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Analyze why a researcher conducting a within-subjects experiment with five conditions (55 conditions) might decide that complete counterbalancing is impractical, using math to support your analysis.

Question: Analyze why a researcher conducting a within-subjects experiment with five conditions (55 conditions) might decide that complete counterbalancing is impractical, using math to support your analysis.

Sample answer: Complete counterbalancing requires participants to be randomly assigned to every possible sequence of conditions. For five conditions, the number of unique sequences is 5!5!, which equals 5×4×3×2×1=1205 \times 4 \times 3 \times 2 \times 1 = 120 unique orders. To ensure an equal number of participants complete each order, the researcher would need a minimum sample size of 120120 participants (or multiples of 120120, such as 240240), which is often logistically impractical for a within-subjects study.

Key points:

  • Calculates the number of required sequences for five conditions as 5!=1205! = 120.
  • Explains that an equal number of participants must be assigned to each of the 120 sequences.
  • Concludes that the resulting sample size requirement (minimum of 120 or multiples thereof) makes the study logistically impractical.

Rubric: The student must show the calculation for five conditions (5!=1205! = 120) and explain that the need to assign an equal number of participants to each of these 120 unique sequences makes the required sample size too large and impractical.

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Updated 2026-05-26

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Research Methods in Psychology - 4th American Edition @ KPU

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