For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, the two means for level A1 are 4 and 1, and the two means for level A2 are 3 and 2.For these data, what is the value of SS_{between treatments}? A)10 B)40 C)50 D)300

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Quizplus · Accepted Answer

The between-treatments sum of squares is calculated as the sum of the squared differences between the treatment means and the overall mean, multiplied by the number of participants in each treatment condition. In this case, the overall mean is (4 + 1 + 3 + 2) / 4 = 2.5. The squared differences between the treatment means and the overall mean are (4 - 2.5)^2 = 2.25, (1 - 2.5)^2 = 2.25, (3 - 2.5)^2 = 0.25, and (2 - 2.5)^2 = 0.25. The between-treatments sum of squares is therefore (2.25 + 2.25 + 0.25 + 0.25) * 10 = 50.

For a Two-Factor Study with 2 Levels of Factor A