| Title: | Pseudo-Ranks |
| Version: | 1.0.4 |
| Date: | 2025-02-18 |
| Maintainer: | Martin Happ <statistics@happ.co.at> |
| Description: | Efficient calculation of pseudo-ranks and (pseudo)-rank based test statistics. In case of equal sample sizes, pseudo-ranks and mid-ranks are equal. When used for inference mid-ranks may lead to paradoxical results. Pseudo-ranks are in general not affected by such a problem. See Happ et al. (2020, <doi:10.18637/jss.v095.c01>) for details. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| Depends: | R (≥ 3.5.0) |
| Imports: | Rcpp (≥ 0.12.16), doBy |
| LinkingTo: | Rcpp |
| URL: | https://github.com/happma/pseudorank/ |
| BugReports: | https://github.com/happma/pseudorank/issues/ |
| RoxygenNote: | 7.3.2 |
| Suggests: | testthat |
| NeedsCompilation: | yes |
| Packaged: | 2025-02-18 17:00:55 UTC; happma |
| Author: | Martin Happ  [aut,
cre],
Georg Zimmermann [aut],
Arne C. Bathke [aut],
Edgar Brunner [aut] |
| Repository: | CRAN |
| Date/Publication: | 2025-02-20 17:20:02 UTC |
Pseudo-Ranks
Description
This packge provides functions to calculate pseudo-ranks. Rank based test statistics (e.g. Kruskal-Wallis test) may lead to paradoxical results as the weighted relative effects (based on ranks) depend on the sample sizes (Brunner, 2018). Pseudo-ranks do not have these problems.
Author(s)
Maintainer: Martin Happ <martin.happ@aon.at>
References
Brunner, E., Konietschke, F., Bathke, A. C., & Pauly, M. (2018). Ranks and Pseudo-Ranks-Paradoxical Results of Rank Tests. arXiv preprint arXiv:1802.05650.
Brunner, E., Bathke, A.C., and Konietschke, F. (2018a). Rank- and Pseudo-Rank Procedures for Independent Observations in Factorial Designs - Using R and SAS. Springer Series in Statistics, Springer, Heidelberg. ISBN: 978-3-030-02912-8.
Happ M, Zimmermann G, Brunner E, Bathke AC (2020). Pseudo-Ranks: How to Calculate Them Efficiently in R. Journal of Statistical Software, Code Snippets, *95*(1), 1-22. doi: 10.18637/jss.v095.c01 (URL:https://doi.org/10.18637/jss.v095.c01).
Artifical data of 54 subjects
Description
An artificial dataset containing data of 54 subjects where where a substance was administered in three different concentrations (1,2 and 3). This data set can be used to show the paradoxical results obtained from rank tests, i.e., the Hettmansperger-Norton test.
Usage
data(ParadoxicalRanks)
Format
A data frame with 54 rows and 2 variables.
Details
The columns are as follows:
conc. Grouping variable specifying which concentration was used. This factor is ordered, i.e., 1 < 2 < 3.
score. The response variable.
References
Happ M, Zimmermann G, Brunner E, Bathke AC (2020). Pseudo-Ranks: How to Calculate Them Efficiently in R. Journal of Statistical Software, Code Snippets, *95*(1), 1-22. doi: 10.18637/jss.v095.c01 (URL:https://doi.org/10.18637/jss.v095.c01).
Examples
data("ParadoxicalRanks")
dat <- ParadoxicalRanks
set.seed(1)
n <- c(60, 360, 120)
x1 <- sample(subset(dat, dat$conc == 1)$score, n[1], replace = TRUE)
x2 <- sample(subset(dat, dat$conc == 2)$score, n[2], replace = TRUE)
x3 <- sample(subset(dat, dat$conc == 3)$score, n[3], replace = TRUE)
dat <- data.frame(score = c(x1, x2, x3),
conc = factor(c( rep(1,n[1]), rep(2,n[2]), rep(5,n[3]) ), ordered=TRUE) )
# Hettmansperger-Norton test with ranks (pseudorannks = FALSE) returns a small p-value (0.011).
# In contrast, the pseudo-rank test returns a large p-value (0.42). By changing the ratio of
# group sizes, we can also obtain a significant decreasing trend with ranks, e.g.
# n <- c(260,20,260) and the same seed.
hettmansperger_norton_test(score ~ conc, data = dat, pseudoranks = FALSE,
alternative = "increasing")
hettmansperger_norton_test(score ~ conc, data = dat, pseudoranks = TRUE,
alternative = "increasing")
Hettmansperger-Norton Trend Test for k-Samples
Description
This function calculates the Hettmansperger-Norton trend test using pseudo-ranks under the null hypothesis H0F: F_1 = ... F_k.
