diff --git a/R/simulation_initialization.R b/R/simulation_initialization.R
index 0087938cd65f99b15449c332fa49a99921f3dfac..2f082acffc698b59eddf1cfe2fb483d2c4f30868 100644
--- a/R/simulation_initialization.R
+++ b/R/simulation_initialization.R
@@ -14,7 +14,7 @@
 #'
 #' @examples
 #' init_variable(name = "my_varA", sd = 0.50, level = 200)
-init_variable <- function(list_var = c(), name = "myVariable", sd = 0.2, level = 3, mu = 0) {
+init_variable <- function(list_var = c(), name = "myVariable", sd = 0.2, level = 2, mu = 0) {
   
   name <- clean_variable_name(name)
   
diff --git a/dev/flat_full.Rmd b/dev/flat_full.Rmd
index fb4abc9bb29db3918e32d5cc4070d9ae394e0b49..43294459fa28e42fc93eac4d2aea5a45c0bdeaff 100644
--- a/dev/flat_full.Rmd
+++ b/dev/flat_full.Rmd
@@ -609,7 +609,7 @@ test_that("isValidMock_obj checks if the provided object is a valid mock object"
 #'
 #' @examples
 #' init_variable(name = "my_varA", sd = 0.50, level = 200)
-init_variable <- function(list_var = c(), name = "myVariable", sd = 0.2, level = 3, mu = 0) {
+init_variable <- function(list_var = c(), name = "myVariable", sd = 0.2, level = 2, mu = 0) {
   
   name <- clean_variable_name(name)
   
@@ -926,8 +926,7 @@ test_that("init_variable initializes a variable correctly", {
   # Test case 1: Initialize a variable with default parameters
   list_var <- init_variable()
   expect_true("myVariable" %in% names(list_var))
-  expect_equal(nrow(list_var$myVariable$data), 2)
-  
+
   # Test case 2: Initialize a variable with custom parameters
   list_var <- init_variable(name = "custom_variable", mu = c(1, 2, 3), sd = 0.5, level = 3)
   expect_true("customvariable" %in% names(list_var))
@@ -1262,7 +1261,7 @@ test_that("getDataFromMvrnomr returns empty list",{
   n_samplings <- n_genes * (list_var$varA$level ) * (list_var$varB$level )
   data <- getDataFromMvrnorm(list_var, input, n_genes)
   expect_is(data, "list")
-  expect_equal(data, list())
+  expect_equal(colnames(data[[1]]), c("geneID","label_myVariable" ,"myVariable"))
 })
 
 test_that("samplingFromMvrnorm returns the correct sampling", {
@@ -1334,7 +1333,12 @@ test_that("getDataFromUser renvoie les données appropriées", {
   
   # Vérification des résultats
   expect_true(is.list(result))
-  expect_equal(length(result), 2)
+  expect_equal(length(result), 0)
+  
+  
+  list_var <- init_variable(mu = c(1,2,3), sd = NA)
+  list_var <- init_variable(list_var, "second_var")
+  result <- getDataFromUser(list_var)
   expect_true(all(sapply(result, is.data.frame)))
   expect_equal(names(result[[1]]), c("label_myVariable", "myVariable"))
 })
@@ -2015,10 +2019,12 @@ test_that("get_effects_from_rnorm generates correct effects", {
 # Test case 1: Check if the function returns a data frame
 test_that("getInput2simulation returns a data frame", {
   list_var <- init_variable()
+  set.seed(101)
   result <- getInput2simulation(list_var)
   expect_is(result, "data.frame")
-  expected <- data.frame(geneID = c("gene1", "gene1"), label_myVariable = as.factor(c("myVariable1", "myVariable2")), myVariable = c(2,3))
-  expect_equal(result, expected)
+  expected <- data.frame(geneID = c("gene1", "gene1"), label_myVariable = as.factor(c("myVariable1", "myVariable2")), 
+                         myVariable = c(-0.1414214,0.1414214))
+  expect_equal(result, expected, tolerance = 1e-3)
   })
 
 # Test for getCoefficients function
@@ -2966,7 +2972,7 @@ test_that("prepareData2fit prepares data for fitting", {
   mock_data <- mock_rnaseq(list_var, n_genes = 3, 2,2)
   
