Which of the following is a statistical test that compares means?

The choice of Student's t test as the statistical test that compares means is well-founded because this test is specifically designed to determine if there is a significant difference between the means of two groups. It assesses whether the differences observed between the sample means reflect true differences in the population means, or if they occur by chance due to random variability.

In practice, the t test is often used in various fields, including clinical research, to evaluate the effects of a treatment or intervention by comparing outcomes between a treatment group and a control group. This makes it a fundamental tool for hypothesis testing, particularly in studies involving two groups.

While other statistical tests mentioned also relate to comparisons involving means, they serve different purposes. For instance, ANOVA (Analysis of Variance) is used when comparing the means of three or more groups rather than just two, making it a broader application than the t test. The Bland Altman method is primarily a graphical approach to assess agreement between two different measurement techniques, rather than a hypothesis test. Pearson's correlation coefficient measures the strength and direction of linear relationships between two variables rather than comparing means.

Thus, the focus of the t test on comparing the means of two groups makes it the most accurate choice for this question.