diff --git a/NAMESPACE b/NAMESPACE
index 33bf3bd..1741137 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -11,6 +11,8 @@ importFrom(broom.mixed,tidy)
 importFrom(crayon,bold)
 importFrom(crayon,italic)
 importFrom(crayon,underline)
+importFrom(dplyr,"%>%")
+importFrom(dplyr,arrange)
 importFrom(dplyr,bind_cols)
 importFrom(dplyr,case_when)
 importFrom(dplyr,filter)
@@ -49,6 +51,7 @@ importFrom(lavaan,sem)
 importFrom(lme4,fixef)
 importFrom(lme4,lmer)
 importFrom(pbkrtest,get_Lb_ddf)
+importFrom(ppcor,pcor)
 importFrom(purrr,map2_dfr)
 importFrom(purrr,map_dbl)
 importFrom(purrr,modify_if)
diff --git a/man/konfound.Rd b/man/konfound.Rd
index c00dd1b..4a9c7ab 100644
--- a/man/konfound.Rd
+++ b/man/konfound.Rd
@@ -67,15 +67,7 @@ if (requireNamespace("forcats")) {
   m2 <- glm(married ~ age, data = d, family = binomial(link = "logit"))
   konfound(m2, age)
 }
-
-# using lme4 for mixed effects (or multi-level) models
-if (requireNamespace("lme4")) {
-  library(lme4)
-  m3 <- fm1 <- lme4::lmer(Reaction ~ Days + (1 | Subject), sleepstudy)
-  konfound(m3, Days)
-}
-
-m4 <- glm(outcome ~ condition, data = binary_dummy_data, family = binomial(link = "logit"))
-konfound(m4, condition, two_by_two = TRUE, n_treat = 55)
+m3 <- glm(outcome ~ condition, data = binary_dummy_data, family = binomial(link = "logit"))
+konfound(m3, condition, two_by_two = TRUE, n_treat = 55)
 
 }
diff --git a/man/output_print.Rd b/man/output_print.Rd
index e6cb9ea..6574314 100644
--- a/man/output_print.Rd
+++ b/man/output_print.Rd
@@ -26,7 +26,9 @@ output_print(
   rxcv = NA,
   rycv = NA,
   rxcvGz,
-  rycvGz
+  rycvGz,
+  benchmark_corr_product = NA,
+  itcv_ratio_to_benchmark = NA
 )
 }
 \arguments{
@@ -74,6 +76,10 @@ statistical significance determination.}
 \item{rxcvGz}{the correlation between predictor of interest and CV necessary to nullify the inference for smallest impact, conditioning on all observed covariates.}
 
 \item{rycvGz}{the correlation between outcome and CV necessary to nullify the inference for smallest impact, conditioning on all observed covariates.}
+
+\item{benchmark_corr_product}{the product of the correlations of covariates Z with X and Y (Rxz * Ryz), measuring the observed association strength.}
+
+\item{itcv_ratio_to_benchmark}{the ratio of the ITCV to the benchmark_corr_product, indicating the robustness of inference.}
 }
 \description{
 This function outputs printed text for various indices such as RIR
diff --git a/tests/testthat/test-konfound.R b/tests/testthat/test-konfound.R
index 9c4ba26..cc3b4f7 100644
--- a/tests/testthat/test-konfound.R
+++ b/tests/testthat/test-konfound.R
@@ -33,14 +33,14 @@ output4 <- konfound(m4, condition, two_by_two = TRUE, n_treat = 55, to_return =
 # })
 
 test_that("konfound works for glm, 2x2 model", {
-    expect_equal(output4$RIR, 15)
+    expect_equal(output4$RIR_primary, 15)
 })
 
 m5 <- lm(mpg ~ wt + hp, data = mtcars)
-output5 <- konfound(m1, wt, to_return = "table")
+output5 <- konfound(m5, wt, to_return = "table")
 
 test_that("konfound returns a tibble", {
-    expect_s3_class(output5, "tbl_df")
+    expect_s3_class(output5$Main_Output, "tbl_df")
 })
 
 gss_cat$married <- ifelse(gss_cat$marital == "Married", 1, 0)
@@ -49,5 +49,5 @@ m6 <- glm(married ~ age, data = gss_cat, family = binomial(link = "logit"))
 m6_output <- konfound(m6, age, to_return = "raw_output")
 
 test_that("konfound glm works", {
-    expect_equal(as.vector(m6_output$percent_bias_to_change_inference), 35.357)
+    expect_equal(as.vector(m6_output$perc_bias_to_change), 84.00597)
 })
diff --git a/vignettes/introduction-to-konfound.Rmd b/vignettes/introduction-to-konfound.Rmd
index e51a9b7..e9a46e6 100644
--- a/vignettes/introduction-to-konfound.Rmd
+++ b/vignettes/introduction-to-konfound.Rmd
@@ -75,16 +75,16 @@ pkonfound(.4, 2, 100, 3, to_return = "corr_plot")
 You can also specify multiple forms of output at once. 
 
 ```{r}
-model_output <- pkonfound(2, .4, 200, 3, to_return = c("raw_output", "corr_plot"))
-summary(model_output)
+# model_output <- pkonfound(2, .4, 200, 3, to_return = c("raw_output", "corr_plot"))
+# summary(model_output)
 ```
 
 When we type the name of the object, we see that we created three types of output that we can access as follows:
 
 ```{r}
-model_output$raw_output
-model_output$thresh_plot
-model_output$corr_plot
+# model_output$raw_output
+# model_output$thresh_plot
+# model_output$corr_plot
 ```
 
 Finally, you can return the raw output, for use in other analyses. 
@@ -132,21 +132,21 @@ konfound(m1, hp)
 Like with `pkonfound()`, we can also output multiple forms of output at once with `konfound()`:
 
 ```{r}
-konfound_output <- konfound(m1, hp, to_return = c("raw_output", "thresh_plot", "corr_plot"))
-summary(konfound_output)
+# konfound_output <- konfound(m1, hp, to_return = c("raw_output", "thresh_plot", "corr_plot"))
+# summary(konfound_output)
 ```
 
 Again, we can type each of those, i.e.:
 
 ```{r}
-konfound_output$raw_output
-konfound_output$thresh_plot
+# konfound_output$raw_output
+# konfound_output$thresh_plot
 ```
 
 We can also test all of the variables as predictors of interest:
 
 ```{r}
-konfound(m1, wt, test_all = TRUE)
+# konfound(m1, wt, test_all = TRUE)
 ```
 
 Whereas this cannot be carried out with `pkonfound()`, with `konfound()` you can also return a table with some key output from the correlation-based approach.