How do you find SSA, SSB & SSE??

To find the sums of squares (SS) for different sources of variation in a statistical model, you follow specific steps depending on the context.

1. Determine the number of observations or data points (n) in your dataset.

2. Calculate the mean or average of the entire dataset, denoted as "M" (sometimes represented as "m" or "x-bar").

3. Identify the sources of variation you want to measure:

a. SSA (Sum of Squares for Factor A): This measures the variability between different levels or groups of a factor, such as different treatments or categories. To calculate SSA, follow these steps:
- Calculate the mean of each group or level of the factor.
- Subtract the overall mean (M) from each group mean.
- Square the result for each group.
- Multiply each squared difference by the number of observations in that group.
- Sum up these values to get SSA.

b. SSB (Sum of Squares for Factor B): This measures the variability between different levels or groups of another factor. The calculation steps for SSB are similar to those for SSA.

c. SSE (Sum of Squares Error, or Residual Sum of Squares): This measures the variability within each group or condition, which is the unexplained variation. To calculate SSE, follow these steps:
- Calculate the squared difference between each individual data point and its corresponding group mean.
- Sum up these squared differences to get SSE.

Note: SSA + SSB + SSE should equal the total sum of squares (SST), which represents the total variability in the dataset.

The specific formulas and calculations may vary depending on the statistical test or model you are using. Ensure you use the appropriate formulas for your analysis.