#28 The following is a partial ANOVA table.

Sum of Mean
Source Squares df Square F

Treatment 2
Error 20
Total 500 11

To determine the missing values in the ANOVA table, we need to understand the calculations involved in each column.

The ANOVA table is typically used in the analysis of variance, which compares the variability between groups (Treatment) to the variability within groups (Error). The F statistic is then calculated by dividing the mean square of Treatment by the mean square of Error.

Here's a breakdown of the calculations for each column in the ANOVA table:

1. Source: This column represents the source of variation. In this case, we have only two sources: Treatment and Error.

2. Sum of Squares: This column represents the sum of the squared deviations of each observation from the grand mean. The Total row provides the total sum of squares, which is typically calculated as the sum of squares for Treatment and Error.

In this case, the sum of squares for Treatment is missing. To calculate it, we need the sum of squares for Error, as well as the total sum of squares. The sum of squares for Treatment can be calculated as the difference between the total sum of squares and the sum of squares for Error. However, since the sum of squares for Error is also missing, we cannot determine the sum of squares for Treatment.

3. df (Degrees of Freedom): This column represents the degrees of freedom associated with each source of variation. The degrees of freedom for Treatment are equal to the number of groups (levels - 1). In this case, the Treatment has 2 levels, so the degrees of freedom would be 2 - 1 = 1.

The degrees of freedom for Error are calculated as the total number of observations minus the total number of groups (levels). In this case, we are given that the total is 500 and the Treatment has 2 levels, so the degrees of freedom for Error would be 500 - 2 = 498.

4. Mean Square: This column represents the mean of squares, which is calculated by dividing the sum of squares by the degrees of freedom.

Since we do not have the sum of squares for Treatment, we cannot calculate the Mean Square for Treatment.

5. F: This column represents the F statistic, which is calculated by dividing the Mean Square for Treatment by the Mean Square for Error.

Since we do not have the Mean Square for Treatment, we cannot calculate the F value.

In summary, without the missing values (Sum of Squares and Mean Square for Treatment), we cannot determine the F statistic or make any conclusions about the significance of the Treatment effect.