7.
Product and Process Comparisons
7.4. Comparisons based on data from more than two processes 7.4.3. Are the means equal?


Formulas for 1way ANOVA hand calculations  Although computer programs that do ANOVA calculations now are common, for reference purposes this page describes how to calculate the various entries in an ANOVA table. Remember, the goal is to produce two variances (of treatments and error) and their ratio. The various computational formulas will be shown and applied to the data from the previous example.  
Step 1: compute CM  STEP 1 Compute
CM, the correction for the mean.


Step 2: compute total SS  STEP 2 Compute
the total SS.
The total SS = sum of squares of all observations  CM The 829.390 SS is called the "raw" or "uncorrected " sum of squares. 

Step 3: compute SST  STEP 3 Compute
SST, the treatment sum of squares.
First we compute the total (sum) for each treatment.
T_{2} = (8.3) + (6.8) + ... + (6.5) = 38.6 T_{1} = (8.0) + (10.5) + ... + (9.3) = 42.8 

Step 4: compute SSE  STEP 4 Compute
SSE, the error sum of squares.
Here we utilize the property that the treatment sum of squares plus the error sum of squares equals the total sum of squares. Hence, SSE = SS Total  SST = 45.349  27.897 = 17.45. 

Step 5: Compute MST, MSE, and F  STEP 5 Compute
MST, MSE and their ratio, F.
MST is the mean square of treatments, MSE is the mean square of error (MSE is also frequently denoted by).
MSE = SSE / (Nk) = 17.452/ 12 = 1.454
