To calculate the Error Sum of Squares (SSE) for a one-way ANOVA, follow these steps:

1. Calculate the Mean of Each Group (Column):

   • For Group A: $\frac{27 + 26 + 23 + 24}{4} = 25$
   • For Group B: $\frac{26 + 22 + 21 + 23}{4} = 23$
   • For Group C: $\frac{27 + 29 + 27 + 26}{4} = 27.25$

2. Calculate the Overall Mean:

   • Total number of data points = 12.
   • Sum of all values: $27 + 26 + 23 + 24 + 26 + 22 + 21 + 23 + 27 + 29 + 27 + 26 = 301$.
   • Overall Mean (Grand Mean): $\frac{301}{12} = 25.08$ (approx).

3. Calculate SSE (Sum of Squares for Error): SSE is calculated as the sum of the squared differences between each individual observation and its respective group mean.

   For each group:

   • Group A: $(27 - 25)^2 + (26 - 25)^2 + (23 - 25)^2 + (24 - 25)^2 = 4 + 1 + 4 + 1 = 10$
   • Group B: $(26 - 23)^2 + (22 - 23)^2 + (21 - 23)^2 + (23 - 23)^2 = 9 + 1 + 4 + 0 = 14$
   • Group C: $(27 - 27.25)^2 + (29 - 27.25)^2 + (27 - 27.25)^2 + (26 - 27.25)^2 = 0.0625 + 3.0625 + 0.0625 + 1.5625 = 4.75$

   Total SSE = $10 + 14 + 4.75 = 28.75$

So, the correct answer is:

• D. 28.75

Would you like further details or explanations on any part?

Related Questions

1. How do we interpret the SSE value in ANOVA?
2. What is the formula for calculating total sum of squares (SST)?
3. How does one calculate the F-statistic in ANOVA?
4. Why is ANOVA used for comparing group means?
5. What assumptions must be met to perform a one-way ANOVA?

Tip

In ANOVA, SSE reflects the variation within each group, and lower SSE values typically indicate less variability within groups.