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The phosphorus content was measured for three different soil locations. Five replicate determinations were made on each soil sample. (This problem requires values in your textbook's specific appendices, which you can access through the OWLv2 MindTap Reader. You should not use the OWLv2 References' Tables to answer this question as the values will not match.) a A partial ANOVA table follows: Variation Source SS df MS F Between soils Within soils 0.0081 Total 0.374 Fill in the missing entries in the ANOVA table.

The phosphorus content was measured for three different soil locations. Five replicate determinations were made on each soil sample. (This problem requires values in your textbook's specific appendices, which you can access through the OWLv2 MindTap Reader. You should not use the OWLv2 References' Tables to answer this question as the values will not match.) a A partial ANOVA table follows: Variation Source SS df MS F Between soils Within soils 0.0081 Total 0.374 Fill in the missing entries in the ANOVA table.

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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The table provided is a partial ANOVA (Analysis of Variance) table related to a study measuring phosphorus content in three different soil locations, with five replicate determinations for each soil sample. To complete this table, you need specific values from your textbook’s appendix, which are not included here. ### ANOVA Table - **Variation Source**: Lists the sources of variance. - **SS (Sum of Squares)**: - Total: 0.374 - Needs values for 'Between soils' and 'Within soils'. - **df (degrees of freedom)**: - Missing values for both 'Between soils', 'Within soils', and Total. - **MS (Mean Square)**: - Provided for 'Within soils' as 0.0081. - Missing for 'Between soils'. - **F (F-ratio)**: - Missing value for 'Between soils'. The objective is to fill in the missing entries by using the textbook's specific appendices values. The complete table helps in determining if there are significant differences between the phosphorus contents of the different soil samples.
Transcribed Image Text:The table provided is a partial ANOVA (Analysis of Variance) table related to a study measuring phosphorus content in three different soil locations, with five replicate determinations for each soil sample. To complete this table, you need specific values from your textbook’s appendix, which are not included here. ### ANOVA Table - **Variation Source**: Lists the sources of variance. - **SS (Sum of Squares)**: - Total: 0.374 - Needs values for 'Between soils' and 'Within soils'. - **df (degrees of freedom)**: - Missing values for both 'Between soils', 'Within soils', and Total. - **MS (Mean Square)**: - Provided for 'Within soils' as 0.0081. - Missing for 'Between soils'. - **F (F-ratio)**: - Missing value for 'Between soils'. The objective is to fill in the missing entries by using the textbook's specific appendices values. The complete table helps in determining if there are significant differences between the phosphorus contents of the different soil samples.
The table presents a format commonly used in ANOVA (Analysis of Variance) for partitioning data variability: | Source of Variation | Sum of Squares (SS) | Degrees of Freedom (df) | Mean Square (MS) | Mean Square Estimates | F | |-----------------------------|---------------------|-------------------------|--------------------------------------------------|----------------------------------------|-------------------| | Between groups (factor effect) | SSF | \( I - 1 \) | \( MSF = \frac{SSF}{I - 1} \) | \( \sigma_E^2 + \sigma_F^2 \) | \( \frac{MSF}{MSE} \) | | Within groups (error) | SSE | \( N - I \) | \( MSE = \frac{SSE}{N - I} \) | \( \sigma_F^2 \) | | | Total | SST | \( N - 1 \) | | | | ### Explanation - **Source of Variation**: Indicates where the variability comes from in the data. - *Between groups (factor effect)*: Variability due to the factor being studied. - *Within groups (error)*: Variability within each group. - *Total*: Overall variability. - **Sum of Squares (SS)**: Measures total variation in the data. - SSF: Sum of squares for factor effect. - SSE: Sum of squares for error. - SST: Total sum of squares. - **Degrees of Freedom (df)**: Number of values in the final calculation of a statistic that are free to vary. - \( I - 1 \): Degrees of freedom for the factor effect. - \( N - I \): Degrees of freedom for the error. - \( N - 1 \): Total degrees of freedom. - **Mean Square (MS)**: Average of sum of squares, used to determine variance. - MSF: Mean square for factor effect, calculated as \( \frac{SSF}{I - 1} \). - MSE: Mean square for error, calculated as \( \frac{SSE}{N - I} \). - **Mean Square Estimates**: - Represents estimates of variance; for the factor effect (\( \sigma_E^2 + \sigma_F^2 \)) and for
Transcribed Image Text:The table presents a format commonly used in ANOVA (Analysis of Variance) for partitioning data variability: | Source of Variation | Sum of Squares (SS) | Degrees of Freedom (df) | Mean Square (MS) | Mean Square Estimates | F | |-----------------------------|---------------------|-------------------------|--------------------------------------------------|----------------------------------------|-------------------| | Between groups (factor effect) | SSF | \( I - 1 \) | \( MSF = \frac{SSF}{I - 1} \) | \( \sigma_E^2 + \sigma_F^2 \) | \( \frac{MSF}{MSE} \) | | Within groups (error) | SSE | \( N - I \) | \( MSE = \frac{SSE}{N - I} \) | \( \sigma_F^2 \) | | | Total | SST | \( N - 1 \) | | | | ### Explanation - **Source of Variation**: Indicates where the variability comes from in the data. - *Between groups (factor effect)*: Variability due to the factor being studied. - *Within groups (error)*: Variability within each group. - *Total*: Overall variability. - **Sum of Squares (SS)**: Measures total variation in the data. - SSF: Sum of squares for factor effect. - SSE: Sum of squares for error. - SST: Total sum of squares. - **Degrees of Freedom (df)**: Number of values in the final calculation of a statistic that are free to vary. - \( I - 1 \): Degrees of freedom for the factor effect. - \( N - I \): Degrees of freedom for the error. - \( N - 1 \): Total degrees of freedom. - **Mean Square (MS)**: Average of sum of squares, used to determine variance. - MSF: Mean square for factor effect, calculated as \( \frac{SSF}{I - 1} \). - MSE: Mean square for error, calculated as \( \frac{SSE}{N - I} \). - **Mean Square Estimates**: - Represents estimates of variance; for the factor effect (\( \sigma_E^2 + \sigma_F^2 \)) and for
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