The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 10 participants in each treatment.Note that several values are missing in the table.What is the missing value for SS_total?? $$\begin{array} { l c c l l } \text { Source } & \mathrm { SS } & \mathrm { df } & \mathrm { MS } & \ \hline \text { Between } & 20 & \mathrm { xx } & \mathrm { xx } & \mathrm { F } = \mathrm { xx } \ \text { Within } & \mathrm { xx } & \mathrm { xx } & 2 & \ \text { Total } & \mathrm { xx } & \mathrm { xx } & & \ \hline \end{array}$$ A)22? B)?30 C)?54 D)?74

Question

Quizplus · Accepted Answer

The total degrees of freedom (df) for the experiment is equal to the total number of observations minus 1. With 3 groups of 10 participants each, there are 30 observations in total, so the total df is 29. The between-groups df is the number of groups minus 1, which is 2. Therefore, the within-groups df is the total df minus the between-groups df, which is 29 - 2 = 27. The total sum of squares (SS) is the sum of the between-groups SS and the within-groups SS. Given the within-groups mean square (MS) is 2 and the within-groups df is 27, the within-groups SS is MS * df = 2 * 27 = 54. Adding the between-groups SS (20) to the within-groups SS (54) gives the total SS, which is 74.

The Following Table Shows the Results of an Analysis of Variance