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(Chapter 14) The following data were obtained from a repeated-measures study comparing three treatment conditions. a....

  1. (Chapter 14) The following data were obtained from a repeated-measures study comparing three treatment conditions.
    a. Use a repeated measures ANOVA with α=.05 to determine whether there are significant mean differences among the three treatments. (Hint: start by filling in the missing values on the table below). Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all steps and all parts of all answers.
    b. Compute n2, the percentage of variance accounted for by the mean differences, to measure the size of the treatment effects.  Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all parts of all answers.
       Treatment I II III P-totals        
    Person
    A 7 7 8 P=
    B 5 3 3 P=
    C 1 1 3 P=
    D 3 1 2 P=
    M= M= M= N=
    T= T= T= G=
    SS= SS= SS= Ex2=

Solutions

Expert Solution

a) From the given data

Person
Treatment A B C D Ti. SS Ti.^2/n Mean
I 7 5 1 3 16 20 64 4
II 7 3 1 1 12 24 36 3
III 8 3 3 2 16 22 64 4
Total Pj 22 11 5 6 44 66 164
Pj^2 /k 161.3333333 40.33333 8.333333 12 222

Anova Table Alpha = 0.05
Source df SS MSS Var. Ratio F F-critic P-Value
B/w groups 2 2.666667 1.333333 1.5 5.143253 0.296296
Within Group 9 66
i) B/w Subject 3 60.66667
ii) Error 6 5.333333 0.888889
Total: 11 68.66667

Since P-value > alpha 0.05 so we accept H0  

Thus we conclude that there is no significance difference among the 3 treatments

b)


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