If 20 students run twice, once with music and then again without, what statistical test should be used?

The paired t test is appropriate in this scenario because the same group of students is being measured under two different conditions: running with music and running without music. Since each student serves as their own control, the paired t test accounts for the correlation between the two sets of measurements. This design allows for a more powerful statistical analysis, as it reduces the variability that could arise from differences between students.

Using this test, you can determine if there is a significant difference in performance (e.g., time taken to complete the run) between the two conditions. This paired approach focuses on the difference in scores for each student, providing insight into how the presence or absence of music affects their running performance.

In contrast, the independent t test would be used if the two groups being compared were entirely different individuals, ANOVA is utilized when comparing more than two groups or conditions, and a correlation test examines the relationship between two variables rather than the differences between paired measurements.