Question

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



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 complete the ANOVA table, we need to understand the relationships between the columns.

1. **Degrees of Freedom (df)**:
- For treatments (C), df = k - 1, where k is the number of groups.
- For error (E), df = N - k, where N is the total number of observations.
- For total (B), df = N - 1.

2. **Mean Square (MS)**:
- For treatments, \( MS_{\text{Treatment}} = \frac{SS_{\text{Treatment}}}{df_{\text{Treatment}}} \),
- For error, \( MS_{\text{Error}} = \frac{SS_{\text{Error}}}{df_{\text{Error}}} \).

3. **F-statistic**:
- \( F = \frac{MS_{\text{Treatment}}}{MS_{\text{Error}}} \).

Let's denote:

- **C** = df Treatment
- **A** = SS Error
- **E** = df Error
- **B** = SS Total
- **F** = F-statistic value for Treatment (we need to calculate this)
- **G** = table F-value at the critical level.

In the provided ANOVA table, we have certain values:

- SS Treatment = 12,689
- F-statistic = 10.6642
- Total df = 11

To proceed:
1. **Find the total sum of squares** (B):
\[
SS_{\text{Total}} = SS_{\text{Treatment}} + SS_{\text{Error}} \quad \Rightarrow \quad B = 12,689 + A.
\]

2. **Determine the degrees of freedom for error (E)** and the total degrees of freedom (11):
\[
C + E = 11.
\]

Given that \( MS_{\text{Error}} = 595.3611 \):
\[
MS_{\text{Error}} = \frac{A}{E} \quad \Rightarrow \quad A = 595.3611 \times E.
\]

We know \( MS_{\text{Treatment}} \) is calculated as follows:
\[
MS_{\text{Treatment}} = \frac{12,689}{C}.
\]

And F-statistic can be expressed as:
\[
F = \frac{MS_{\text{Treatment}}}{MS_{\text{Error}}}.
\]
Substituting:
\[
10.6642 = \frac{\frac{12,689}{C}}{595.3611}.
\]
Solving for \( C \):
\[
10.6642 \times 595.3611 = \frac{12,689}{C},
\]
\[
6355.287537 = \frac{12,689}{C},
\]
\[
C = \frac{12,689}{6355.287537} \approx 2.
\]

So, the value of **C** is **2**.