Fill in the missing values for this ANOVA summary table: s.S. M.S. Between R32.013 Within 2912 7072.065 TOTAL

MATLAB: An Introduction with Applications
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**Understanding ANOVA Summary Tables**

An Analysis of Variance (ANOVA) summary table is a crucial part of statistical analysis, particularly when comparing more than two groups. It helps determine if there are significant differences among group means. Here's an outline of the components found in a typical ANOVA table:

**Complete the ANOVA Summary Table:**

| Source   | S.S.   | d.f. | M.S.    | F       |
|----------|--------|------|---------|---------|
| Between  |        |      | 832.013 |         |
| Within   | 2912   |      |         |         |
| TOTAL    | 7072.065 | 37   |         |         |

**Explanation of the Table Components:**

- **Source**: Identifies the variation sources, here being "Between" (variation due to the interaction between groups) and "Within" (variation within each group).

- **S.S. (Sum of Squares)**: This column indicates the total variation for each source. "Between" and "Within" together make up the "TOTAL."

- **d.f. (Degrees of Freedom)**: Represents the number of independent values or quantities which can be assigned to a statistical distribution.

- **M.S. (Mean Square)**: Calculated by dividing the S.S. by the corresponding d.f. It represents the average variation for each source.

- **F**: The F-statistic is used to determine if the observed variances are significantly different.

In this partially filled table, your task is to calculate the missing values, which will provide the detailed results for hypothesis testing in the ANOVA analysis.
Transcribed Image Text:**Understanding ANOVA Summary Tables** An Analysis of Variance (ANOVA) summary table is a crucial part of statistical analysis, particularly when comparing more than two groups. It helps determine if there are significant differences among group means. Here's an outline of the components found in a typical ANOVA table: **Complete the ANOVA Summary Table:** | Source | S.S. | d.f. | M.S. | F | |----------|--------|------|---------|---------| | Between | | | 832.013 | | | Within | 2912 | | | | | TOTAL | 7072.065 | 37 | | | **Explanation of the Table Components:** - **Source**: Identifies the variation sources, here being "Between" (variation due to the interaction between groups) and "Within" (variation within each group). - **S.S. (Sum of Squares)**: This column indicates the total variation for each source. "Between" and "Within" together make up the "TOTAL." - **d.f. (Degrees of Freedom)**: Represents the number of independent values or quantities which can be assigned to a statistical distribution. - **M.S. (Mean Square)**: Calculated by dividing the S.S. by the corresponding d.f. It represents the average variation for each source. - **F**: The F-statistic is used to determine if the observed variances are significantly different. In this partially filled table, your task is to calculate the missing values, which will provide the detailed results for hypothesis testing in the ANOVA analysis.
Expert Solution
Step 1

The total sum of squares is obtained as,

TSS = SSB + SSW, where SSB is the between sum of square SSW is the within sum of squares.

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