T-Test Simulation

The t-test is a fundamental statistical tool used to assess the significance of estimated coefficients in regression analysis. This test helps us determine whether the relationship we observe between variables is statistically significant or merely due to random chance. Understanding how t-tests work and their interpretation is crucial for making valid statistical inferences.

1. The T-Statistic: The t-statistic is calculated by dividing the estimated coefficient by its standard error. This ratio tells us how many standard deviations our estimate is from zero. A larger absolute value of the t-statistic suggests stronger evidence against the null hypothesis.

2. P-Values: The p-value represents the probability of observing a t-statistic as extreme as, or more extreme than, the one calculated from our data, assuming the null hypothesis is true. A small p-value (typically less than 0.05) suggests that the observed relationship is unlikely to have occurred by chance alone.

3. Confidence Intervals: These intervals provide a range of values within which we can be reasonably confident (usually 95%) that the true population parameter lies. If the confidence interval does not include zero, it suggests that the coefficient is statistically significant.

The following simulation allows you to explore how the t-test performs under different conditions, including various error distributions and sample sizes: