diff --git a/DESCRIPTION b/DESCRIPTION
index 5aec96ffa..a2bf90f45 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,7 +1,7 @@
 Type: Package
 Package: parameters
 Title: Processing of Model Parameters
-Version: 0.22.2.8
+Version: 0.22.2.9
 Authors@R:
     c(person(given = "Daniel",
              family = "Lüdecke",
diff --git a/NEWS.md b/NEWS.md
index 39b9a541d..d8cda798b 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -12,6 +12,10 @@
 * `p_function()` gets a `vcov` and `vcov_args` argument to compute robust
   standard errors for the confidence curves.
 
+* Functions `p_significance()` and `equivalence_test()` now pass arguments
+  `vcov` and `vcov_args` to `p_value()` and `ci()`, hence, tests can be based
+  on robust standard errors.
+
 * Revision / enhancement of some documentation.
 
 # parameters 0.22.2
diff --git a/R/2_ci.R b/R/2_ci.R
index 79e3e59da..c010dcf37 100644
--- a/R/2_ci.R
+++ b/R/2_ci.R
@@ -24,13 +24,25 @@
 #' @param iterations The number of bootstrap replicates. Only applies to models
 #'   of class `merMod` when `method=boot`.
 #' @param verbose Toggle warnings and messages.
-#' @param ... Additional arguments
+#' @param ... Additional arguments passed down to the underlying functions.
+#' E.g., arguments like `vcov` or `vcov_args` can be used to compute confidence
+#' intervals using a specific variance-covariance matrix for the standard
+#' errors.
 #'
 #' @return A data frame containing the CI bounds.
 #'
 #' @inheritSection model_parameters Confidence intervals and approximation of degrees of freedom
 #'
-#' @examplesIf require("glmmTMB")
+#' @examplesIf require("glmmTMB") && requireNamespace("sandwich")
+#' data(qol_cancer)
+#' model <- lm(QoL ~ time + age + education, data = qol_cancer)
+#'
+#' # regular confidence intervals
+#' ci(model)
+#'
+#' # using heteroscedasticity-robust standard errors
+#' ci(model, vcov = "HC3")
+#'
 #' \donttest{
 #' library(parameters)
 #' data(Salamanders, package = "glmmTMB")
diff --git a/R/equivalence_test.R b/R/equivalence_test.R
index 3d2b44ea5..71f07d11f 100644
--- a/R/equivalence_test.R
+++ b/R/equivalence_test.R
@@ -19,7 +19,10 @@ bayestestR::equivalence_test
 #' See [`?ggeffects::test_predictions`](https://strengejacke.github.io/ggeffects/reference/test_predictions.html)
 #' for details.
 #' @param verbose Toggle warnings and messages.
-#' @param ... Arguments passed to or from other methods.
+#' @param ... Arguments passed to or from other methods, e.g. `ci()`. Arguments
+#' like `vcov` or `vcov_args` can be used to compute confidence intervals or
+#' p-values using a specific variance-covariance matrix for the standard
+#' errors..
 #' @inheritParams model_parameters.merMod
 #' @inheritParams p_value
 #'
@@ -218,13 +221,16 @@ bayestestR::equivalence_test
 #'     Synthese 200, 89 (2022). \doi{10.1007/s11229-022-03560-x}
 #'
 #' @return A data frame.
-#' @examples
+#' @examplesIf requireNamespace("sandwich")
 #' data(qol_cancer)
 #' model <- lm(QoL ~ time + age + education, data = qol_cancer)
 #'
 #' # default rule
 #' equivalence_test(model)
 #'
+#' # using heteroscedasticity-robust standard errors
+#' equivalence_test(model, vcov = "HC3")
+#'
 #' # conditional equivalence test
 #' equivalence_test(model, rule = "cet")
 #'
@@ -504,14 +510,14 @@ equivalence_test.ggeffects <- function(x,
 
   # ==== requested confidence intervals ====
 
-  params <- conf_int <- .ci_generic(x, ci = ci)
+  params <- conf_int <- .ci_generic(x, ci = ci, ...)
   conf_int <- as.data.frame(t(conf_int[, c("CI_low", "CI_high")]))
 
