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Back Transform Z-Score to Original Log-Transformed Scale

Source: R/back_transform_log_z.R
back_transform_log_z.Rd

This function takes z-scores and transforms them back to their original values where the data was originally log-transformed. It performs a two-step transformation: first converting z-scores back to log values using the log-scale mean and standard deviation, then exponentiating to return to the original scale.

Usage

back_transform_log_z(z_scores, log_mean, log_sd)

Arguments

z_scores

A numeric value or vector of z-scores to be transformed back to the original scale.

log_mean

The mean of the log-transformed dataset from which the z-scores were calculated.

log_sd

The standard deviation of the log-transformed dataset from which the z-scores were calculated.

Value

Returns a numeric value or vector of the original scale values corresponding to the input z-scores.

Examples

# Given log-transformed data with log_mean = 1.5 and log_sd = 0.5
original_value <- back_transform_log_z(z_scores = 1.2, log_mean = 1.5, log_sd = 0.5)
print(original_value)
#> [1] 8.16617

# Multiple z-scores can be transformed at once
z_scores <- c(-1, 0, 1, 2)
original_values <- back_transform_log_z(z_scores = z_scores, log_mean = 1.5, log_sd = 0.5)
print(original_values)
#> [1]  2.718282  4.481689  7.389056 12.182494

# Real-world example: back-transforming household income z-scores
# Get mean and sd from original log-transformed data
log_mean_inc <- mean(original_df$t0_log_household_inc, na.rm = TRUE)
#> Error: object 'original_df' not found
log_sd_inc <- sd(original_df$t0_log_household_inc, na.rm = TRUE)
#> Error: object 'original_df' not found

# Back-transform all z-scores in the dataset
original_data_scale <- back_transform_log_z(
  df_grf$t0_log_household_inc_z,
  log_mean = log_mean_inc,
  log_sd = log_sd_inc
)
#> Error: object 'df_grf' not found
head(original_data_scale)
#> Error: object 'original_data_scale' not found

# Interpret key points on the distribution (-1 SD, mean, +1 SD)
z_scores <- c(-1, 0, 1)
scale_values <- back_transform_log_z(
  z_scores,
  log_mean = log_mean_inc,
  log_sd = log_sd_inc
)
#> Error: object 'log_mean_inc' not found

# Create a data frame to display the relationship between z-scores and original values
results_df <- data.frame(
  z_score = z_scores,
  data_scale = scale_values
)
#> Error: object 'scale_values' not found
print(results_df) # Shows what values on the original scale correspond to each z-score
#> Error: object 'results_df' not found