Question

chapter 3 | statistical experiments and the problem of confounding
the news reported that \the los angeles students scored 2% higher than their orange county counterparts in their ability to understand and analyze ratios and fractions—concepts 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 fair - treatment 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 l.a. students to do better.
i. the group in orange county had both traditional and automated mathematics instruction (not just automated).
ii. the group in l.a. had both traditional and automated mathematics instruction (not just automated).
iii. the group in orange county had both traditional and automated mathematics instruction (not just traditional).
iv. the group in l.a. had both traditional and automated mathematics instruction (not just traditional).

Explanation:

a. Random - assignment requires that subjects have an equal chance of being in any treatment group. If students self - select, there is no randomization. In this case, students at the 95th Street School self - selected treatments, so there was no randomization.
b. Confounding occurs when an extraneous variable is related to both the independent and dependent variables. If the instructional methods (traditional and automated mathematics instruction) are different between the two groups, it can be a confounding variable. Since we don't know if the instructional methods were the same across groups, this could be a confounding factor.

Answer:

a. i. The article excerpt says that the students at the 95th Street School self - selected which treatment they wanted to be in.
b. iv. The group in L.A. had both traditional and automated mathematics instruction (not just traditional).