R Simulations: Understanding Alpha Errors in Two-Sample t-Tests

This project explores α-errors (Type I errors) in a two-sample t-test under different sample sizes.
The idea: simulate, test, and visualize how often we falsely reject the null hypothesis when the samples actually come from the same normal distribution.

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How it works

1. Simulation setup

   • Define a vector of sample sizes → sample_sizes
   • Set significance level → sign_level
   • Choose number of simulations → total_simulations
   • Specify tests per simulation → tests_per_simulation

2. Within each simulation

   • Two samples of equal size are drawn from a normal distribution (rnorm() with random mean & sd).
   • A series of t-tests is performed.
   • Results are classified as significant / not significant based on sign_level.

3. Output

   • For each sample size, the ratio of significant tests is computed.
   • Results are visualized with boxplots, showing the empirical Type I error vs. the theoretical sign_level.