Usage
hettmansperger_norton_test(x, ...)
## S3 method for class 'numeric'
hettmansperger_norton_test(
x,
y,
na.rm = FALSE,
alternative = c("decreasing", "increasing", "custom"),
trend = NULL,
pseudoranks = TRUE,
...
)
## S3 method for class 'formula'
hettmansperger_norton_test(
formula,
data,
na.rm = FALSE,
alternative = c("decreasing", "increasing", "custom"),
trend = NULL,
pseudoranks = TRUE,
...
)
Arguments
x |
vector containing the observations |
... |
further arguments are ignored |
y |
vector specifiying the group to which the observations from the x vector belong to |
na.rm |
a logical value indicating if NA values should be removed |
alternative |
either decreasing (trend k, k-1, ..., 1) or increasing (1, 2, ..., k) or custom (then argument trend must be specified) |
trend |
custom numeric vector indicating the trend for the custom alternative, only used if alternative = "custom" |
pseudoranks |
logical value indicating if pseudo-ranks or ranks should be used |
formula |
formula object |
data |
data.frame containing the variables in the formula (observations and group) |
Value
Returns an object.
References
Brunner, E., Bathke, A.C., and Konietschke, F. (2018a). Rank- and Pseudo-Rank Procedures for Independent Observations in Factorial Designs - Using R and SAS. Springer Series in Statistics, Springer, Heidelberg. ISBN: 978-3-030-02912-8.
Happ M, Zimmermann G, Brunner E, Bathke AC (2020). Pseudo-Ranks: How to Calculate Them Efficiently in R. Journal of Statistical Software, Code Snippets, *95*(1), 1-22. doi: 10.18637/jss.v095.c01 (URL:https://doi.org/10.18637/jss.v095.c01).
Hettmansperger, T. P., & Norton, R. M. (1987). Tests for patterned alternatives in k-sample problems. Journal of the American Statistical Association, 82(397), 292-299
Examples
# create some data, please note that the group factor needs to be ordered
df <- data.frame(data = c(rnorm(40, 3, 1), rnorm(40, 2, 1), rnorm(20, 1, 1)),
group = c(rep(1,40),rep(2,40),rep(3,20)))
df$group <- factor(df$group, ordered = TRUE)
# you can either test for a decreasing, increasing or custom trend
hettmansperger_norton_test(df$data, df$group, alternative="decreasing")
hettmansperger_norton_test(df$data, df$group, alternative="increasing")
hettmansperger_norton_test(df$data, df$group, alternative="custom", trend = c(1, 3, 2))
Hettmansperger-Norton Trend Test for k-Samples
Description
This function calculates the Hettmansperger-Norton trend test using pseudo-ranks under the null hypothesis H0F: F_1 = ... F_k.
Usage
hettmansperger_norton_test_internal(
data,
group,
na.rm,
alternative = c("decreasing", "increasing", "custom"),
formula = NULL,
trend = NULL,
pseudoranks = TRUE,
...
)
Arguments
data |
numeric vector containing the data |
group |
ordered factor vector for the groups |
na.rm |
a logical value indicating if NA values should be removed |
alternative |
either decreasing or increasing |
formula |
formula object |
trend |
custom numeric vector indicating the trend for the custom alternative, only used if alternative = "custom" |
... |
further arguments are ignored |
Value
Returns a data.frame with the results
References
Brunner, E., Bathke, A.C., and Konietschke, F. (2018a). Rank- and Pseudo-Rank Procedures for Independent Observations in Factorial Designs - Using R and SAS. Springer Series in Statistics, Springer, Heidelberg. ISBN: 978-3-030-02912-8.
Hettmansperger, T. P., & Norton, R. M. (1987). Tests for patterned alternatives in k-sample problems. Journal of the American Statistical Association, 82(397), 292-299
Examples
# create some data, please note that the group factor needs to be ordered
df <- data.frame(data = c(rnorm(40, 3, 1), rnorm(40, 2, 1), rnorm(20, 1, 1)),
group = c(rep(1,40),rep(2,40),rep(3,20)))
df$group <- factor(df$group, ordered = TRUE)
# you can either test for a decreasing, increasing or custom trend
hettmansperger_norton_test(df$data, df$group, alternative="decreasing")
hettmansperger_norton_test(df$data, df$group, alternative="increasing")
hettmansperger_norton_test(df$data, df$group, alternative="custom", trend = c(1, 3, 2))
Kepner-Robinson Test
Description
This function calculates the Kepner-Robinson test using ranks under the null hypothesis H0F: F_1 = ... F_k where F_i are the marginal distributions. Each subject needs to have k measurements. This test assumes that the covariance matrix of a subject has a compound symmetry structure.
