conover_test: Conover's All-Pairs Rank Comparison Test
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conover_test

R Documentation

Conover's All-Pairs Rank Comparison Test

Description

Performs Conover's test (also known as the Conover-Iman test) for pairwise multiple comparisons of the ranked data, following a significant Kruskal-Wallis test. It is closely related to dunn_test(), but uses the pooled within-group rank variance and refers the test statistic to a t-distribution (with N - k degrees of freedom) instead of the standard normal distribution. The Conover-Iman test is generally more powerful than Dunn's test, but should only be used as a post-hoc procedure when the Kruskal-Wallis test is itself significant (Conover, 1999).

If a reference group is specified (via ref.group), then each of the remaining group levels is compared only to the reference (control) group, and the p-value adjustment for multiple comparisons is computed over only these k - 1 comparisons (instead of all k(k - 1)/2 pairwise comparisons), exactly as for dunn_test().

See the Datanovia tutorial Kruskal-Wallis Test in R for a worked walkthrough.

Usage

conover_test(
  data,
  formula,
  p.adjust.method = "holm",
  ref.group = NULL,
  detailed = FALSE
)

Arguments

`data`	a data.frame containing the variables in the formula.
`formula`	a formula of the form `x ~ group` where `x` is a numeric variable giving the data values and `group` is a factor with one or multiple levels giving the corresponding groups. For example, `formula = TP53 ~ cancer_group`.
`p.adjust.method`	method to adjust p values for multiple comparisons. Used when pairwise comparisons are performed. Allowed values include "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", "none". If you don't want to adjust the p value (not recommended), use p.adjust.method = "none".
`ref.group`	a character string specifying the reference group. If specified, for a given grouping variable, each of the group levels will be compared to the reference (control) group, and the p-value adjustment is computed over only these comparisons. Note that, like `dunn_test()`, `conover_test()` does not support `ref.group = "all"`.
`detailed`	logical value. Default is FALSE. If TRUE, a detailed result is shown.

Details

The Conover-Iman pairwise statistic for comparing groups i and j is

t_{ij} = \frac{\bar{R}_i - \bar{R}_j}{\sqrt{S^2 \, \frac{N - 1 - H}{N - k} \left(\frac{1}{n_i} + \frac{1}{n_j}\right)}}

where \bar{R} are the mean ranks, H is the (tie-corrected) Kruskal-Wallis statistic, N is the total sample size, k is the number of groups, and S^2 is the variance of the ranks (S^2 = N(N+1)/12 when there are no ties; otherwise S^2 = \frac{1}{N - 1}\left(\sum r^2 - \frac{N(N+1)^2}{4}\right)). The statistic is referred to a t-distribution with N - k degrees of freedom.

In the returned table each row is oriented with i = group2 and j = group1: estimate is \bar{R}_{group2} - \bar{R}_{group1} and statistic carries its sign, the same convention as dunn_test().

The results match PMCMRplus::kwAllPairsConoverTest().

Value

return a data frame with some of the following columns:

.y.: the y (outcome) variable used in the test.
group1,group2: the compared groups in the pairwise tests.
n1,n2: Sample counts.
estimate: mean ranks difference.
estimate1, estimate2: show the mean rank values of the two groups, respectively.
statistic: Test statistic (t-value) used to compute the p-value.
df: degrees of freedom (N - k, the same for every comparison).
p: p-value.
p.adj: the adjusted p-value.
method: the statistical test used to compare groups.
p.adj.signif: the significance level of the adjusted p-values.

The returned object has an attribute called args, which is a list holding the test arguments.

References

Conover, W. J. (1999) Practical Nonparametric Statistics, 3rd edition. Wiley.

Conover, W. J. and Iman, R. L. (1979) On multiple-comparisons procedures. Technical Report LA-7677-MS, Los Alamos Scientific Laboratory.

Examples

# Simple test
ToothGrowth %>% conover_test(len ~ dose)

# Comparison against a reference (control) group
# each group is compared to the reference; the p-value
# adjustment corrects for only these k - 1 comparisons
ToothGrowth %>% conover_test(len ~ dose, ref.group = "0.5")

# Grouped data
ToothGrowth %>%
  group_by(supp) %>%
  conover_test(len ~ dose)

rstatix documentation built on July 24, 2026, 1:06 a.m.