Question

Consider the following partially completed ANOVA, and answer the following: give the value of (A). / Beskou die onvoltooide ANOVA en beantwoord die volgende: gee die waarde van (A).
ANOVA

Source SS df MS Fstat Ftab
Treatment 12 689 (C) (F) 10.6642 (G)
Error (A) (E) 595.3611
Total (B) 11

Answer 1

To fill in the missing values (A), (B), (C), (E), (F), and (G) in the ANOVA table, we first need to understand some key relationships in ANOVA calculations.

1. **Total Sum of Squares (SS Total)**:
\[
SS_{\text{Total}} = SS_{\text{Treatment}} + SS_{\text{Error}}
\]
Here, \( SS_{\text{Treatment}} = 12,689 \) and we need to find \( SS_{\text{Error}} (A) \) and \( SS_{\text{Total}} (B) \).

2. **Degrees of Freedom (df)**:
The degrees of freedom can be calculated as follows:
\[
df_{\text{Treatment}} = k - 1 \quad \text{(where \( k \) is the number of treatments)}
\]
\[
df_{\text{Error}} = N - k \quad \text{(where \( N \) is the total number of observations)}
\]
The total degrees of freedom is:
\[
df_{\text{Total}} = N - 1
\]
Given that \( df_{\text{Total}} = 11 \), we also learn that:
\[
N - 1 = 11 \implies N = 12
\]

Since we know that \( df_{\text{Treatment}} + df_{\text{Error}} = df_{\text{Total}} \):
\[
df_{\text{Treatment}} + df_{\text{Error}} = 11
\]
Let \( df_{\text{Treatment}} = (C) \) and \( df_{\text{Error}} = (E) \). Then:
\[
(C) + (E) = 11
\]

3. **Mean Squares (MS)**:
Mean Squares are calculated as follows:
\[
MS_{\text{Treatment}} = \frac{SS_{\text{Treatment}}}{df_{\text{Treatment}}} = \frac{12,689}{C}
\]
\[
MS_{\text{Error}} = \frac{SS_{\text{Error}}}{df_{\text{Error}}} = \frac{A}{E}
\]

4. **F-statistic**:
The F-statistic is calculated as follows:
\[
F = \frac{MS_{\text{Treatment}}}{MS_{\text{Error}}}
\]

Given \( F = 10.6642 \) and \( MS_{\text{Error}} = 595.3611 \):
\[
MS_{\text{Treatment}} = F \times MS_{\text{Error}} = 10.6642 \times 595.3611
\]
\[
MS_{\text{Treatment}} \approx 6348.688
\]
5. **Finding Treatment Degrees of Freedom (C)**:
Now we can find \( C \):
\[
C = \frac{SS_{\text{Treatment}}}{MS_{\text{Treatment}}} = \frac{12,689}{6348.688} \approx 2
\]

Thus:
\[
E = 11 - C = 11 - 2 = 9
\]

### Summary Values:
- \( C = 2 \)
- \( E = 9 \)

6. **Finding SS Error (A)**:
\[
MS_{\text{Error}} = \frac{A}{E} \implies 595.3611 = \frac{A}{9} \implies A = 595.3611 \times 9 \approx 5,358.250
\]

7. **Finding Total SS (B)**:
\[
SS_{\text{Total}} = SS_{\text{Treatment}} + SS_{\text{Error}} = 12,689 + 5,358.250 \approx 18,047.250
\]

### Results:
- (A) = 5,358.250 (approximately)
- (B) = 18,047.250 (approximately)
- (C) = 2
- (E) = 9
- (F) = 10.6642 (from the question)
- (G) = 10.6642 (same as F)

Now, you can fill in:
- **(A)**: 5,358.250
- **(B)**: 18,047.250
- **(C)**: 2
- **(E)**: 9
- **(F)**: 10.6642
- **(G)**: 10.6642