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Package ‘outliers’
March 26, 2022
Version 0.
Date 2022-03-
Title Tests for Outliers
Author Lukasz Komsta
Maintainer Lukasz Komsta
Depends R (>= 2.0)
Description A collection of some tests commonly used for identifying outliers.
License GPL (>= 2)
URL https://www.R-project.org, http://www.komsta.net/
Repository CRAN
NeedsCompilation no
Date/Publication 2022-03-26 09:00:02 UTC
R topics documented:
chisq.out.test........................................ 2 cochran.test......................................... 3 dixon.test.......................................... 4 grubbs.test.......................................... 6 outlier............................................ 7 qcochran........................................... 8 qdixon............................................ 9 qgrubbs........................................... 10 qtable............................................ 11 rm.outlier.......................................... 12 scores............................................ 13
Index 15
2 chisq.out.test
chisq.out.test Chi-squared test for outlier
Description
Performs a chisquared test for detection of one outlier in a vector.
Usage
chisq.out.test(x, variance=var(x), opposite = FALSE)
Arguments
x a numeric vector for data values. variance known variance of population. if not given, estimator from sample is taken, but there is not so much sense in such test (it is similar to z-scores) opposite a logical indicating whether you want to check not the value with largest differ- ence from the mean, but opposite (lowest, if most suspicious is highest etc.)
Details
This function performs a simple test for one outlier, based on chisquared distribution of squared differences between data and sample mean. It assumes known variance of population. It is rather not recommended today for routine use, because several more powerful tests are implemented (see other functions mentioned below). It was discussed by Dixon (1950) for the first time, as one of the tests taken into account by him.
Value
A list with class htest containing the following components:
statistic the value of chisquared-statistic. p.value the p-value for the test. alternative a character string describing the alternative hypothesis. method a character string indicating what type of test was performed. data.name name of the data argument.
Note
This test is known to reject only extreme outliers, if no known variance is specified.
Author(s)
Lukasz Komsta
4 dixon.test
method a character string indicating what type of test was performed. data.name name of the data argument. estimate vector of variance estimates
Author(s)
Lukasz Komsta
References
Snedecor, G.W., Cochran, W.G. (1980). Statistical Methods (seventh edition). Iowa State University Press, Ames, Iowa.
See Also
qcochran
Examples
set.seed(1234) x=rnorm(100) d=data.frame(x=x,group=rep(1:10,10)) cochran.test(x~group,d) cochran.test(x~group,d,inlying=TRUE) x=runif(5) cochran.test(x,rep(5,5)) cochran.test(x,rep(100,5))
dixon.test Dixon tests for outlier
Description
Performs several variants of Dixon test for detecting outlier in data sample.
Usage
dixon.test(x, type = 0, opposite = FALSE, two.sided = TRUE)
Arguments
x a numeric vector for data values. opposite a logical indicating whether you want to check not the value with largest differ- ence from the mean, but opposite (lowest, if most suspicious is highest etc.) type an integer specyfying the variant of test to be performed. Possible values are compliant with these given by Dixon (1950): 10, 11, 12, 20, 21. If this value is set to zero, a variant of the test is chosen according to sample size (10 for 3-7, 11 for 8-10, 21 for 11-13, 22 for 14 and more). The lowest or highest value is selected automatically, and can be reversed used opposite parameter.
dixon.test 5
two.sided treat test as two-sided (default).
Details
The p-value is calculating by interpolation using qdixon and qtable. According to Dixon (1951) conclusions, the critical values can be obtained numerically only for n=3. Other critical values are obtained by simulations, taken from original Dixon’s paper, and regarding corrections given by Rorabacher (1991).
Value
A list with class htest containing the following components:
statistic the value of Dixon Q-statistic. p.value the p-value for the test. alternative a character string describing the alternative hypothesis. method a character string indicating what type of test was performed. data.name name of the data argument.
Author(s)
Lukasz Komsta
References
Dixon, W.J. (1950). Analysis of extreme values. Ann. Math. Stat. 21, 4, 488-506. Dixon, W.J. (1951). Ratios involving extreme values. Ann. Math. Stat. 22, 1, 68-78. Rorabacher, D.B. (1991). Statistical Treatment for Rejection of Deviant Values: Critical Values of Dixon Q Parameter and Related Subrange Ratios at the 95 percent Confidence Level. Anal. Chem. 83, 2, 139-146.
See Also
chisq.out.test, grubbs.test
Examples
set.seed(1234) x = rnorm(10) dixon.test(x) dixon.test(x,opposite=TRUE) dixon.test(x,type=10)
outlier 7
alternative a character string describing the alternative hypothesis. method a character string indicating what type of test was performed. data.name name of the data argument.
Author(s)
Lukasz Komsta
References
Grubbs, F.E. (1950). Sample Criteria for testing outlying observations. Ann. Math. Stat. 21, 1, 27-58.
See Also
dixon.test, chisq.out.test
Examples
set.seed(1234) x = rnorm(10) grubbs.test(x) grubbs.test(x,type=20) grubbs.test(x,type=11)
outlier Find value with largest difference from the mean
Description
Finds value with largest difference between it and sample mean, which can be an outlier.
Usage
outlier(x, opposite = FALSE, logical = FALSE)
Arguments
x a data sample, vector in most cases. If argument is a dataframe, then outlier is calculated for each column by sapply. The same behavior is applied by apply when the matrix is given. opposite if set to TRUE, gives opposite value (if largest value has maximum difference from the mean, it gives smallest and vice versa) logical if set to TRUE, gives vector of logical values, and possible outlier position is marked by TRUE
8 qcochran
Value
A vector of value(s) with largest difference from the mean.
