Question
The given ANOVA table only has three values provided, but these can be used to find the missing values. Source of Variation Sum of Squares
The given ANOVA table only has three values provided, but these can be used to find the missing values.
Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p - value |
Treatments | 600 | ____________ | ____________ | ____________ | ____________ |
Blocks | 800 | ____________ | ____________ | ||
Error | ____________ | ____________ | ____________ | ||
Total | 1,700 | ____________ |
Use = 0.05 to test for any significant differences.
The ANOVA table for a randomized block design has the following form. Note that all the values within this table will be positive.
Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p - value |
Treatments | SSTR | k - 1 | MSTR = SSTR / k - 1 | F = MSTR / MSE | |
Blocks | SSBL | b - 1 | MSBL = SSBL / b - 1 | ||
Error | SSE | (k - 1)(b - 1) | MSE = SSE / (k - 1)(b - 1) | ||
Total | SST | nT 1 |
The values in the column for the degrees of freedom are based on the number of k population means, or treatments, the number of b blocks, and the total number of observations, nT = kb. The total degrees of freedom is the sum of the degrees of freedom for the treatments, blocks, and error.
In this design, there were four treatments with seven blocks. Therefore, k = ____________, b = ____________, and nT=kb = ____________. Complete the column for the degrees of freedom in the ANOVA table.
Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p - value |
Treatments | 600 | k - 1 = ____________ | |||
Blocks | 800 | b - 1 = ____________ | |||
Error | 300 | (k - 1)(b - 1) = ____________ | |||
Total | 1,700 | nT 1 = ____________ |
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