 
   # ==== the "narrower" intervals (1-2*alpha) for CET-rules. ====
 
   alpha <- 1 - ci
-  conf_int2 <- .ci_generic(x, ci = (ci - alpha))
+  conf_int2 <- .ci_generic(x, ci = (ci - alpha), ...)
   conf_int2 <- as.data.frame(t(conf_int2[, c("CI_low", "CI_high")]))
 
 
@@ -544,7 +550,7 @@ equivalence_test.ggeffects <- function(x,
 
   # ==== (adjusted) p-values for tests ====
 
-  out$p <- .add_p_to_equitest(x, ci, range)
+  out$p <- .add_p_to_equitest(x, ci, range, ...)
 
   attr(out, "rope") <- range
   out
@@ -786,7 +792,7 @@ equivalence_test.ggeffects <- function(x,
 }
 
 
-.add_p_to_equitest <- function(model, ci, range) {
+.add_p_to_equitest <- function(model, ci, range, ...) {
   tryCatch(
     {
       params <- insight::get_parameters(model)
@@ -798,7 +804,7 @@ equivalence_test.ggeffects <- function(x,
       params$mu <- params$Estimate * -1
 
       # se
-      se <- standard_error(model)
+      se <- standard_error(model, ...)
 
       stats::pt((range[1] - params$mu) / se$SE, df = dof, lower.tail = TRUE) +
         stats::pt((range[2] - params$mu) / se$SE, df = dof, lower.tail = FALSE)
diff --git a/R/p_direction.R b/R/p_direction.R
index 4030cbc85..c0d975663 100644
--- a/R/p_direction.R
+++ b/R/p_direction.R
@@ -16,7 +16,9 @@ bayestestR::p_direction
 #' @param x A statistical model.
 #' @inheritParams bayestestR::p_direction
 #' @inheritParams model_parameters.default
-#' @param ... Arguments passed to other methods, e.g. `ci()`.
+#' @param ... Arguments passed to other methods, e.g. `ci()`. Arguments like
+#' `vcov` or `vcov_args` can be used to compute confidence intervals using a
+#' specific variance-covariance matrix for the standard errors.
 #'
 #' @seealso See also [`equivalence_test()`], [`p_function()`] and
 #' [`p_significance()`] for functions related to checking effect existence and
@@ -70,11 +72,14 @@ bayestestR::p_direction
 #'
 #' @return A data frame.
 #'
-#' @examplesIf requireNamespace("bayestestR") && require("see", quietly = TRUE)
+#' @examplesIf requireNamespace("bayestestR") && require("see", quietly = TRUE) && requireNamespace("sandwich")
 #' data(qol_cancer)
 #' model <- lm(QoL ~ time + age + education, data = qol_cancer)
 #' p_direction(model)
 #'
+#' # based on heteroscedasticity-robust standard errors
+#' p_direction(model, vcov = "HC3")
+#'
 #' result <- p_direction(model)
 #' plot(result)
 #' @export
diff --git a/R/p_function.R b/R/p_function.R
index 54596f701..cfb5aeda3 100644
--- a/R/p_function.R
+++ b/R/p_function.R
@@ -119,9 +119,11 @@
 #' whereas values values far from the observed point estimate (where _p_
 #' approaches 0) are least compatible with the data and model assumptions
 #' (_Schweder and Hjort 2016, pp. 60-61; Amrhein and Greenland 2022_). In this
-#' regards, _p_-values are are statements about confidence/compatibility, not
-#' probability per se, but still the interpretation of _p_-values might be
-#' guided using [`bayestestR::p_to_pd()`]
+#' regards, _p_-values are statements about _confidence_ or _compatibility_ and
+#' can be considered as _epistemic probability_ - "not necessarily of the
+#' hypothesis being true, but of it _possibly_ being true" (_Schweder 2018_).
+#' Hence, the interpretation of _p_-values might be guided using
+#' [`bayestestR::p_to_pd()`]
 #'
 #' ## Compatibility intervals - is their interpretation conditional or not?
 #'
diff --git a/R/p_significance.R b/R/p_significance.R
index 2629d793f..d22e06e7d 100644
--- a/R/p_significance.R
+++ b/R/p_significance.R
@@ -28,7 +28,9 @@ bayestestR::p_significance
 #' @inheritParams bayestestR::p_significance
 #' @inheritParams model_parameters.default
 #' @param verbose Toggle warnings and messages.
-#' @param ... Arguments passed to other methods, e.g. `ci()`.
+#' @param ... Arguments passed to other methods, e.g. `ci()`. Arguments like
+#' `vcov` or `vcov_args` can be used to compute confidence intervals using a
+#' specific variance-covariance matrix for the standard errors.
 #'
 #' @seealso For more details, see [`bayestestR::p_significance()`]. See also
 #' [`equivalence_test()`], [`p_function()`] and [`bayestestR::p_direction()`]
@@ -126,14 +128,16 @@ bayestestR::p_significance
 #' intervals and the values for practical significance. Higher values indicate
 #' more practical significance (upper bound is one).
 #'
-#' @examplesIf requireNamespace("bayestestR") && packageVersion("bayestestR") > "0.14.0"
+#' @examplesIf requireNamespace("bayestestR") && packageVersion("bayestestR") > "0.14.0" && requireNamespace("sandwich")
 #' data(qol_cancer)
 #' model <- lm(QoL ~ time + age + education, data = qol_cancer)
 #'
 #' p_significance(model)
 #' p_significance(model, threshold = c(-0.5, 1.5))
 #'
-#' # plot method
+#' # based on heteroscedasticity-robust standard errors
+#' p_significance(model, vcov = "HC3")
+#'
 #' if (require("see", quietly = TRUE)) {
 #'   result <- p_significance(model)
 #'   plot(result)
diff --git a/man/ci.default.Rd b/man/ci.default.Rd
index 2e86093f1..e1ca2e1eb 100644
--- a/man/ci.default.Rd
+++ b/man/ci.default.Rd
@@ -40,7 +40,10 @@ options (which vary depending on the model class): \code{"residual"},
 \emph{Confidence intervals and approximation of degrees of freedom} in
 \code{\link[=model_parameters]{model_parameters()}} for further details.}
 