Usage
kepner_robinson_test(x, ...)
## S3 method for class 'numeric'
kepner_robinson_test(
x,
time,
subject,
na.rm = FALSE,
distribution = c("Chisq", "F"),
...
)
## S3 method for class 'formula'
kepner_robinson_test(
formula,
data,
subject,
na.rm = FALSE,
distribution = c("Chisq", "F"),
...
)
Arguments
x |
numeric vector containing the data |
... |
further arguments are ignored |
time |
factor specifying the groups |
subject |
factor specifying the subjects or the name of the subject column if a data.frame is used |
na.rm |
a logical value indicating if NA values should be removed |
distribution |
either 'Chisq' or 'F' approximation |
formula |
optional formula object |
data |
optional data.frame of the data |
Value
Returns an object of class 'pseudorank'
References
James L. Kepner & David H. Robinson (1988) Nonparametric Methods for Detecting Treatment Effects in Repeated-Measures Designs, Journal of the American Statistical Association, 83:402, 456-461.
Examples
# create some artificial data with 20 subjects measured at two time points
data <- rnorm(40)
time <- rep(c(1,2),20)
subject <- gl(20,2)
df <- data.frame(data=data,time=time,subject=subject)
kepner_robinson_test(data,time,subject)
kepner_robinson_test(data~time,data=df,subject="subject")
Kepner-Robinson Test
Description
This function calculates the Kepner-Robinsin test under the null hypothesis H0F: F_1 = ... F_k.
Usage
kepner_robinson_test_internal(
data,
time,
subject,
distribution,
na.rm,
formula = NULL,
...
)
Arguments
data |
numeric vector containing the data |
time |
factor vector containing time points |
subject |
factor vector containing subjects |
distribution |
specified distribution, either Chisq or F |
na.rm |
a logical value indicating if NA values should be removed |
formula |
formula object |
... |
further arguments are ignored |
Value
Returns a data.frame with the results
References
Kepner, J. L., & Robinson, D. H. (1988). Nonparametric methods for detecting treatment effects in repeated-measures designs. Journal of the American Statistical Association, 83(402), 456-461.
Examples
# create some artificial data with 20 subjects measured at two time points
data <- rnorm(40)
time <- rep(c(1,2),20)
subject <- gl(20,2)
df <- data.frame(data=data,time=time,subject=subject)
kepner_robinson_test(data,time,subject)
kepner_robinson_test(data~time,data=df,subject="subject")
Hettmansperger-Norton Trend Test for k-Samples
Description
This function calculates the Kruskal-Wallis test using pseudo-ranks under the null hypothesis H0F: F_1 = ... F_k.
Usage
kruskal_wallis_internal(
data,
group,
na.rm,
formula = NULL,
pseudoranks = TRUE,
...
)
Arguments
data |
numeric vector containing the data |
group |
factor specifying the groups |
na.rm |
a logical value indicating if NA values should be removed |
formula |
formula object |
pseudoranks |
logical value indicating if pseudo-ranks or ranks should be used |
... |
further arguments are ignored |
Value
Returns a data.frame with the results
References
Brunner, E., Bathke, A.C., and Konietschke, F. (2018a). Rank- and Pseudo-Rank Procedures for Independent Observations in Factorial Designs - Using R and SAS. Springer Series in Statistics, Springer, Heidelberg. ISBN: 978-3-030-02912-8.
Hettmansperger, T. P., & Norton, R. M. (1987). Tests for patterned alternatives in k-sample problems. Journal of the American Statistical Association, 82(397), 292-299
Examples
x = c(1, 1, 1, 1, 2, 3, 4, 5, 6)
grp = as.factor(c('A','A','B','B','B','D','D','D','D'))
# calculate Kruskal-Wallis test using pseudo-ranks
kruskal_wallis_test(x, grp, na.rm = FALSE, pseudoranks = TRUE)
Kruskal-Wallis Test
Description
This function calculates the Kruskal-Wallis test using pseudo-ranks under the null hypothesis H0F: F_1 = ... F_k.
Usage
kruskal_wallis_test(x, ...)
## S3 method for class 'numeric'
kruskal_wallis_test(x, grp, na.rm = FALSE, pseudoranks = TRUE, ...)
## S3 method for class 'formula'
kruskal_wallis_test(formula, data, na.rm = FALSE, pseudoranks = TRUE, ...)
