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Based on the strategy of visually examining individual score distributions, explain why relying solely on the initial group mean was misleading in this scenario and summarize what the bimodal distribution indicates about the training program's effect.
Case context: A research team evaluates a new cognitive training program for memory improvement. After the study, the researchers calculate the group mean improvement score, which is exactly , suggesting the program had no overall effect. However, the lead researcher decides to visually examine the distribution of individual scores using a histogram. The histogram reveals a clear bimodal distribution: one large cluster of participants showed a significant 15-point improvement, while another large cluster showed a 15-point decline.
Question: Based on the strategy of visually examining individual score distributions, explain why relying solely on the initial group mean was misleading in this scenario and summarize what the bimodal distribution indicates about the training program's effect.
Sample answer: The initial group mean of was misleading because it mathematically averaged out the divergent individual responses, obscuring the fact that the program actually had strong but opposite effects on different people. The bimodal distribution indicates that the treatment did not simply have 'no effect'; instead, it positively affected one distinct subset of participants while negatively affecting another distinct subset.
Key points:
- The group mean of obscured divergent individual responses by averaging them out.
- A bimodal distribution indicates two distinct response patterns within the sample.
- The treatment had a significant effect, but it was not uniform (positive for some, negative for others).
Rubric: Award full credit if the student explains that the group mean obscured divergent individual responses and correctly identifies that the bimodal distribution reveals the treatment helped some participants but hindered others.
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Research Methods in Psychology - 4th American Edition @ KPU
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