Given the following Anova table and that CF=2782.53, calculate the sum of all the observations.
ANOVA
Source of variation SS df MS Fstat Ftab
Treatments 17.76 3 C G J
Blocks 52.71 B D H K
Error A 15 E I
Total 103.45 23 F
To answer this question, we need the values for A, B, C, D, E, F, G, H, I, and J from the Anova table. Unfortunately, these values are not provided in the given information.
Without these values, it is not possible to calculate the sum of all the observations.
To calculate the sum of all the observations, we need to find the value of treatment and error sum of squares (SS).
In the given ANOVA table, the treatment SS is 17.76 and the error SS is A. However, the specific value for A is not provided. Therefore, we cannot determine the exact sum of all the observations with the given information.
If you have the value for A, you can calculate the sum of all the observations using the following formula:
Sum of observations = CF + Treatment SS + Error SS
Here, we are given that CF (Correction Factor) is 2782.53.
So, Sum of observations = 2782.53 + 17.76 + A
Please provide the value of A in order to calculate the sum of all the observations accurately.
To calculate the sum of all the observations, we need to use the information provided in the ANOVA table.
The column headers in the ANOVA table are as follows:
Source of variation (SOV), Sum of Squares (SS), Degrees of Freedom (df), Mean Squares (MS), F-statistic (Fstat), and F-table (Ftab).
From the table, we can see that the sum of squares (SS) for Treatments is 17.76.
To calculate the sum of all the observations, we need to find the total number of observations (N).
To find the total number of observations (N), we can sum up the degrees of freedom (df) for Treatments, Blocks, and Error:
df(Treatments) = 3
df(Blocks) = 2
df(Error) = 15
N = df(Treatments) + df(Blocks) + df(Error)
N = 3 + 2 + 15
N = 20
Next, we can use the sum of squares (SS) for Treatments to calculate the sum of all the observations.
SS(Total) = SS(Treatments) + SS(Blocks) + SS(Error)
SS(Total) = 17.76 + 52.71 + A
From the table, we can see that the total sum of squares (SS(Total)) is 103.45.
Therefore, we can write the equation:
103.45 = 17.76 + 52.71 + A
To solve for A, we subtract 17.76 and 52.71 from both sides:
A = 103.45 - 17.76 - 52.71
A = 32.98
So, the sum of all the observations is 32.98.