Chapter 4 Hypothesis testing using the likelihood ratio test

We started the book with the t-test. There, we had the following general procedure:

• Given independent and identically distributed data \(y\), define a null hypothesis relating to the parameter \(\mu\), which represents the: \(H_0: \mu=\mu_0\).
• Compute the sample mean \(\bar{y}\) and the standard error SE.
• Reject the null hypothesis if the absolute value of \((\bar{y}-\mu_0)/SE\) is larger than the critical t-value (approximately \(2\) for sample sizes larger than 20).

The two main classes of t-test discussed in chapter 2, paired and unpaired, are basically just the same t-test. The paired/unpaired nature of the t-test affects the way the standard error is computed in paired vs. unpaired data.

Here, we turn to a closely related test: the likelihood ratio test statistic. The reason for considering this alternative test is that in reality we will almost never use the t-test, due to its many limitations.