CS(20) Monte Carlo Methods for Hypothesis Testing

Monte Carlo methods are not only powerful for estimating but also highly effective for hypothesis testing. These methods allow us to approximate the distribution of test statistics when the theoretical distribution is unknown or difficult to compute. Hypothesis testing with Monte Carlo simulations can provide an alternative or complement to classical methods, especially in complex scenarios.

Introduction to Hypothesis Testing

In classical statistical inference, hypothesis testing evaluates whether there is sufficient evidence in a sample to support or reject a claim about a population. The two competing hypotheses are:

1. The null hypothesis (H0), represents the default assumption (e.g. no effect or no difference).
2. The alternative hypothesis (H1), which represents a competing claim.

The process involves calculating a test statistic based on the sample data and determining how extreme this statistic is under the assumption that H0 is true.

Errors in Hypothesis Testing

Hypothesis testing involves two potential types of errors:
→ Type I errors (𝛂): Rejecting H0 when it is true.
→ Type II error (𝛃): Failing to reject H0 when it is false.