-\item{...}{Additional arguments}
+\item{...}{Additional arguments passed down to the underlying functions.
+E.g., arguments like \code{vcov} or \code{vcov_args} can be used to compute confidence
+intervals using a specific variance-covariance matrix for the standard
+errors.}
 
 \item{component}{Model component for which parameters should be shown. See
 the documentation for your object's class in \code{\link[=model_parameters]{model_parameters()}} or
@@ -224,7 +227,16 @@ which is converted into a p-value using \code{\link[bayestestR:pd_to_p]{bayestes
 }
 
 \examples{
-\dontshow{if (require("glmmTMB")) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf}
+\dontshow{if (require("glmmTMB") && requireNamespace("sandwich")) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf}
+data(qol_cancer)
+model <- lm(QoL ~ time + age + education, data = qol_cancer)
+
+# regular confidence intervals
+ci(model)
+
+# using heteroscedasticity-robust standard errors
+ci(model, vcov = "HC3")
+
 \donttest{
 library(parameters)
 data(Salamanders, package = "glmmTMB")
diff --git a/man/cluster_analysis.Rd b/man/cluster_analysis.Rd
index 7d2e9cd81..c7659aeeb 100644
--- a/man/cluster_analysis.Rd
+++ b/man/cluster_analysis.Rd
@@ -69,7 +69,10 @@ this argument.}
 
 \item{iterations}{The number of replications.}
 
-\item{...}{Arguments passed to or from other methods.}
+\item{...}{Arguments passed to or from other methods, e.g. \code{ci()}. Arguments
+like \code{vcov} or \code{vcov_args} can be used to compute confidence intervals or
+p-values using a specific variance-covariance matrix for the standard
+errors..}
 }
 \value{
 The group classification for each observation as vector. The
diff --git a/man/equivalence_test.lm.Rd b/man/equivalence_test.lm.Rd
index 8796960d9..9e8ec0b0c 100644
--- a/man/equivalence_test.lm.Rd
+++ b/man/equivalence_test.lm.Rd
@@ -48,7 +48,10 @@ equivalence. Can be \code{"bayes"}, \code{"classic"} or \code{"cet"}. See 'Detai
 