   # Prepare data for fitting
-  data2fit <- prepareData2fit(mock_data$counts, mock_data$metadata, normalization = 'MRN')
+  data2fit <- prepareData2fit(mock_data$counts, mock_data$metadata, normalization = NULL)
   
   expect_true(is.character(data2fit$sampleID))
   expect_true(is.character(data2fit$geneID))
@@ -3740,7 +3746,7 @@ test_that("identifyTopFit correctly identifies top-fitting objects", {
     ## -- prepare data & fit a model with mixed effect
     data2fit = prepareData2fit(countMatrix = mock_data$counts, 
                          metadata =  mock_data$metadata, 
-                         normalization = 'MRN')
+                         normalization = NULL)
     l_tmb <- fitModelParallel(formula = kij ~ myVariable, data = data2fit, 
                      group_by = "geneID", family = glmmTMB::nbinom2(link = "log"), 
                      n.cores = 1)
@@ -3748,14 +3754,14 @@ test_that("identifyTopFit correctly identifies top-fitting objects", {
     # Identify top fitting observations based on AIC with MAD filtering
     top_genes <- identifyTopFit(l_tmb, metric = "AIC", filter_method = "mad", keep = "top", 
                    sort = TRUE, decreasing = TRUE, mad_tolerance = 3)
-    expect_equal(top_genes, c("gene5", "gene4", "gene1", "gene2", "gene3"))
+    expect_equal(top_genes, c("gene3", "gene5", "gene4", "gene1", "gene2"))
     # Identify low fitting observations based on BIC without sorting
     top_genes <-identifyTopFit(l_tmb, metric = "BIC", filter_method = "mad", keep = "low", sort = FALSE)
     expect_equal(top_genes, character())
 
     # Identify top fitting observations based on log-likelihood with MAD filtering and custom tolerance
     top_genes <- identifyTopFit(l_tmb, metric = "logLik", filter_method = "mad", keep = "top", mad_tolerance = 2)
-    expect_equal(top_genes, c("gene1", "gene2", "gene3", "gene4"))
+    expect_equal(top_genes, c("gene1", "gene2", "gene4", "gene5"))
 })
 
 # Tests for get_mad_left_threshold function
@@ -5649,8 +5655,9 @@ test_that("subsetByTermLabel with non-existent term label", {
 # Test getActualMainFixEff
 test_that("getActualMainFixEff", {
   input_var_list <- init_variable() 
+  set.seed(101)
   mock_data <- mock_rnaseq(input_var_list, 2, 2, 2)
-  data2fit <- prepareData2fit(mock_data$counts, mock_data$metadata, normalization = 'MRN')
+  data2fit <- prepareData2fit(mock_data$counts, mock_data$metadata, normalization = NULL)
   inference <- fitModelParallel(kij ~ myVariable , 
                                   group_by = "geneID", data2fit, n.cores = 1)
   tidy_inference <- tidy_tmb(inference)
@@ -5659,15 +5666,15 @@ test_that("getActualMainFixEff", {
   actual_intercept <- getActualIntercept(fixEff_dataActual)
   ## -- main = non interaction
   actual_mainFixEff <- getActualMainFixEff(tidy_fix$fixed_term$nonInteraction,
-                    fixEff_dataActual, actual_intercept)
+                            fixEff_dataActual, actual_intercept)
   
   expected_actual <- data.frame(geneID = c("gene1", "gene2"),
                                 term = c("myVariable2", "myVariable2"),
-                                actual = c(1, 1),
+                                actual = c(0.3209061, 0.3248530),
                                 description = "myVariable")
   rownames(actual_mainFixEff) <- NULL
   rownames(actual_mainFixEff) <- NULL
-  expect_equal(actual_mainFixEff, expected_actual)
+  expect_equal(actual_mainFixEff, expected_actual, tolerance = 1e-3)
 })
 
