0 and 1. Default is 0.95.

Value

A list with the following components:

statistic

The Kendall correlation coefficient.

p_value

The p-value of the test.

alternative

A character string describing the alternative hypothesis.

References

Knight, W. R. (1966). "A Computer Method for Calculating Kendall's Tau with Ungrouped Data". Journal of the American Statistical Association, 61(314), 436–439.

Abrevaya J. (1999). Computation of the Maximum Rank Correlation Estimator. Economic Letters 62, 279-285.

Christensen D. (2005). Fast algorithms for the calculation of Kendall's Tau. Journal of Computational Statistics 20, 51-62.

Emara (2024). Khufu: Object-Oriented Programming using C++

Examples

x <- c(1, 0, 2)
y <- c(5, 3, 4)
kendall_cor_test(x, y)