Author(s)
Lukasz Komsta, corrections by Markus Graube
See Also
rm.outlier
Examples
set.seed(1234) y=rnorm(100) outlier(y) outlier(y,opposite=TRUE) dim(y) <- c(20,5) outlier(y) outlier(y,opposite=TRUE)
qcochran Critical values and p-values for Cochran outlying variance test
Description
This functions calculates quantiles (critical values) and reversively p-values for Cochran test for outlying variance.
Usage
qcochran(p, n, k) pcochran(q, n, k)
Arguments
p vector of probabilities. q vector of quantiles. n number of values in each group (if not equal, use arithmetic mean). k number of groups.
Value
Vector of p-values or critical values.
Author(s)
Lukasz Komsta
10 qgrubbs
References
Dixon, W.J. (1950). Analysis of extreme values. Ann. Math. Stat. 21, 4, 488-506. Dixon, W.J. (1951). Ratios involving extreme values. Ann. Math. Stat. 22, 1, 68-78. Rorabacher, D.B. (1991). Statistical Treatment for Rejection of Deviant Values: Critical Values of Dixon Q Parameter and Related Subrange Ratios at the 95 percent Confidence Level. Anal. Chem. 83, 2, 139-146.
See Also
qtable, dixon.test
qgrubbs Calculate critical values and p-values for Grubbs tests
Description
This function is designed to calculate critical values for Grubbs tests for outliers detecting and to approximate p-values reversively.
Usage
qgrubbs(p, n, type = 10, rev = FALSE) pgrubbs(q, n, type = 10)
Arguments
p vector of probabilities. q vector of quantiles. n sample size. type Integer value indicating test variant. 10 is a test for one outlier (side is detected automatically and can be reversed by opposite parameter). 11 is a test for two outliers on opposite tails, 20 is test for two outliers in one tail. rev if set to TRUE, function qgrubbs acts as pgrubbs.
Details
The critical values for test for one outlier is calculated according to approximations given by Pearson and Sekar (1936). The formula is simply reversed to obtain p-value. The values for two outliers test (on opposite sides) are calculated according to David, Hartley, and Pearson (1954). Their formula cannot be rearranged to obtain p-value, thus such values are obtained by uniroot. For test checking presence of two outliers at one tail, the tabularized distribution (Grubbs, 1950) is used, and approximations of p-values are interpolated using qtable.
qtable 11
Value
A vector of quantiles or p-values.
Author(s)
Lukasz Komsta
References
Grubbs, F.E. (1950). Sample Criteria for testing outlying observations. Ann. Math. Stat. 21, 1, 27-58. Pearson, E.S., Sekar, C.C. (1936). The efficiency of statistical tools and a criterion for the rejection of outlying observations. Biometrika, 28, 3, 308-320. David, H.A, Hartley, H.O., Pearson, E.S. (1954). The distribution of the ratio, in a single normal sample, of range to standard deviation. Biometrika, 41, 3, 482-493.
See Also
grubbs.test
qtable Interpolate tabularized distribution
Description
This function calculates critical values or p-values which cannot be obtained numerically, and only tabularized version is available.
Usage
qtable(p, probs, quants)
Arguments
p vector of probabilities. probs vector of given probabilities. quants vector of given corresponding quantiles.
Details
This function is internal routine used to obtain Grubbs and Dixon critical values. It fits linear or cubical regression to closests values of its argument, then uses obtained function to obtain quantile by interpolation.
Value
A vector of interpolated values
scores 13
Examples
set.seed(1234) y=rnorm(100) outlier(y) outlier(y,opposite=TRUE) rm.outlier(y) rm.outlier(y,opposite=TRUE) dim(y) <- c(20,5) outlier(y) outlier(y,logical=TRUE) outlier(y,logical=TRUE,opposite=TRUE) rm.outlier(y) rm.outlier(y,opposite=TRUE)
scores Calculate scores of the sample
Description
This function calculates normal, t, chi-squared, IQR and MAD scores of given data.
Usage
scores(x, type = c("z", "t", "chisq", "iqr", "mad"), prob = NA, lim = NA)
Arguments
x a vector of data. type "z" calculates normal scores (differences between each value and the mean di- vided by sd), "t" calculates t-Student scores (transformed by (z*sqrt(n-2))/sqrt(z-1-t^2) formula, "chisq" gives chi-squared scores (squares of differences between val- ues and mean divided by variance. For the "iqr" type, all values lower than first and greater than third quartile is considered, and difference between them and nearest quartile divided by IQR are calculated. For the values between these quartiles, scores are always equal to zero. "mad" gives differences between each value and median, divided by median absolute deviation. prob If set, the corresponding p-values instead of scores are given. If value is set to 1, p-value are returned. Otherwise, a logical vector is formed, indicating which values are exceeding specified probability. In "z" and "mad" types, there is also possibility to set this value to zero, and then scores are confirmed to (n-1)/sqrt(n) value, according to Shiffler (1998). The "iqr" type does not support probabilities, but "lim" value can be specified. lim This value can be set for "iqr" type of scores, to form logical vector, which values has this limit exceeded.
Value
A vector of scores, probabilities, or logical vector.
14 scores
Author(s)
Lukasz Komsta, corrections by Alan Richter
References
Schiffler, R.E (1998). Maximum Z scores and outliers. Am. Stat. 42, 1, 79-80.
See Also
mad, IQR, grubbs.test,
Examples
set.seed(1234) x = rnorm(10) scores(x) scores(x,prob=1) scores(x,prob=0.5) scores(x,prob=0.1) scores(x,prob=0.93) scores(x,type="iqr") scores(x,type="mad") scores(x,prob=0)
