We want to know if selenium levels are diffenrt among the 4 meat groups. Use signifcance level 0.01.a.) What is sum of squares tratment equal to ? What is degrees if freedom for treatment? and Error?b.)What is the mean square treatment equal to? what is the mean square error equal to? ### Analysis of Variance (ANOVA) TableIn the context of hypothesis testing and statistical analysis, an ANOVA table helps in determining the spread and distribution of data. Below is an example ANOVA table:| Source | Sum of Squares | DF | Mean Squares | F ||------------|----------------|------|--------------|-----|| Treatment | | | | || Error | 36747.2267 | | | || Total | 58009.0556 | 143 | | |**Explanation of Columns:**1. **Source**: This column lists the sources of variability. The typical sources are 'Treatment' (or 'Between Groups') and 'Error' (or 'Within Group'). In this table, the last row ('Total') shows the overall variability in the data.2. **Sum of Squares (SS)**: This column shows the total variability for each source. For instance, the 'Error' source here has a Sum of Squares equal to 36747.2267, and the total Sum of Squares across all sources is 58009.0556.3. **DF (Degrees of Freedom)**: This indicates the number of independent values that can vary in the dataset while estimating a statistical parameter. Here, the 'Total' degrees of freedom is 143.4. **Mean Squares (MS)**: This is the variance estimate for each source, calculated as the Sum of Squares divided by the respective degrees of freedom (DF). However, the values in this column are not provided in this table.5. **F**: The F-value is the test statistic used to determine whether the variability between group means is more than what would be expected by chance. It is calculated as the ratio of mean squares between the treatment groups to the mean squares within the groups (error).This table is crucial in summarizing the data for various sources of variance, helping researchers to understand the effectiveness of the treatments being evaluated.

Let a treatment A be classified into k levels then, to test the equality of k levels means, we will…

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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We want to know if selenium levels are diffenrt among the 4 meat groups. Use signifcance level 0.01.

a.) What is sum of squares tratment equal to ? What is degrees if freedom for treatment? and Error?

b.)What is the mean square treatment equal to? what is the mean square error equal to?

### Analysis of Variance (ANOVA) Table

In the context of hypothesis testing and statistical analysis, an ANOVA table helps in determining the spread and distribution of data. Below is an example ANOVA table:

| Source | Sum of Squares | DF | Mean Squares | F |
|------------|----------------|------|--------------|-----|
| Treatment | | | | |
| Error | 36747.2267 | | | |
| Total | 58009.0556 | 143 | | |

**Explanation of Columns:**
1. **Source**: This column lists the sources of variability. The typical sources are 'Treatment' (or 'Between Groups') and 'Error' (or 'Within Group'). In this table, the last row ('Total') shows the overall variability in the data.

2. **Sum of Squares (SS)**: This column shows the total variability for each source. For instance, the 'Error' source here has a Sum of Squares equal to 36747.2267, and the total Sum of Squares across all sources is 58009.0556.

3. **DF (Degrees of Freedom)**: This indicates the number of independent values that can vary in the dataset while estimating a statistical parameter. Here, the 'Total' degrees of freedom is 143.

4. **Mean Squares (MS)**: This is the variance estimate for each source, calculated as the Sum of Squares divided by the respective degrees of freedom (DF). However, the values in this column are not provided in this table.

5. **F**: The F-value is the test statistic used to determine whether the variability between group means is more than what would be expected by chance. It is calculated as the ratio of mean squares between the treatment groups to the mean squares within the groups (error).

This table is crucial in summarizing the data for various sources of variance, helping researchers to understand the effectiveness of the treatments being evaluated.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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