This function performs a Kruskal-Wallis rank sum test, which is
a non-parametric method to test the null hypothesis that the population median
of all of the groups are equal. The alternative is that they differ in at
least one. Unlike the underlying base R function kruskal.test(), this
function allows for weighted tests.
kruskal_wallis_test(data, select = NULL, by = NULL, weights = NULL)A data frame.
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.
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.
Name of an (optional) weighting variable to be used for the test.
A data frame with test results.
The function simply is a wrapper around kruskal.test(). The
weighted version of the Kruskal-Wallis test is based on the survey package,
using survey::svyranktest().
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.
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
t_test() for parametric t-tests of dependent and independent samples.
mann_whitney_test() for non-parametric tests of unpaired (independent)
samples.
wilcoxon_test() for Wilcoxon rank sum tests for non-parametric tests
of paired (dependent) samples.
kruskal_wallis_test() for non-parametric tests with more than two
independent samples.
chi_squared_test() for chi-squared tests (two categorical variables,
dependent and independent).
data(efc)
# Kruskal-Wallis test for elder's age by education
kruskal_wallis_test(efc, "e17age", by = "c172code")
#> # Kruskal-Wallis test
#>
#> Data: e17age by c172code (3 groups, n = 506, 180 and 156)
#>
#> χ² = 4.05, df = 2, p = 0.132
#>
# 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),
scale3 = runif(20)
)
kruskal_wallis_test(wide_data, select = c("scale1", "scale2", "scale3"))
#> # Kruskal-Wallis test
#>
#> Data: scale1 by scale2 (3 groups, n = 20, 20 and 20)
#>
#> χ² = 4.86, df = 2, p = 0.088
#>
# same as if we had data in long format, with grouping variable
long_data <- data.frame(
scales = c(wide_data$scale1, wide_data$scale2, wide_data$scale3),
groups = rep(c("A", "B", "C"), each = 20)
)
kruskal_wallis_test(long_data, select = "scales", by = "groups")
#> # Kruskal-Wallis test
#>
#> Data: scales by groups (3 groups, n = 20, 20 and 20)
#>
#> χ² = 4.86, df = 2, p = 0.088
#>
# base R equivalent
kruskal.test(scales ~ groups, data = long_data)
#>
#> Kruskal-Wallis rank sum test
#>
#> data: scales by groups
#> Kruskal-Wallis chi-squared = 4.8633, df = 2, p-value = 0.08789
#>