# Why does One Way ANOVA not have an SSE Term?

For a Two Way ANOVA with two factors A and B, the Sum of Square equation is:-

SSTO = SSA + SSB + SSAB + SSE

Where,
SSTO = Total Sum of Squares
SSA = Sum of Squares due to Factor A
SSB = Sum of Squares due to Factor B SSAB = Sum of Squares due to Interaction of Factor A and Factor B SSE = Amount of Variability left unexplained taken as error

Now my question is, why does One Way ANOVA not have a SSE Term?

FYI,
Im reading this book, Intermediate Statistics for Dummies. I was reading about ANOVA. For one way ANOVA the book says that the Total Sum of Squares is the Sum of Squares within and Sum of Squares Between. There is no Sum of Square Error Term in one way ANOVA. That's why I am asking this question.

• What leads you to believe it doesn't? Jan 3 '19 at 17:32
• Im sorry gung, but I dont know. Im just starting to learn advance statistics. Im reading from this book, Intermediate Statistics for dummies. The book says that for One way ANOVA, SSTO = SSW + SSB. So i just assumed that SSE is not there. If you could suggest me a better book to read, that will be helpful :) Jan 3 '19 at 18:05
• I'm not familiar with that book. The quote sounds bizarre. FWIW, we have some statistics textbook recommendations here: Free statistical textbooks. Jan 3 '19 at 18:05
• Please do not delete & repaste identical comments. Jan 3 '19 at 18:06
• @gung It's not really that bizarre. See my answer. This notation is not uncommon. Jan 4 '19 at 9:49

One way ANOVA does have an SSE term, see e.g. ANOVA notes.

The labeling can get confusing; it's important to remember what is actually going on in ANOVA. I wrote about this (in very simple terms) here. For your particular question:

When we divide a sample into groups, there will be variation within each group and variation between the groups. The latter is what we want to model, the former is noise. So, the variation within each group is sometimes abbreviated SSW (W for Within) and sometimes SSE (E for error).

Even worse, when there are two or more factors, the second one is sometimes called SSB (B for factor B).

And SST! Sometimes the T is total and sometimes it is treatment.

• Im sorry Sir, but I dont know. Im just starting to learn advance statistics. Im reading from this book, Intermediate Statistics for dummies. The book says that for One way ANOVA, SSTO = SSW + SSB. So i just assumed that SSE is not there. If you could suggest me a better book to read, that will be helpful :) Jan 3 '19 at 18:05
• SSB is SSE. The labeling does get confusing. I will edit my answer. Jan 3 '19 at 22:22
• There's a typo in the above comment. He means that SSW is SSE, as the answer says.
– Dave
Oct 28 '20 at 16:58