 \item{verbose}{Toggle warnings and messages.}
 
-\item{...}{Arguments passed to or from other methods.}
+\item{...}{Arguments passed to or from other methods, e.g. \code{ci()}. Arguments
+like \code{vcov} or \code{vcov_args} can be used to compute confidence intervals or
+p-values using a specific variance-covariance matrix for the standard
+errors..}
 
 \item{effects}{Should parameters for fixed effects (\code{"fixed"}), random
 effects (\code{"random"}), or both (\code{"all"}) be returned? Only applies
@@ -249,12 +252,16 @@ documentation in \code{\link[=p_function]{p_function()}}).
 }
 
 \examples{
+\dontshow{if (requireNamespace("sandwich")) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf}
 data(qol_cancer)
 model <- lm(QoL ~ time + age + education, data = qol_cancer)
 
 # default rule
 equivalence_test(model)
 
+# using heteroscedasticity-robust standard errors
+equivalence_test(model, vcov = "HC3")
+
 # conditional equivalence test
 equivalence_test(model, rule = "cet")
 
@@ -263,6 +270,7 @@ if (require("see", quietly = TRUE)) {
   result <- equivalence_test(model)
   plot(result)
 }
+\dontshow{\}) # examplesIf}
 }
 \references{
 \itemize{
diff --git a/man/p_direction.lm.Rd b/man/p_direction.lm.Rd
index c057861be..2337eefe2 100644
--- a/man/p_direction.lm.Rd
+++ b/man/p_direction.lm.Rd
@@ -17,7 +17,9 @@ such as \code{"kernel"}, \code{"logspline"} or \code{"KernSmooth"}. See details.
 \item{null}{The value considered as a "null" effect. Traditionally 0, but
 could also be 1 in the case of ratios of change (OR, IRR, ...).}
 
-\item{...}{Arguments passed to other methods, e.g. \code{ci()}.}
+\item{...}{Arguments passed to other methods, e.g. \code{ci()}. Arguments like
+\code{vcov} or \code{vcov_args} can be used to compute confidence intervals using a
+specific variance-covariance matrix for the standard errors.}
 }
 \value{
 A data frame.
@@ -150,11 +152,14 @@ documentation in \code{\link[=p_function]{p_function()}}).
 }
 
 \examples{
-\dontshow{if (requireNamespace("bayestestR") && require("see", quietly = TRUE)) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf}
+\dontshow{if (requireNamespace("bayestestR") && require("see", quietly = TRUE) && requireNamespace("sandwich")) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf}
 data(qol_cancer)
 model <- lm(QoL ~ time + age + education, data = qol_cancer)
 p_direction(model)
 
+# based on heteroscedasticity-robust standard errors
+p_direction(model, vcov = "HC3")
+
 result <- p_direction(model)
 plot(result)
 \dontshow{\}) # examplesIf}
diff --git a/man/p_function.Rd b/man/p_function.Rd
index b7b2be9c0..77a587a17 100644
--- a/man/p_function.Rd
+++ b/man/p_function.Rd
@@ -248,9 +248,11 @@ estimated to be \emph{most compatible} with the data and model assumptions,
 whereas values values far from the observed point estimate (where \emph{p}
 approaches 0) are least compatible with the data and model assumptions
 (\emph{Schweder and Hjort 2016, pp. 60-61; Amrhein and Greenland 2022}). In this
-regards, \emph{p}-values are are statements about confidence/compatibility, not
-probability per se, but still the interpretation of \emph{p}-values might be
-guided using \code{\link[bayestestR:pd_to_p]{bayestestR::p_to_pd()}}
+regards, \emph{p}-values are statements about \emph{confidence} or \emph{compatibility} and
+can be considered as \emph{epistemic probability} - "not necessarily of the
+hypothesis being true, but of it \emph{possibly} being true" (\emph{Schweder 2018}).
+Hence, the interpretation of \emph{p}-values might be guided using
+\code{\link[bayestestR:pd_to_p]{bayestestR::p_to_pd()}}
 }
 
 \subsection{Compatibility intervals - is their interpretation conditional or not?}{
diff --git a/man/p_significance.lm.Rd b/man/p_significance.lm.Rd
index 4c598e487..37a0adb36 100644
--- a/man/p_significance.lm.Rd
+++ b/man/p_significance.lm.Rd
@@ -25,7 +25,9 @@ asymmetric intervals.
 
