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a. Compute the sum or squares between treatments (to the nearest whole number). b. Compute the mean square between treatments (to 1 decimal). c. Compute the sum of squares due to error (to the nearest whole number). Compute the mean square due to error (to 1 decimal)

a. Compute the sum or squares between treatments (to the nearest whole number). b. Compute the mean square between treatments (to 1 decimal). c. Compute the sum of squares due to error (to the nearest whole number). Compute the mean square due to error (to 1 decimal)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**ANOVA Table Calculation and Interpretation** This exercise involves calculating and interpreting an ANOVA (Analysis of Variance) table. Follow the steps below to complete the ANOVA table and determine the conclusion for the means of the three treatments. 1. **Sum of Squares Between Treatments (SST):** - Compute the sum of squares between treatments to the nearest whole number. 2. **Mean Square Between Treatments (MST):** - Compute the mean square between treatments to 1 decimal place. 3. **Sum of Squares Due to Error (SSE):** - Compute the sum of squares due to error to the nearest whole number. 4. **Mean Square Due to Error (MSE):** - Compute the mean square due to error to 1 decimal place. 5. **Setting Up ANOVA Table:** - Set up the ANOVA table for this problem. Round all Sum of Squares to the nearest whole number. Round all Mean Squares to 1 decimal place. Round F to 2 decimal places. Round your p-value to 4 decimal places. **ANOVA Table:** | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value | |---------------------|----------------|--------------------|-------------|-------|---------| | Treatments | | | | | | | Error | | | | | | | Total | | | | | | 6. **Testing for Significance:** - At the \( \alpha = 0.05 \) level of significance, test whether the means for the three treatments are equal. - Calculate the value of the test statistic to 2 decimal places. **The p-value is between 0.01 and 0.025.** 7. **Conclusion:** - Based on the p-value obtained and the significance level \( \alpha \), conclude whether the treatment means are equal or not. To conclude correctly, if the p-value is less than the significance level \( \alpha \) (0.05 in this case), it means that there is a significant difference between the treatments. Hence, you would conclude that **not all treatment means are equal**. **Partially Correct Interpretation:** - The provided calculations and table setup need correctness verification as indicated by the incorrect marks (cross symbols). For detailed accuracy,
Transcribed Image Text:**ANOVA Table Calculation and Interpretation** This exercise involves calculating and interpreting an ANOVA (Analysis of Variance) table. Follow the steps below to complete the ANOVA table and determine the conclusion for the means of the three treatments. 1. **Sum of Squares Between Treatments (SST):** - Compute the sum of squares between treatments to the nearest whole number. 2. **Mean Square Between Treatments (MST):** - Compute the mean square between treatments to 1 decimal place. 3. **Sum of Squares Due to Error (SSE):** - Compute the sum of squares due to error to the nearest whole number. 4. **Mean Square Due to Error (MSE):** - Compute the mean square due to error to 1 decimal place. 5. **Setting Up ANOVA Table:** - Set up the ANOVA table for this problem. Round all Sum of Squares to the nearest whole number. Round all Mean Squares to 1 decimal place. Round F to 2 decimal places. Round your p-value to 4 decimal places. **ANOVA Table:** | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value | |---------------------|----------------|--------------------|-------------|-------|---------| | Treatments | | | | | | | Error | | | | | | | Total | | | | | | 6. **Testing for Significance:** - At the \( \alpha = 0.05 \) level of significance, test whether the means for the three treatments are equal. - Calculate the value of the test statistic to 2 decimal places. **The p-value is between 0.01 and 0.025.** 7. **Conclusion:** - Based on the p-value obtained and the significance level \( \alpha \), conclude whether the treatment means are equal or not. To conclude correctly, if the p-value is less than the significance level \( \alpha \) (0.05 in this case), it means that there is a significant difference between the treatments. Hence, you would conclude that **not all treatment means are equal**. **Partially Correct Interpretation:** - The provided calculations and table setup need correctness verification as indicated by the incorrect marks (cross symbols). For detailed accuracy,
### Analysis of Variance (ANOVA) in Completely Randomized Design #### Data Summary The following data originates from a completely randomized experiment involving three different treatments, labeled as A, B, and C. | Treatment | A | B | C | |-----------|----|----|----| | | 164| 145| 123| | | 142| 157| 122| | | 167| 128| 139| | | 145| 145| 147| | | 149| 137| 151| | | 187| 146| 122| Sample statistics: - Sample mean: - Treatment A: 159 - Treatment B: 143 - Treatment C: 134 - Sample variance: - Treatment A: 291.6 - Treatment B: 94.8 - Treatment C: 178.4 #### Calculation Instructions 1. **Sum of Squares Between Treatments (SSB)** Compute the sum of squares between treatments (to the nearest whole number). ``` Input box for SSB ``` 2. **Mean Square Between Treatments (MSB)** Compute the mean square between treatments (to 1 decimal place). ``` Input box for MSB ``` 3. **Sum of Squares Due to Error (SSE)** Compute the sum of squares due to error (to the nearest whole number). ``` Input box for SSE ``` 4. **Mean Square Due to Error (MSE)** Compute the mean square due to error (to 1 decimal place). ``` Input box for MSE ``` 5. **ANOVA Table** Set up the ANOVA table for this problem, rounding all Sum of Squares to nearest whole numbers. Round all Mean Squares to one decimal place, F-ratio to two decimal places, and p-value to four decimal places. | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value | |---------------------|----------------|--------------------|-------------|-----|---------| | Treatments | Input box | Input box | Input box | Input box | Input box | | Error | Input box | Input box | Input box | | |
Transcribed Image Text:### Analysis of Variance (ANOVA) in Completely Randomized Design #### Data Summary The following data originates from a completely randomized experiment involving three different treatments, labeled as A, B, and C. | Treatment | A | B | C | |-----------|----|----|----| | | 164| 145| 123| | | 142| 157| 122| | | 167| 128| 139| | | 145| 145| 147| | | 149| 137| 151| | | 187| 146| 122| Sample statistics: - Sample mean: - Treatment A: 159 - Treatment B: 143 - Treatment C: 134 - Sample variance: - Treatment A: 291.6 - Treatment B: 94.8 - Treatment C: 178.4 #### Calculation Instructions 1. **Sum of Squares Between Treatments (SSB)** Compute the sum of squares between treatments (to the nearest whole number). ``` Input box for SSB ``` 2. **Mean Square Between Treatments (MSB)** Compute the mean square between treatments (to 1 decimal place). ``` Input box for MSB ``` 3. **Sum of Squares Due to Error (SSE)** Compute the sum of squares due to error (to the nearest whole number). ``` Input box for SSE ``` 4. **Mean Square Due to Error (MSE)** Compute the mean square due to error (to 1 decimal place). ``` Input box for MSE ``` 5. **ANOVA Table** Set up the ANOVA table for this problem, rounding all Sum of Squares to nearest whole numbers. Round all Mean Squares to one decimal place, F-ratio to two decimal places, and p-value to four decimal places. | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value | |---------------------|----------------|--------------------|-------------|-----|---------| | Treatments | Input box | Input box | Input box | Input box | Input box | | Error | Input box | Input box | Input box | | |
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