Arguments
x |
numeric vector containing the data |
... |
further arguments are ignored |
grp |
factor specifying the groups |
na.rm |
a logical value indicating if NA values should be removed |
pseudoranks |
logical value indicating if pseudo-ranks or ranks should be used |
formula |
optional formula object |
data |
optional data.frame of the data |
Value
Returns an object of class 'pseudorank'
References
Brunner, E., Bathke, A.C., and Konietschke, F. (2018a). Rank- and Pseudo-Rank Procedures for Independent Observations in Factorial Designs - Using R and SAS. Springer Series in Statistics, Springer, Heidelberg. ISBN: 978-3-030-02912-8.
Examples
x = c(1, 1, 1, 1, 2, 3, 4, 5, 6)
grp = as.factor(c('A','A','B','B','B','D','D','D','D'))
# calculate Kruskal-Wallis test using pseudo-ranks
kruskal_wallis_test(x, grp, na.rm = FALSE, pseudoranks = TRUE)
Calculation of Pseudo-Ranks
Description
Calculation of (mid) pseudo-ranks of a sample. In case of ties (i.e. equal values), the average of min pseudo-ranks and max-pseudo-ranks are taken (similar to rank with ties.method="average").
Usage
pseudorank(x, ...)
## S3 method for class 'numeric'
pseudorank(x, y, na.last = NA, ties.method = c("average", "max", "min"), ...)
## S3 method for class 'formula'
pseudorank(
formula,
data,
na.last = NA,
ties.method = c("average", "max", "min"),
...
)
Arguments
x |
vector containing the observations |
... |
further arguments |
y |
vector specifiying the group to which the observations from the x vector belong to |
na.last |
for controlling the treatment of NAs. If TRUE, missing values in the data are put last; if FALSE, they are put first; if NA, they are removed (recommended). |
ties.method |
type of pseudo-ranks: either 'average' (recommended), 'min' or 'max'. |
formula |
formula object |
data |
data.frame containing the variables in the formula (observations and group) |
Value
Returns a numerical vector containing the pseudo-ranks.
References
Brunner, E., Bathke, A.C., and Konietschke, F. (2018a). Rank- and Pseudo-Rank Procedures for Independent Observations in Factorial Designs - Using R and SAS. Springer Series in Statistics, Springer, Heidelberg. ISBN: 978-3-030-02912-8.
Happ M, Zimmermann G, Brunner E, Bathke AC (2020). Pseudo-Ranks: How to Calculate Them Efficiently in R. Journal of Statistical Software, Code Snippets, *95*(1), 1-22. doi: 10.18637/jss.v095.c01 (URL:https://doi.org/10.18637/jss.v095.c01).
Examples
df <- data.frame(data = round(rnorm(100)), group = c(rep(1,40),rep(2,40),rep(3,20)))
df$group <- as.factor(df$group)
## two ways to calculate pseudo-ranks
# Variant 1: use a vector for the data and a group vector
pseudorank(df$data,df$group)
# Variant 2: use a formula object, Note that only one group factor can be used
# that is, in data~group*group2 only 'group' will be used
pseudorank(data~group,df)
Calculation of Pseudo-Ranks (Deprecated)
Description
Calculation of (mid) pseudo-ranks of a sample. In case of ties (i.e. equal values), the average of min pseudo-ranks and max-pseudo-ranks are taken (similar to rank with ties.method="average").
Usage
psrank(x, ...)
Arguments
x |
vector containing the observations |
... |
further arguments (see help for pseudorank) |
Value
Returns a numerical vector containing the pseudo-ranks.
References
Happ M, Zimmermann G, Brunner E, Bathke AC (2020). Pseudo-Ranks: How to Calculate Them Efficiently in R. Journal of Statistical Software, Code Snippets, *95*(1), 1-22. doi: 10.18637/jss.v095.c01 (URL:https://doi.org/10.18637/jss.v095.c01).
Examples
df <- data.frame(data = round(rnorm(100)), group = c(rep(1,40),rep(2,40),rep(3,20)))
df$group <- as.factor(df$group)
## two ways to calculate pseudo-ranks
# Variant 1: use a vector for the data and a group vector
pseudorank(df$data,df$group)
# Variant 2: use a formula object, Note that only one group factor can be used
# that is, in data~group*group2 only 'group' will be used
pseudorank(data~group,df)
Calculation of Pseudo-Ranks
Description
Calculation of (mid) pseudo-ranks of a sample. In case of ties (i.e. equal values), the average of min pseudo-rank and max-pseudor-rank are taken (similar to rank with ties.method="average").
Usage
recursiveCalculation(data, group, na.last, ties.method)
Arguments
data |
numerical vector |
group |
vector coding for the groups |
Value
Returns a numerical vector containing the pseudo-ranks