 \item{verbose}{Toggle warnings and messages.}
 
-\item{...}{Arguments passed to other methods, e.g. \code{ci()}.}
+\item{...}{Arguments passed to other methods, e.g. \code{ci()}. Arguments like
+\code{vcov} or \code{vcov_args} can be used to compute confidence intervals using a
+specific variance-covariance matrix for the standard errors.}
 }
 \value{
 A data frame with columns for the parameter names, the confidence
@@ -151,14 +153,16 @@ documentation in \code{\link[=p_function]{p_function()}}).
 }
 
 \examples{
-\dontshow{if (requireNamespace("bayestestR") && packageVersion("bayestestR") > "0.14.0") (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf}
+\dontshow{if (requireNamespace("bayestestR") && packageVersion("bayestestR") > "0.14.0" && requireNamespace("sandwich")) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf}
 data(qol_cancer)
 model <- lm(QoL ~ time + age + education, data = qol_cancer)
 
 p_significance(model)
 p_significance(model, threshold = c(-0.5, 1.5))
 
-# plot method
+# based on heteroscedasticity-robust standard errors
+p_significance(model, vcov = "HC3")
+
 if (require("see", quietly = TRUE)) {
   result <- p_significance(model)
   plot(result)
diff --git a/man/p_value_betwithin.Rd b/man/p_value_betwithin.Rd
index 17d814646..9f2c7069d 100644
--- a/man/p_value_betwithin.Rd
+++ b/man/p_value_betwithin.Rd
@@ -18,7 +18,10 @@ p_value_betwithin(model, dof = NULL, ...)
 
 \item{ci}{Confidence Interval (CI) level. Default to \code{0.95} (\verb{95\%}).}
 
-\item{...}{Additional arguments}
+\item{...}{Additional arguments passed down to the underlying functions.
+E.g., arguments like \code{vcov} or \code{vcov_args} can be used to compute confidence
+intervals using a specific variance-covariance matrix for the standard
+errors.}
 
 \item{dof}{Degrees of Freedom.}
 }
diff --git a/man/p_value_ml1.Rd b/man/p_value_ml1.Rd
index 0fb9229f6..c272fe8d9 100644
--- a/man/p_value_ml1.Rd
+++ b/man/p_value_ml1.Rd
@@ -17,7 +17,10 @@ p_value_ml1(model, dof = NULL, ...)
 
 \item{ci}{Confidence Interval (CI) level. Default to \code{0.95} (\verb{95\%}).}
 
-\item{...}{Additional arguments}
+\item{...}{Additional arguments passed down to the underlying functions.
+E.g., arguments like \code{vcov} or \code{vcov_args} can be used to compute confidence
+intervals using a specific variance-covariance matrix for the standard
+errors.}
 
 \item{dof}{Degrees of Freedom.}
 }
diff --git a/man/p_value_satterthwaite.Rd b/man/p_value_satterthwaite.Rd
index 5ac41192c..ebe3586b3 100644
--- a/man/p_value_satterthwaite.Rd
+++ b/man/p_value_satterthwaite.Rd
@@ -21,7 +21,10 @@ se_satterthwaite(model)
 
 \item{ci}{Confidence Interval (CI) level. Default to \code{0.95} (\verb{95\%}).}
 
-\item{...}{Additional arguments}
+\item{...}{Additional arguments passed down to the underlying functions.
+E.g., arguments like \code{vcov} or \code{vcov_args} can be used to compute confidence
+intervals using a specific variance-covariance matrix for the standard
+errors.}
 
 \item{dof}{Degrees of Freedom.}
 }
diff --git a/tests/testthat/_snaps/equivalence_test.md b/tests/testthat/_snaps/equivalence_test.md
index 8bec29040..325858efa 100644
--- a/tests/testthat/_snaps/equivalence_test.md
+++ b/tests/testthat/_snaps/equivalence_test.md
@@ -15,3 +15,20 @@
       cyl         | [-1.94,  0.32] | 0.351  |   Undecided | 0.644 
       hp          | [-0.05,  0.01] | > .999 |    Accepted | < .001
 
