mann_whitney_test: Mann-Whitney test
In sjstats: Collection of Convenient Functions for Common Statistical Computations

mann_whitney_test

R Documentation

Mann-Whitney test

Description

This function performs a Mann-Whitney test (or Wilcoxon rank sum test for unpaired samples). Unlike the underlying base R function wilcox.test(), this function allows for weighted tests and automatically calculates effect sizes. For paired (dependent) samples, or for one-sample tests, please use the wilcoxon_test() function.

A Mann-Whitney test is a non-parametric test for the null hypothesis that two independent samples have identical continuous distributions. It can be used for ordinal scales or when the two continuous variables are not normally distributed. For large samples, or approximately normally distributed variables, the t_test() function can be used.

Usage

mann_whitney_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`).

Details

This function is based on wilcox.test() and coin::wilcox_test() (the latter to extract effect sizes). The weighted version of the test is based on survey::svyranktest().

Interpretation of the effect size r, as a rule-of-thumb:

small effect >= 0.1
medium effect >= 0.3
large effect >= 0.5

r is calcuated as r = \frac{|Z|}{\sqrt{n1 + n2}}.

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

Ben-Shachar, M.S., Patil, I., Thériault, R., Wiernik, B.M., Lüdecke, D. (2023). Phi, Fei, Fo, Fum: Effect Sizes for Categorical Data That Use the Chi‑Squared Statistic. Mathematics, 11, 1982. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3390/math11091982")}
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(efc)
# Mann-Whitney-U tests for elder's age by elder's sex.
mann_whitney_test(efc, "e17age", by = "e16sex")
# base R equivalent
wilcox.test(e17age ~ e16sex, data = efc)

# when data is in wide-format, specify all relevant continuous
# variables in `select` and omit `by`
set.seed(123)
wide_data <- data.frame(scale1 = runif(20), scale2 = runif(20))
mann_whitney_test(wide_data, select = c("scale1", "scale2"))
# base R equivalent
wilcox.test(wide_data$scale1, wide_data$scale2)
# same as if we had data in long format, with grouping variable
long_data <- data.frame(
  scales = c(wide_data$scale1, wide_data$scale2),
  groups = as.factor(rep(c("A", "B"), each = 20))
)
mann_whitney_test(long_data, select = "scales", by = "groups")
# base R equivalent
wilcox.test(scales ~ groups, long_data)

sjstats documentation built on May 29, 2024, 12:09 p.m.