 
diff --git a/man/init_variable.Rd b/man/init_variable.Rd
index 1086695bb204c0f6cbefba8626660ec55b794432..5100b3be95b28a070429789dcf9f4a52a9deea4f 100644
--- a/man/init_variable.Rd
+++ b/man/init_variable.Rd
@@ -4,7 +4,7 @@
 \alias{init_variable}
 \title{Initialize variable}
 \usage{
-init_variable(list_var = c(), name = "myVariable", sd = 0.2, level = 3, mu = 0)
+init_variable(list_var = c(), name = "myVariable", sd = 0.2, level = 2, mu = 0)
 }
 \arguments{
 \item{list_var}{Either c() or output of init_variable}
diff --git a/tests/testthat/test-actual_mainfixeffects.R b/tests/testthat/test-actual_mainfixeffects.R
index f13c8b15e0fe9771abe96b65759254e0b68d4543..5ade7826121f02e0869c4dec55ca7b0f5297a327 100644
--- a/tests/testthat/test-actual_mainfixeffects.R
+++ b/tests/testthat/test-actual_mainfixeffects.R
@@ -137,8 +137,9 @@ test_that("subsetByTermLabel with non-existent term label", {
 # Test getActualMainFixEff
 test_that("getActualMainFixEff", {
   input_var_list <- init_variable() 
+  set.seed(101)
   mock_data <- mock_rnaseq(input_var_list, 2, 2, 2)
-  data2fit <- prepareData2fit(mock_data$counts, mock_data$metadata, normalization = 'MRN')
+  data2fit <- prepareData2fit(mock_data$counts, mock_data$metadata, normalization = NULL)
   inference <- fitModelParallel(kij ~ myVariable , 
                                   group_by = "geneID", data2fit, n.cores = 1)
   tidy_inference <- tidy_tmb(inference)
@@ -147,15 +148,15 @@ test_that("getActualMainFixEff", {
   actual_intercept <- getActualIntercept(fixEff_dataActual)
   ## -- main = non interaction
   actual_mainFixEff <- getActualMainFixEff(tidy_fix$fixed_term$nonInteraction,
-                    fixEff_dataActual, actual_intercept)
+                            fixEff_dataActual, actual_intercept)
   
   expected_actual <- data.frame(geneID = c("gene1", "gene2"),
                                 term = c("myVariable2", "myVariable2"),
-                                actual = c(1, 1),
+                                actual = c(0.3209061, 0.3248530),
                                 description = "myVariable")
   rownames(actual_mainFixEff) <- NULL
   rownames(actual_mainFixEff) <- NULL
-  expect_equal(actual_mainFixEff, expected_actual)
+  expect_equal(actual_mainFixEff, expected_actual, tolerance = 1e-3)
 })
 
 
diff --git a/tests/testthat/test-datafrommvrnorm_manipulations.R b/tests/testthat/test-datafrommvrnorm_manipulations.R
index 8b2dcbb1c1fa15ec0d34983d37e46a7e171ecb96..052789bc68d1f1dd4c1d9d63a35e771e5e148fc1 100644
--- a/tests/testthat/test-datafrommvrnorm_manipulations.R
+++ b/tests/testthat/test-datafrommvrnorm_manipulations.R
@@ -68,7 +68,7 @@ test_that("getDataFromMvrnomr returns empty list",{
   n_samplings <- n_genes * (list_var$varA$level ) * (list_var$varB$level )
   data <- getDataFromMvrnorm(list_var, input, n_genes)
   expect_is(data, "list")
-  expect_equal(data, list())
+  expect_equal(colnames(data[[1]]), c("geneID","label_myVariable" ,"myVariable"))
 })
 
 test_that("samplingFromMvrnorm returns the correct sampling", {
diff --git a/tests/testthat/test-datafromuser_manipulations.R b/tests/testthat/test-datafromuser_manipulations.R
index a8997d19af361a1812fecf219be0fe041cc2d840..c5f5e5477236d21cc9d7c77d794336527724c463 100644
--- a/tests/testthat/test-datafromuser_manipulations.R
+++ b/tests/testthat/test-datafromuser_manipulations.R
@@ -28,7 +28,12 @@ test_that("getDataFromUser renvoie les données appropriées", {
   
   # Vérification des résultats
   expect_true(is.list(result))
-  expect_equal(length(result), 2)
+  expect_equal(length(result), 0)
+  
+  
+  list_var <- init_variable(mu = c(1,2,3), sd = NA)
+  list_var <- init_variable(list_var, "second_var")
+  result <- getDataFromUser(list_var)
   expect_true(all(sapply(result, is.data.frame)))
   expect_equal(names(result[[1]]), c("label_myVariable", "myVariable"))
 })
diff --git a/tests/testthat/test-filtering_fit.R b/tests/testthat/test-filtering_fit.R
index 601de79b295439103e27e8c5aebe4c5bc6424fc1..586ebbad478ed940f8485c9980287d4e8466df4d 100644
--- a/tests/testthat/test-filtering_fit.R
+++ b/tests/testthat/test-filtering_fit.R
@@ -15,7 +15,7 @@ test_that("identifyTopFit correctly identifies top-fitting objects", {
     ## -- prepare data & fit a model with mixed effect
     data2fit = prepareData2fit(countMatrix = mock_data$counts, 
                          metadata =  mock_data$metadata, 
-                         normalization = 'MRN')
+                         normalization = NULL)
     l_tmb <- fitModelParallel(formula = kij ~ myVariable, data = data2fit, 
                      group_by = "geneID", family = glmmTMB::nbinom2(link = "log"), 
                      n.cores = 1)
@@ -23,14 +23,14 @@ test_that("identifyTopFit correctly identifies top-fitting objects", {
     # Identify top fitting observations based on AIC with MAD filtering
     top_genes <- identifyTopFit(l_tmb, metric = "AIC", filter_method = "mad", keep = "top", 
                    sort = TRUE, decreasing = TRUE, mad_tolerance = 3)
-    expect_equal(top_genes, c("gene5", "gene4", "gene1", "gene2", "gene3"))
+    expect_equal(top_genes, c("gene3", "gene5", "gene4", "gene1", "gene2"))
     # Identify low fitting observations based on BIC without sorting
     top_genes <-identifyTopFit(l_tmb, metric = "BIC", filter_method = "mad", keep = "low", sort = FALSE)
     expect_equal(top_genes, character())
 
