one-way ANOVA model

Question

In the one-way ANOVA model, the model variation SSM is equal to the between-group variation SSB. I found that SSE=SST-SSB => SSB=SST-SSE And that SSM is the difference of STT and SSE => SSM=SST-SSE SSB=SSM But this holds for ANOVA does it make a difference if I am looking for one-way ANOVA?

Answer 1

This answer may not help almost two years later...

When calculating the sum of squares there is definitely a difference depending on the number of groups in the model.

Let's say you were comparing test scores between two different classes of students. To find the sum of squared error (SSE) for one-way ANOVA:

  SS_ERROR = SS_TOTAL - SS_CLASSES

Since the rules of addition and subtraction apply:

  SS_TOTAL = SS_CLASSES + SS_ERROR

  SS_CLASSES = SS_TOTAL - SS_ERROR

For a two-way ANOVA, you need another group. The second group represents students how that either sat in the front half of the classroom and those that sat in the back half. The group is named 'seating' for simplicity. Now to calculate the residual sum of squares:

  SS_ERROR = SS_TOTAL - (SS_CLASSES + SS_SEATING)

Since the rules of addition and subtraction apply:

  SS_TOTAL = (SS_CLASSES + SS_SEATING) + SS_ERROR

  SS_CLASSES + SS_SEATING = SS_TOTAL - SS_ERROR