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Consider the following ANOVA table from a randomized block design with 4 treatment levels and 7 blocks. Round your answer to three decimal places. Source SS df MS Treatment Block Error Total 15 43.5 20 Calculate the F-test statistics and fill in the blanks.

Consider the following ANOVA table from a randomized block design with 4 treatment levels and 7 blocks. Round your answer to three decimal places. Source SS df MS Treatment Block Error Total 15 43.5 20 Calculate the F-test statistics and fill in the blanks.

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
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### ANOVA Analysis for Randomized Block Design Consider the following ANOVA table from a randomized block design with 4 treatment levels and 7 blocks. Round your answer to three decimal places. | Source | SS | df | MS | F | |-----------|------|----|-----|------| | Treatment | 15 | | | | | Block | 43.5 | | | | | Error | 20 | | | | | Total | | | | | #### Steps to Calculate the F-test Statistics: 1. **Degrees of Freedom (df):** - **Treatment:** The degrees of freedom for the treatment can be calculated as the number of treatment levels minus 1. - **Block:** The degrees of freedom for the block can be calculated as the number of blocks minus 1. - **Error:** The degrees of freedom for the error can be calculated as the product of (number of treatment levels - 1) and (number of blocks - 1). - **Total:** The total degrees of freedom can be calculated as the number of observations minus 1 or the sum of the degrees of freedom for treatment, block, and error. 2. **Mean Square (MS):** - MS is obtained by dividing SS by its respective degrees of freedom (df). - **MS (Treatment):** \( \frac{SS_{\text{Treatment}}}{df_{\text{Treatment}}} \) - **MS (Block):** \( \frac{SS_{\text{Block}}}{df_{\text{Block}}} \) - **MS (Error):** \( \frac{SS_{\text{Error}}}{df_{\text{Error}}} \) 3. **F-value:** - The F-value for treatment is obtained by dividing \( MS_{\text{Treatment}} \) by \( MS_{\text{Error}} \). - The F-value for block is obtained by dividing \( MS_{\text{Block}} \) by \( MS_{\text{Error}} \). #### Calculate the F-test statistics and fill in the blanks in the ANOVA table. Note: - SS stands for Sum of Squares. - df stands for Degrees of Freedom. - MS stands for Mean Square. - F stands for F-value.
Transcribed Image Text:### ANOVA Analysis for Randomized Block Design Consider the following ANOVA table from a randomized block design with 4 treatment levels and 7 blocks. Round your answer to three decimal places. | Source | SS | df | MS | F | |-----------|------|----|-----|------| | Treatment | 15 | | | | | Block | 43.5 | | | | | Error | 20 | | | | | Total | | | | | #### Steps to Calculate the F-test Statistics: 1. **Degrees of Freedom (df):** - **Treatment:** The degrees of freedom for the treatment can be calculated as the number of treatment levels minus 1. - **Block:** The degrees of freedom for the block can be calculated as the number of blocks minus 1. - **Error:** The degrees of freedom for the error can be calculated as the product of (number of treatment levels - 1) and (number of blocks - 1). - **Total:** The total degrees of freedom can be calculated as the number of observations minus 1 or the sum of the degrees of freedom for treatment, block, and error. 2. **Mean Square (MS):** - MS is obtained by dividing SS by its respective degrees of freedom (df). - **MS (Treatment):** \( \frac{SS_{\text{Treatment}}}{df_{\text{Treatment}}} \) - **MS (Block):** \( \frac{SS_{\text{Block}}}{df_{\text{Block}}} \) - **MS (Error):** \( \frac{SS_{\text{Error}}}{df_{\text{Error}}} \) 3. **F-value:** - The F-value for treatment is obtained by dividing \( MS_{\text{Treatment}} \) by \( MS_{\text{Error}} \). - The F-value for block is obtained by dividing \( MS_{\text{Block}} \) by \( MS_{\text{Error}} \). #### Calculate the F-test statistics and fill in the blanks in the ANOVA table. Note: - SS stands for Sum of Squares. - df stands for Degrees of Freedom. - MS stands for Mean Square. - F stands for F-value.
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