Demonstrating Standard Error

demo_se.R

# Title: Demonstration of Standard Error

# Description: The purpose of this script is to demonstrate standard error. 
# A sample is repeatedly drawn then the mean is calculated. The result, each 
# sample mean is then plotted 

# Setup ----

library(tidyverse) # ol faithful

# Generating Data ----

set.seed(123)  # for reproducibility
population <- rnorm(10000, mean = 50, sd = 10)  # a normal distribution with mean = 50 and sd = 10

# Draw samples and calculate their means
sample_size <- 500  # size of each sample
num_samples <- 1000  # number of samples to draw 

# Repeatedly sampling then calculating the mean
sample_means <- replicate(num_samples, mean(sample(population, sample_size)))

# Calculating the standard error ----

# Calculating the standard error. This is the standard deviation of the sampling distribution 
# in this case the statistic is the mean, so standard deviation of the means.
se_sample_means <- sd(sample_means)

# Plotting Results ----

# Plot the distribution of sample means

ggplot(data.frame(sample_means), aes(x = sample_means)) +
  geom_histogram(bins = 30, color = "black", fill = "blue", alpha = 0.7) +
  
  # Adding titles
  
  labs(title = " Sampling Distribution",
       subtitle = paste("N = 500, Sample Drawn 1000 Times, SE =", round(se_sample_means, 2)),
       x = "Sample Mean", 
       y = "Frequency") +
  theme_minimal() + # changing to minimal theme
  
  # Setting y scale
  
  scale_y_continuous(limits = c(0, 120), 
                     breaks = c(0, 20, 40, 60, 80, 100, 120)) + 
  
  # Centering title and increasing font size 
  
  theme(
    text = element_text(size = 14),
    plot.title = element_text(hjust = 0.5), 
    plot.subtitle = element_text(hjust = 0.5)
  )