Study on the flyACTMathematicsData collection methods and study design
Mathematics
Random assignment is the idea at the heart of Data collection methods and study design, because it balances hidden differences between groups so that a cause-and-effect claim becomes reasonable.
Sampling at random is a separate tool that lets results be generalized to a larger population. A confounding variable is a second factor that changes along with the treatment, such as giving a new method only to people who work in the morning, so the two effects cannot be separated.
ACT items describe a short study and ask why a step was taken, what limits a conclusion, or which factor is confounded. Correct choices name the specific flaw.
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Question 1Easier
Marcus measures soil quality in 72 greenhouse plots, then randomly assigns fertilizer A or B. Which of the following best explains why the fertilizers are assigned at random?
Answer: C — It tends to balance soil quality between the fertilizer groups.
Random assignment tends to distribute soil quality and other lurking factors across the fertilizer groups. This makes the groups more comparable before outcomes are measured.
Question 2Easier
Anika randomly assigns 120 similar seedlings to either constant light or alternating light and darkness. Why does random assignment strengthen a comparison of their growth after 4 weeks?
Answer: C — It tends to balance other growth-related variables between groups
Random assignment tends to distribute lurking variables, such as initial health, across treatment groups. This makes a difference in growth more plausibly attributable to the light condition.
Question 3Easier
At a factory, morning-shift workers receive a new training program, and evening-shift workers receive the old training program. The morning group produces 14 more units per day. Which of the following factors is confounded with the training program?
Answer: B — Work shift
Every worker receiving the new program is on the morning shift, and every worker receiving the old program is on the evening shift. The effects of shift and training cannot be separated.
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