diff --git a/R/back_transformations.R b/R/back_transformations.R
index 0bb1f82..097a775 100644
--- a/R/back_transformations.R
+++ b/R/back_transformations.R
@@ -16,12 +16,12 @@ NULL
 
 #' @describeIn back Back transform beta estimates for models with log-link
 #' @export
-log_back <- function(beta, se, sim) {
+log <- function(beta, se, sim) {
   simulated <- rnorm(sim, beta, se)
   original <- exp(simulated) %>% # exponential = inverse of log
     na.omit()
   m_est <- mean(original)
-  se_est <- sd(original)
+  se_est <- sd(original) / sqrt(length(original))
   quantiles <- quantile(original, c(0.025, 0.975), na.rm = TRUE)
   set <- data.frame(mean_origin = m_est, se_origin = se_est, lower = quantiles[[1]], upper = quantiles[[2]])
   if (flatten_dbl(set) %>%
@@ -35,12 +35,12 @@ log_back <- function(beta, se, sim) {
 
 #' @describeIn back Back transform beta estimates for models with logit-link
 #' @export
-logit_back <- function(beta, se, sim) {
+logit <- function(beta, se, sim) {
   simulated <- rnorm(sim, beta, se)
   original <- plogis(simulated) %>% # invlogit
     na.omit()
   m_est <- mean(original)
-  se_est <- sd(original)
+  se_est <- sd(original) / sqrt(length(original))
   quantiles <- quantile(original, c(0.025, 0.975), na.rm = TRUE)
   set <- data.frame(mean_origin = m_est, se_origin = se_est, lower = quantiles[[1]], upper = quantiles[[2]])
   if (flatten_dbl(set) %>%
@@ -54,12 +54,12 @@ logit_back <- function(beta, se, sim) {
 
 #' @describeIn back Back transform beta estimates for models with probit-link
 #' @export
-probit_back <- function(beta, se, sim) {
+probit <- function(beta, se, sim) {
   simulated <- rnorm(sim, beta, se)
   original <- pnorm(simulated) %>% # inv-probit
     na.omit()
   m_est <- mean(original)
-  se_est <- sd(original)
+  se_est <- sd(original) / sqrt(length(original))
   quantiles <- quantile(original, c(0.025, 0.975), na.rm = TRUE)
   set <- data.frame(mean_origin = m_est, se_origin = se_est, lower = quantiles[[1]], upper = quantiles[[2]])
   if (flatten_dbl(set) %>%
@@ -73,12 +73,12 @@ probit_back <- function(beta, se, sim) {
 
 #' @describeIn back Back transform beta estimates for models with \eqn{1/x} link
 #' @export
-inverse_back <- function(beta, se, sim) {
+inverse <- function(beta, se, sim) {
   simulated <- rnorm(sim, beta, se)
   original <- 1 / simulated %>% # inverse
     na.omit()
   m_est <- mean(original)
-  se_est <- sd(original)
+  se_est <- sd(original) / sqrt(length(original))
   quantiles <- quantile(original, c(0.025, 0.975), na.rm = TRUE)
   set <- data.frame(mean_origin = m_est, se_origin = se_est, lower = quantiles[[1]], upper = quantiles[[2]])
   if (flatten_dbl(set) %>%
@@ -92,12 +92,12 @@ inverse_back <- function(beta, se, sim) {
 
 #' @describeIn back Back transform beta estimates for models with \eqn{x^2}-link
 #' @export
-square_back <- function(beta, se, sim) {
+square <- function(beta, se, sim) {
   simulated <- rnorm(sim, beta, se)
   original <- sqrt(simulated) %>% # inverse of x^2
     na.omit()
   m_est <- mean(original)
-  se_est <- sd(original)
+  se_est <- sd(original) / sqrt(length(original))
   quantiles <- quantile(original, c(0.025, 0.975), na.rm = TRUE)
   set <- data.frame(mean_origin = m_est, se_origin = se_est, lower = quantiles[[1]], upper = quantiles[[2]])
   if (flatten_dbl(set) %>%
@@ -111,12 +111,12 @@ square_back <- function(beta, se, sim) {
 
