,
Georg Zimmermann [aut],
Arne C. Bathke [aut],
Edgar Brunner [aut]| Title: | Pseudo-Ranks |
|---|---|
| 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. |
| Authors: | Martin Happ [aut, cre] ,
Georg Zimmermann [aut],
Arne C. Bathke [aut],
Edgar Brunner [aut] |
| Maintainer: | Martin Happ <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0.4 |
| Built: | 2025-02-21 05:23:10 UTC |
| Source: | https://github.com/happma/pseudorank |
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.
Maintainer: Martin Happ <[email protected]>
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).
This function calculates the Hettmansperger-Norton trend test using pseudo-ranks under the null hypothesis H0F: F_1 = ... F_k.
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, ... )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, ... )
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) |
Returns an object.
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
# 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))# 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))
This function calculates the Kruskal-Wallis test using pseudo-ranks under the null hypothesis H0F: F_1 = ... F_k.
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, ...)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, ...)
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 |
Returns an object of class 'pseudorank'
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.
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)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)
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.
data(ParadoxicalRanks)data(ParadoxicalRanks)
A data frame with 54 rows and 2 variables.
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.
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).
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")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")
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").
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"), ... )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"), ... )
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) |
Returns a numerical vector containing the pseudo-ranks.
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).
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)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 (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").
psrank(x, ...)psrank(x, ...)
x |
vector containing the observations |
... |
further arguments (see help for pseudorank) |
Returns a numerical vector containing the pseudo-ranks.
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).
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)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)