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Let's start with the degrees of freedom (DF) column: If there are n total data points collected, then there are n−1 total degrees of freedom. If there are m groups being compared, then there are m−1 degrees of freedom associated with the factor of interest.
The first one gives critical values of F at the p = 0.05 level of significance. The second table gives critical values of F at the p = 0.01 level of significance. Obtain your F-ratio. This has (x,y) degrees of freedom associated with it. Go along x columns, and down y rows.
Degrees of freedom: The total degrees of freedom is also partitioned into the Factor and Error components. Mean Square: This represents calculation of the variance by dividing Sum of Squares by the appropriate degrees of freedom.
The total degrees of freedom is N-1 (and it is also true that (k-1) + (N-k) = N-1). The fourth column contains "Mean Squares (MS)" which are computed by dividing sums of squares (SS) by degrees of freedom (df), row by row. Specifically, MSB=SSB/ (k-1) and MSE=SSE/ (N-k). Dividing SST/ (N-1) produces the variance of the total sample.
CRITICAL VALUES for the "F" Distribution, ALPHA = .05. Denominator Numerator DF DF 1 2 3 4 5 6 7 8 9 10 51 4.030 3.179 2.786 2.553 2.397 2.283 2.195 2.126 2.069 2.022
In sum, whatever the type of ANOVA you have, your general process will be: Calculate the degrees of freedom. Calculate the Sum of Squares. Use SS to calculate the Mean Square (SS/df). Calculate the F as a ratio of the MS BG divided by the MS WG (or MS Error, they are the same thing).
The degrees of freedom associated with SSE is n-2 = 49-2 = 47. And the degrees of freedom add up: 1 + 47 = 48. The sums of squares add up: SSTO = SSR + SSE. That is, here: 53637 = 36464 + 17173. Let's tackle a few more columns of the analysis of variance table, namely the "mean square" column, labeled MS, and the F-statistic column labeled F.