 #' @describeIn back Back transform beta estimates for models with \eqn{x^3}-link
 #' @export
-cube_back <- function(beta, se, sim) {
+cube <- function(beta, se, sim) {
   simulated <- rnorm(sim, beta, se)
   original <- pracma::nthroot(simulated, n = 3) %>% # inverse of x^3, use non-base to allow for -ve numbers
     na.omit()
   m_est <- mean(original)
-  se_est <- sd(original)
+  se_est <- sd(original) / sqrt(length(original))
   quantiles <- quantile(original, c(0.025, 0.975), na.rm = TRUE)
   set <- data.frame(mean_origin = m_est, se_origin = se_est, lower = quantiles[[1]], upper = quantiles[[2]])
   if (flatten_dbl(set) %>%
@@ -130,12 +130,12 @@ cube_back <- function(beta, se, sim) {
 
 #' @describeIn back Back transform beta estimates for models with identity-link
 #' @export
-identity_back <- function(beta, se, sim) { # identity (typo) TODO
+identity <- function(beta, se, sim) { # identity (typo) TODO
   simulated <- rnorm(sim, beta, se)
   original <- simulated %>% #  no transformation
     na.omit()
   m_est <- mean(original)
-  se_est <- sd(original)
+  se_est <- sd(original) / sqrt(length(original))
   quantiles <- quantile(original, c(0.025, 0.975), na.rm = TRUE)
   set <- data.frame(mean_origin = m_est, se_origin = se_est, lower = quantiles[[1]], upper = quantiles[[2]])
   if (flatten_dbl(set) %>%
@@ -150,12 +150,12 @@ identity_back <- function(beta, se, sim) { # identity (typo) TODO
 
 #' @describeIn back Back transform beta estimates for models with power-link
 #' @export
-power_back <- function(beta, se, sim, n) {
+power <- function(beta, se, sim, n) {
   simulated <- rnorm(sim, beta, se)
   original <- pracma::nthroot(simulated, n = n) %>% # inverse of x^n, use non-base to allow for -ve numbers
     na.omit()
   m_est <- mean(original)
-  se_est <- sd(original)
+  se_est <- sd(original) / sqrt(length(original))
   quantiles <- quantile(original, c(0.025, 0.975), na.rm = TRUE)
   set <- data.frame(mean_origin = m_est, se_origin = se_est, lower = quantiles[[1]], upper = quantiles[[2]])
   if (flatten_dbl(set) %>%
@@ -170,12 +170,12 @@ power_back <- function(beta, se, sim, n) {
 #' @describeIn back Back transform beta estimates or out-of-sample predictions from models whose response variable has been divided by some number, `n`.
 #' @param n Denominator used by analyst to divide the response variable.
 #' @export
-divide_back <- function(beta, se, sim, n) {
+divide <- function(beta, se, sim, n) {
   simulated <- rnorm(sim, beta, se)
   original <- simulated * n %>%
     na.omit()
   m_est <- mean(original, na.rm = TRUE)
-  se_est <- sd(original, na.rm = TRUE)
+  se_est <- sd(original, na.rm = TRUE) / sqrt(length(original))
   quantiles <- quantile(original,
     c(0.025, 0.975),
     na.rm = TRUE
@@ -200,12 +200,12 @@ divide_back <- function(beta, se, sim, n) {
 
 #' @describeIn back Back transform beta estimates or out-of-sample predictions from models whose response variable has been transformed by the square root
 #' @export
-square_root_back <- function(beta, se, sim) {
+square_root <- function(beta, se, sim) {
   simulated <- rnorm(sim, beta, se)
   original <- simulated^2 %>%
     na.omit()
   m_est <- mean(original)
-  se_est <- sd(original)
+  se_est <- sd(original) / sqrt(length(original))
   quantiles <- quantile(original, c(0.025, 0.975), na.rm = TRUE)
   set <- data.frame(mean_origin = m_est, se_origin = se_est, lower = quantiles[[1]], upper = quantiles[[2]])
   if (flatten_dbl(set) %>%