Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D) . We will conduct an ANOVA analysis of this.

$\begin{array}{c}\text { Groups }\\\begin{array}{rrrr}\text { A } & \text { B } & \text { C } & \text { D } \\6 & 7 & 9 & 11 \\8 & 10 & 11 & 14 \\10 & 11 & 12 & 15 \\12 & 12 & 13 & 16 \\14 & 15 & 15 & 19\end{array}\end{array}$
-What is the SS_error?

Question

Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D) . We will conduct an ANOVA analysis of this.

\begin{array}{c}\text { Groups }\\\begin{array}{rrrr}\text { A } & \text { B } & \text { C } & \text { D } \\6 & 7 & 9 & 11 \\8 & 10 & 11 & 14 \\10 & 11 & 12 & 15 \\12 & 12 & 13 & 16 \\14 & 15 & 15 & 19\end{array}\end{array}

-What is the SS_error?

Quizplus · Accepted Answer

The Sum of Squares within groups (SS_error) is calculated by summing the squared deviations of each observation from its group mean. For each group (A, B, C, D), we first calculate the mean:- Mean of A = (6+8+10+12+14)/5 = 50/5 = 10- Mean of B = (7+10+11+12+15)/5 = 55/5 = 11- Mean of C = (9+11+12+13+15)/5 = 60/5 = 12- Mean of D = (11+14+15+16+19)/5 = 75/5 = 15Then, we calculate the squared deviations from the mean for each observation in each group and sum them:- For A: (6-10)^2 + (8-10)^2 + (10-10)^2 + (12-10)^2 + (14-10)^2 = 16 + 4 + 0 + 4 + 16 = 40- For B: (7-11)^2 + (10-11)^2 + (11-11)^2 + (12-11)^2 + (15-11)^2 = 16 + 1 + 0 + 1 + 16 = 34- For C: (9-12)^2 + (11-12)^2 + (12-12)^2 + (13-12)^2 + (15-12)^2 = 9 + 1 + 0 + 1 + 9 = 20- For D: (11-15)^2 + (14-15)^2 + (15-15)^2 + (16-15)^2 + (19-15)^2 = 16 + 1 + 0 + 1 + 16 = 34Summing these gives the total SS_error = 40 + 34 + 20 + 34 = 128.

Consider the Data Table Shown with Values for Five Individuals