To complete the partially completed ANOVA table, we'll use the properties of ANOVA. The components we need include the sum of squares (SS), degrees of freedom (df), mean squares (MS), and F statistics.
Given:
Treatments:
- SS = 142.67
- df = (d)
- MS = 35.6675 (MS = SS/df)
- Fstat = (g)
- Ftab = (i)
Blocks:
- SS = 68.14
- df = 5
- MS = (f) (MS = SS/df)
- Fstat = (h)
- Ftab = (j)
Errors:
- SS = (b)
- df = 20
- MS = 1.9165
Total:
- SS = (c)
- df = (e)
Steps to find (b):
-
Find (b):
- We know that the total SS is the sum of the treatment, block, and error SS.
- So, SS_Total = SS_Treatments + SS_Blocks + SS_Errors
Using the notation: \[ (c) = 142.67 + 68.14 + (b) \]
-
Find Degrees of Freedom:
- The total degrees of freedom can be calculated as: \[ df_{Total} = df_{Treatments} + df_{Blocks} + df_{Errors} \]
The degrees of freedom for treatments can be calculated, given we assume k levels in treatments where k is typically based on the data. Given unknown values, we might make some assumptions — usually \(n - 1\) when \(n\) is the count of treatment means.
-
Calculate MS for Blocks: \[ (f) = \frac{SS_{Blocks}}{df_{Blocks}} = \frac{68.14}{5} = 13.628 \]
-
Calculate Total Degrees of Freedom:
- Typically, for a two-factor ANOVA setup: \[ df_{Total} = df_{Treatments} + df_{Blocks} + df_{Errors} = (d) + 5 + 20 \]
For number of treatments \(d\), assume it's an integer.
-
Calculating F-statistics:
- F-statistic for Treatments: \[ (g) = \frac{MS_{Treatments}}{MS_{Errors}} = \frac{35.6675}{1.9165} \approx 18.6 \text{ (just a reference)} \]
And if we had \(h\) and \(j\), similar calculations would be needed.
Assuming \(d = 4\) (as an example), then substituting values:
- Then from our calculations, we can say:
Using \(d = 4\): \[ c = 142.67 + 68.14 + b \] \[ 4 + 5 + 20 = 29 \quad(df total = 29) \] Thus, \[ b = c - 210.81 \]
Finally, if you needed exactly \(b\), basic settings give around the value representative from the overall SS.
Ultimately, compile the total sum, simplify based on the assumptions for degrees, and this \(b\) happens to be calculated from a few adjustments of blocks.
To summarize, find \(b\) [...potential context needed to understand \(c\)] derive corrected numbers duly for exact calculations. You can align utilizing contexts for the \(d\) or any additional restrictions implied.