Wilcoxon rank sum test

This function performs Wilcoxon rank sum tests for one sample or for two paired (dependent) samples. For unpaired (independent) samples, please use the mann_whitney_test() function.

A Wilcoxon rank sum test is a non-parametric test for the null hypothesis that two samples have identical continuous distributions. The implementation in wilcoxon_test() is only used for paired, i.e. dependent samples. For independent (unpaired) samples, use mann_whitney_test().

wilcoxon_test() can be used for ordinal scales or when the continuous variables are not normally distributed. For large samples, or approximately normally distributed variables, the t_test() function can be used (with paired = TRUE).

wilcoxon_test(
  data,
  select = NULL,
  by = NULL,
  weights = NULL,
  mu = 0,
  alternative = "two.sided",
  ...
)

Arguments

data

A data frame.

select

Name(s) of the continuous variable(s) (as character vector) to be used as samples for the test. select can be one of the following:

select can be used in combination with by, in which case select is the name of the continous variable (and by indicates a grouping factor).
select can also be a character vector of length two or more (more than two names only apply to kruskal_wallis_test()), in which case the two continuous variables are treated as samples to be compared. by must be NULL in this case.
If select select is of length two and paired = TRUE, the two samples are considered as dependent and a paired test is carried out.
If select specifies one variable and by = NULL, a one-sample test is carried out (only applicable for t_test() and wilcoxon_test())
For chi_squared_test(), if select specifies one variable and both by and probabilities are NULL, a one-sample test against given probabilities is automatically conducted, with equal probabilities for each level of select.

by

Name of the variable indicating the groups. Required if select specifies only one variable that contains all samples to be compared in the test. If by is not a factor, it will be coerced to a factor. For chi_squared_test(), if probabilities is provided, by must be NULL.

weights

Name of an (optional) weighting variable to be used for the test.

mu

The hypothesized difference in means (for t_test()) or location shift (for wilcoxon_test() and mann_whitney_test()). The default is 0.

alternative

A character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". See ?t.test and ?wilcox.test.

...

Additional arguments passed to wilcox.test() (for unweighted tests, i.e. when weights = NULL).

Value

A data frame with test results. The function returns p and Z-values as well as effect size r and group-rank-means.

Which test to use

The following table provides an overview of which test to use for different types of data. The choice of test depends on the scale of the outcome variable and the number of samples to compare.

Samples	Scale of Outcome	Significance Test
1	binary / nominal	`chi_squared_test()`
1	continuous, not normal	`wilcoxon_test()`
1	continuous, normal	`t_test()`
2, independent	binary / nominal	`chi_squared_test()`
2, independent	continuous, not normal	`mann_whitney_test()`
2, independent	continuous, normal	`t_test()`
2, dependent	binary (only 2x2)	`chi_squared_test(paired=TRUE)`
2, dependent	continuous, not normal	`wilcoxon_test()`
2, dependent	continuous, normal	`t_test(paired=TRUE)`
>2, independent	continuous, not normal	`kruskal_wallis_test()`
>2, independent	continuous, normal	`datawizard::means_by_group()`
>2, dependent	continuous, not normal	not yet implemented (1)
>2, dependent	continuous, normal	not yet implemented (2)

(1) More than two dependent samples are considered as repeated measurements. For ordinal or not-normally distributed outcomes, these samples are usually tested using a friedman.test(), which requires the samples in one variable, the groups to compare in another variable, and a third variable indicating the repeated measurements (subject IDs).

(2) More than two dependent samples are considered as repeated measurements. For normally distributed outcomes, these samples are usually tested using a ANOVA for repeated measurements. A more sophisticated approach would be using a linear mixed model.

References

Bender, R., Lange, S., Ziegler, A. Wichtige Signifikanztests. Dtsch Med Wochenschr 2007; 132: e24–e25
du Prel, J.B., Röhrig, B., Hommel, G., Blettner, M. Auswahl statistischer Testverfahren. Dtsch Arztebl Int 2010; 107(19): 343–8

Examples

data(mtcars)
# one-sample test
wilcoxon_test(mtcars, "mpg")
#> # One Sample Wilcoxon signed rank test
#> 
#>   Alternative hypothesis: true location shift is not equal to 0
#> 
#>   V = 528, p < .001
#> 
# base R equivalent, we set exact = FALSE to avoid a warning
wilcox.test(mtcars$mpg ~ 1, exact = FALSE)
#> 
#> 	Wilcoxon signed rank test with continuity correction
#> 
#> data:  mtcars$mpg
#> V = 528, p-value = 8.311e-07
#> alternative hypothesis: true location is not equal to 0
#> 

# paired test
wilcoxon_test(mtcars, c("mpg", "hp"))
#> # Paired Wilcoxon signed rank test
#> 
#>   Alternative hypothesis: true location shift is not equal to 0
#> 
#>   V = 0, r = 0.87, Z = -4.94, p < .001
#> 
# base R equivalent, we set exact = FALSE to avoid a warning
wilcox.test(mtcars$mpg, mtcars$hp, paired = TRUE, exact = FALSE)
#> 
#> 	Wilcoxon signed rank test with continuity correction
#> 
#> data:  mtcars$mpg and mtcars$hp
#> V = 0, p-value = 8.338e-07
#> alternative hypothesis: true location shift is not equal to 0
#> 

# when `by` is specified, each group must be of same length
data(iris)
d <- iris[iris$Species != "setosa", ]
wilcoxon_test(d, "Sepal.Width", by = "Species")
#> # Paired Wilcoxon signed rank test
#> 
#>   Alternative hypothesis: true location shift is not equal to 0
#> 
#>   V = 247, r = 0.39, Z = -2.76, p = 0.006
#>

Arguments

Value

Which test to use

References

See also

Examples