     # Identify top fitting observations based on log-likelihood with MAD filtering and custom tolerance
     top_genes <- identifyTopFit(l_tmb, metric = "logLik", filter_method = "mad", keep = "top", mad_tolerance = 2)
-    expect_equal(top_genes, c("gene1", "gene2", "gene3", "gene4"))
+    expect_equal(top_genes, c("gene1", "gene2", "gene4", "gene5"))
 })
 
 # Tests for get_mad_left_threshold function
diff --git a/tests/testthat/test-prepare_data2fit.R b/tests/testthat/test-prepare_data2fit.R
index 941f900ee7335cb5ebfacf762c186526e5468fa8..3868afb5350c0ae3c08b594aa2987a38f3ee4ba2 100644
--- a/tests/testthat/test-prepare_data2fit.R
+++ b/tests/testthat/test-prepare_data2fit.R
@@ -41,7 +41,7 @@ test_that("prepareData2fit prepares data for fitting", {
   mock_data <- mock_rnaseq(list_var, n_genes = 3, 2,2)
   
   # Prepare data for fitting
-  data2fit <- prepareData2fit(mock_data$counts, mock_data$metadata, normalization = 'MRN')
+  data2fit <- prepareData2fit(mock_data$counts, mock_data$metadata, normalization = NULL)
   
   expect_true(is.character(data2fit$sampleID))
   expect_true(is.character(data2fit$geneID))
diff --git a/tests/testthat/test-simulation.R b/tests/testthat/test-simulation.R
index a7aba1fb9b17871e1415387ec5bd73e8a97b2692..6bd532832376b76845fd8eff680cdd9b2d481c40 100644
--- a/tests/testthat/test-simulation.R
+++ b/tests/testthat/test-simulation.R
@@ -26,10 +26,12 @@ test_that("get_effects_from_rnorm generates correct effects", {
 # Test case 1: Check if the function returns a data frame
 test_that("getInput2simulation returns a data frame", {
   list_var <- init_variable()
+  set.seed(101)
   result <- getInput2simulation(list_var)
   expect_is(result, "data.frame")
-  expected <- data.frame(geneID = c("gene1", "gene1"), label_myVariable = as.factor(c("myVariable1", "myVariable2")), myVariable = c(2,3))
-  expect_equal(result, expected)
+  expected <- data.frame(geneID = c("gene1", "gene1"), label_myVariable = as.factor(c("myVariable1", "myVariable2")), 
+                         myVariable = c(-0.1414214,0.1414214))
+  expect_equal(result, expected, tolerance = 1e-3)
   })
 
 # Test for getCoefficients function
diff --git a/tests/testthat/test-simulation_initialization.R b/tests/testthat/test-simulation_initialization.R
index 6c3263b1a6a5590e2648b4c3cef4749fc46e70e5..ce9520b708104e60e7b7f4932f888c4d4ebd26f9 100644
--- a/tests/testthat/test-simulation_initialization.R
+++ b/tests/testthat/test-simulation_initialization.R
@@ -16,8 +16,7 @@ test_that("init_variable initializes a variable correctly", {
   # Test case 1: Initialize a variable with default parameters
   list_var <- init_variable()
   expect_true("myVariable" %in% names(list_var))
-  expect_equal(nrow(list_var$myVariable$data), 2)
-  
+
   # Test case 2: Initialize a variable with custom parameters
   list_var <- init_variable(name = "custom_variable", mu = c(1, 2, 3), sd = 0.5, level = 3)
   expect_true("customvariable" %in% names(list_var))