Degrees of Sum of Mean Square Consider an experiment with nine groups, with seven values in each. For the ANOVA summary table shown to the right, fill in all the missing results. Source Freedom Squares Among (Variance) F c-1=? SSA = ? MSA = 20 FSTAT = ? groups Within n-c=? SSW = 540 MSW = ? groups Total n-1=? SST =? ..... Complete the ANOVA summary table below. Mean Square (Variance) Degrees of Sum of Source Freedom Squares F Among groups c-1 = SSA = MSA = 20 FSTAT = Within groups SSW = 540 MSW = n-c= Total n-1= SST = (Simplify your answers.)

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Below is a transcription of the image with explanations for the ANOVA summary table:

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Consider an experiment with nine groups, with seven values in each. For the ANOVA summary table shown to the right, fill in all the missing results.

**ANOVA Summary Table:**

| Source          | Degrees of Freedom | Sum of Squares | Mean Square (Variance) | F         |
|-----------------|--------------------|----------------|------------------------|-----------|
| Among groups    | c - 1 = ?          | SSA = ?        | MSA = 20               | F_STAT = ?|
| Within groups   | n - c = ?          | SSW = 540      | MSW = ?                |           |
| Total           | n - 1 = ?          | SST = ?        |                        |           |

---

Complete the ANOVA summary table below.

**ANOVA Table Completion:**

| Source          | Degrees of Freedom | Sum of Squares | Mean Square (Variance) | F         |
|-----------------|--------------------|----------------|------------------------|-----------|
| Among groups    | c - 1 =            | SSA = [      ] | MSA = 20               | F_STAT = [ ] |
| Within groups   | n - c =            | SSW = 540      | MSW = [     ]          |           |
| Total           | n - 1 =            | SST = [     ]  |                        |           |

(Simplify your answers.)

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**Explanation:**

- The table is a framework for conducting an Analysis of Variance (ANOVA).
- It has three main sources of variation: "Among groups," "Within groups," and "Total."
- Each source has associated values for "Degrees of Freedom," "Sum of Squares," "Mean Square (Variance)," and the F-statistic (F_STAT).
- "Degrees of Freedom" are calculated based on the number of groups (c) and total observations (n).
- "Sum of Squares" represents the variability, where SSA is for among groups, SSW is for within groups, and SST is the total sum of squares.
- "Mean Square" is calculated by dividing Sum of Squares by Degrees of Freedom, and it's used to compute the F-statistic (F_STAT), which helps in determining statistical significance.
Transcribed Image Text:Below is a transcription of the image with explanations for the ANOVA summary table: --- Consider an experiment with nine groups, with seven values in each. For the ANOVA summary table shown to the right, fill in all the missing results. **ANOVA Summary Table:** | Source | Degrees of Freedom | Sum of Squares | Mean Square (Variance) | F | |-----------------|--------------------|----------------|------------------------|-----------| | Among groups | c - 1 = ? | SSA = ? | MSA = 20 | F_STAT = ?| | Within groups | n - c = ? | SSW = 540 | MSW = ? | | | Total | n - 1 = ? | SST = ? | | | --- Complete the ANOVA summary table below. **ANOVA Table Completion:** | Source | Degrees of Freedom | Sum of Squares | Mean Square (Variance) | F | |-----------------|--------------------|----------------|------------------------|-----------| | Among groups | c - 1 = | SSA = [ ] | MSA = 20 | F_STAT = [ ] | | Within groups | n - c = | SSW = 540 | MSW = [ ] | | | Total | n - 1 = | SST = [ ] | | | (Simplify your answers.) --- **Explanation:** - The table is a framework for conducting an Analysis of Variance (ANOVA). - It has three main sources of variation: "Among groups," "Within groups," and "Total." - Each source has associated values for "Degrees of Freedom," "Sum of Squares," "Mean Square (Variance)," and the F-statistic (F_STAT). - "Degrees of Freedom" are calculated based on the number of groups (c) and total observations (n). - "Sum of Squares" represents the variability, where SSA is for among groups, SSW is for within groups, and SST is the total sum of squares. - "Mean Square" is calculated by dividing Sum of Squares by Degrees of Freedom, and it's used to compute the F-statistic (F_STAT), which helps in determining statistical significance.
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