3. Brains and Beats Do children who study music perform better in school? One ofthe studies supporting this claim was conducted by University of California professor Gordon Shaw and reported in a 1999 edition of the Deseret News. In this study, students in the 95th Street School, one of Los Angeles' 100 poorest-performing institutions, received both piano lessons and automated mathematics training. Their ability to understand and analyze ratios and fractions was then compared to a 1997 study involving students from under J achieving schools in Orange County who were given automated and traditional mathematics instruction (but no musical training). all Beyond the Numbers: A StudentCentered Approach for Learning Statistical Reasoning 55 Chapter 3 I Statistical Experiments and the Problem of Confounding The News reported that \"[t]he Los Angeles students scored 2% higher than their Orange County counterparts in their ability to understand and analyze ratios and fractionsconcepts usually not introduced until sixth grade." a. How do you know that the subjects in this study could not have been randomized to the treatments that were compared? This was one of the more widely-reported studies that supported music training as positively impacting general academic performance. i. The article excerpt says that the students at the 95th Street School self-selected which treatment they wanted to be in. ii. The article excerpt implies that random assignment was against fairtreatment policies in the Orange County system and, therefore, could not be utilized. iii. The treatments were paired, so every student ended up getting both treatments and, hence, no randomization was needed. iv. The treatments were at two separate schools at two separate points in time. b. Aside from randomization issues, what is another possible source of confounding (other than lack of randomization) that might challenge a conclusion that exposure to music caused the LA. students to do better. i. The group in Orange County had both traditional and automated mathematics instruction (notjust automated). ii. The group in LA. had both traditional and automated mathematics instruction (notjust automated). iii. The group in Orange County had both traditional and automated mathematics instruction (notjust traditional). The group in LA. had both traditional and automated mathematics instruction (not just traditional). & iv