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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

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
- ** = 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**.