ABSTRACT
t-Tests involving one or two means research shows that students typically hold statistical misconceptions that are persistent and resistant to change. A correlated t-test focuses on the measured relationship between two variables, with the null hypothesis being Ho. The formula for a correlated t-test contains r, the observed correlation between the two sets of sample data: Despite the fact that r is contained in this formula's denominator, it is the numerator that establishes the primary focus of this t-test. When this happens, erroneous conclusions can be drawn about the difference between the sample means. Because of these connections, a t-test's p-value is determined as much by sample size or within-group variability as it is by the difference between the two sample means. An independent-samples t-test is robust to violations of assumptions if the two sample sizes are equal In certain scientific disciplines, however, it is not unusual to see published studies in which t-tests are used with very small samples.
