One of the primary advantages of a repeated-measures design, compared to an independent-measures design, is that it reduces the overall variability by removing variance caused by individual differences. The following data are from a research study comparing three treatment conditions. Treatments

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One of the primary advantages of a repeated-measures design, compared to an independent-measures design, is that it reduces the overall variability by removing variance caused by individual differences. The following data are from a research study comparing three treatment conditions.
Treatments
Person
I
II
III
Totals
A 6 8 10 P = 24
B 5 5 5 P = 15
C 1 2 3 P = 6
D 0 1 2 P = 3
  M = 3 M = 4 M = 5 N = 12
  T = 12 T = 16 T = 20 G = 48
  SS = 26 SS = 30 SS = 38 ∑X² = 294
 
A. Assume that the data are from an independent-measures study using three separate samples, each with n = 4 participants. Ignore the column of P totals and use an independent-measures ANOVA with α = .05 to test the significance of the mean differences. (Use three decimal places where needed.)
 
B. What is the value of Fcriticalcritical? (Use three decimal places.)
 
C. Conclusion: Reject or Fail to reject the null hypothesis, why?
 
D. Explain why the two analyses lead to different conclusions.
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