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Analyze the researcher's decision to switch to a within-subjects design. How would the student baseline reading speed differences have affected the within-groups variance () and the -ratio in the originally planned one-way ANOVA? Explain how the repeated-measures ANOVA analyzes and resolves this specific problem.
Case context: An educational researcher is comparing the effectiveness of three different reading interventions. Initially, they plan a between-subjects design where 45 students are randomly assigned to three separate groups (15 students per group) and analyzed via a one-way ANOVA. However, during pre-testing, the researcher realizes that the students have extremely diverse baseline reading speeds (some read twice as fast as others). Concerned that this baseline variability will obscure the effects of the interventions, the researcher decides to switch to a within-subjects design where all 15 students experience all three reading interventions, allowing for a repeated-measures ANOVA.
Question: Analyze the researcher's decision to switch to a within-subjects design. How would the student baseline reading speed differences have affected the within-groups variance () and the -ratio in the originally planned one-way ANOVA? Explain how the repeated-measures ANOVA analyzes and resolves this specific problem.
Sample answer: In the original one-way ANOVA (between-subjects design), the large differences in students' baseline reading speeds would act as stable individual differences that inflate the within-groups variance (). An inflated would lead to a lower -ratio, decreasing the sensitivity of the test and making it harder to detect a significant difference between the reading interventions. By switching to a within-subjects design and using a repeated-measures ANOVA, the stable individual differences in reading speed are measured and subtracted from the . This subtraction reduces the value of , resulting in a higher -ratio and a more sensitive test that can detect intervention effects despite high baseline variability.
Key points:
- Identify baseline reading speed variation as stable individual differences among participants.
- Analyze that stable individual differences inflate and decrease the -ratio in a one-way ANOVA.
- Deduce that repeated-measures ANOVA measures and subtracts stable individual differences from .
- Justify how subtracting stable individual differences lowers , leading to a higher -ratio and a more sensitive test.
Rubric: Grading Rubric: - 1 point: Identifies baseline reading speed variation as stable individual differences. - 1 point: Analyzes how stable individual differences inflate and lower the -ratio in a one-way ANOVA. - 1 point: Explains how a repeated-measures ANOVA resolves this by subtracting these stable individual differences from . - 1 point: Concludes that the subtraction lowers , thereby increasing the -ratio and sensitivity of the test.
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Research Methods in Psychology - 4th American Edition @ KPU
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