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Based on the case context, decide whether the researcher's proposed task presentation sequence constitutes a valid Latin square design and justify your answer based on the structural rules of the design.
Case context: A cognitive psychologist is designing a within-subjects study with four experimental conditions: A, B, C, and D. Due to a high number of conditions, testing all possible sequences is impractical, so they opt for partial counterbalancing. The researcher creates a matrix with the following task presentation sequences for four participant groups: Group 1: A-B-C-D Group 2: B-C-D-A Group 3: C-D-A-B Group 4: D-A-B-C
Question: Based on the case context, decide whether the researcher's proposed task presentation sequence constitutes a valid Latin square design and justify your answer based on the structural rules of the design.
Sample answer: No, this does not constitute a valid Latin square design. Although it meets the requirement that each condition appears exactly once in every ordinal position (for example, A is presented first, fourth, third, and second across the groups), it violates the second rule. In a valid Latin square, each condition must precede and follow every other condition exactly one time. In this layout, A always precedes B and always follows D. Condition A never precedes C or D, and never follows B or C. Therefore, the sequencing effects are not balanced.
Key points:
- Diagnose that the proposed matrix is not a valid Latin square design.
- Explain that each condition appearing once in every ordinal position is met.
- Explain that the rule requiring each condition to precede and follow every other condition exactly once is violated.
- Provide a concrete example of the sequencing rule violation from the proposed groups.
Rubric: To receive full credit, the student must: 1) State clearly that the proposed design is not a valid Latin square; 2) Identify that the ordinal position rule is met (each condition appears once in every position); 3) Identify that the sequencing/predecessor-successor rule is violated (conditions do not precede and follow each other exactly once); 4) Provide a specific example of this violation (e.g., A always precedes B or always follows D).
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Research Methods in Psychology - 4th American Edition @ KPU
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