+# equivalence_test, robust
+
+    Code
+      print(x)
+    Output
+      # TOST-test for Practical Equivalence
+      
+        ROPE: [-0.60 0.60]
+      
+      Parameter   |         90% CI |   SGPV | Equivalence |      p
+      ------------------------------------------------------------
+      (Intercept) | [23.10, 50.28] | < .001 |    Rejected | > .999
+      gear        | [-1.63,  2.36] | 0.421  |   Undecided | 0.628 
+      wt          | [-4.59, -1.45] | 0.001  |    Rejected | 0.993 
+      cyl         | [-2.24,  0.62] | 0.361  |   Undecided | 0.649 
+      hp          | [-0.05,  0.01] | > .999 |    Accepted | < .001
+
diff --git a/tests/testthat/_snaps/p_significance.md b/tests/testthat/_snaps/p_significance.md
index b80688ac1..81b4cb7ce 100644
--- a/tests/testthat/_snaps/p_significance.md
+++ b/tests/testthat/_snaps/p_significance.md
@@ -13,3 +13,18 @@
       cyl         | [-2.17,  0.55] | 61.88%
       hp          | [-0.05,  0.01] |  0.00%
 
+# p_significance, robust
+
+    Code
+      print(x)
+    Output
+      Practical Significance (threshold: -0.60, 0.60)
+      
+      Parameter   |         95% CI |     ps
+      -------------------------------------
+      (Intercept) | [20.32, 53.06] |   100%
+      gear        | [-2.04,  2.77] | 41.23%
+      wt          | [-4.91, -1.13] | 99.39%
+      cyl         | [-2.53,  0.91] | 59.51%
+      hp          | [-0.06,  0.01] |  0.00%
+
diff --git a/tests/testthat/test-equivalence_test.R b/tests/testthat/test-equivalence_test.R
index 3c95f7625..e358b690d 100644
--- a/tests/testthat/test-equivalence_test.R
+++ b/tests/testthat/test-equivalence_test.R
@@ -10,6 +10,14 @@ test_that("equivalence_test", {
   expect_snapshot(print(x))
 })
 
+test_that("equivalence_test, robust", {
+  skip_if_not_installed("sandwich")
+  data(mtcars)
+  m <- lm(mpg ~ gear + wt + cyl + hp, data = mtcars)
+  x <- equivalence_test(m, vcov = "HC3")
+  expect_snapshot(print(x))
+})
+
 test_that("equivalence_test, unequal rope-range", {
   data(iris)
   m <- lm(Sepal.Length ~ Species, data = iris)
diff --git a/tests/testthat/test-p_function.R b/tests/testthat/test-p_function.R
index 9d937aef4..c1090a2cf 100644
--- a/tests/testthat/test-p_function.R
+++ b/tests/testthat/test-p_function.R
@@ -1,5 +1,3 @@
-skip_if_not_installed("sandwich")
-
 data(iris)
 model <- lm(Sepal.Length ~ Species, data = iris)
 
@@ -43,6 +41,7 @@ test_that("p_function ci-levels", {
     tolerance = 1e-4
   )
 
+  skip_if_not_installed("sandwich")
   out <- p_function(model, vcov = "HC3")
   expect_equal(
     out$CI_low,
diff --git a/tests/testthat/test-p_significance.R b/tests/testthat/test-p_significance.R
index 7ec769851..092abf8bf 100644
--- a/tests/testthat/test-p_significance.R
+++ b/tests/testthat/test-p_significance.R
@@ -39,3 +39,12 @@ test_that("p_significance, glmmTMB", {
     )
   )
 })
+
+test_that("p_significance, robust", {
+  skip_if_not_installed("sandwich")
+  data(mtcars)
+  m <- lm(mpg ~ gear + wt + cyl + hp, data = mtcars)
+  set.seed(123)
+  x <- p_significance(m, vcov = "HC3")
+  expect_snapshot(print(x))
+})