What is 1SS and 2SS?
There isn’t a single, universal definition for 1SS and 2SS. In statistics, when these abbreviations appear, they are often used as shorthand for different ways of partitioning variation in a model, typically related to sums of squares. This article explains the most common interpretation and why notation can vary by source.
Beyond statistics, the terms 1SS and 2SS are not widely standardized across fields, so it’s important to consult the specific text or software documentation you’re using to see how an author defines them. Here we focus on the well-documented statistical usage and note the potential for variation.
Statistical sums of squares: the likely interpretation of 1SS and 2SS
In ANOVA and regression analysis, “SS” stands for sum of squares, a measure of how much variation in the data is explained by a term in the model. Some authors use 1SS and 2SS as shorthand for two common ways to partition that variation when fitting factors in a design. The most widely discussed interpretations are:
- 1SS: Type I sums of squares (sequential). The SS for a term depends on the order in which terms are added to the model; each term’s contribution is tallied after accounting for the terms that came before it in the specified sequence.
- 2SS: Type II sums of squares (marginal). Each main effect is tested after removing the effects of all other main effects, but without explicitly incorporating interactions unless they are part of the model. This approach can be more appropriate for balanced or nearly balanced designs when interactions are not being tested.
In practice, many texts and software packages label sums of squares explicitly as SS(Type I), SS(Type II), or SS(Type III). The shorthand 1SS/2SS appears in some notes and references, but it is not universally standardized. When you see 1SS or 2SS, check the source to confirm which type of sum of squares is being used, and be mindful of how unbalanced designs or interactions might affect interpretation.
Concluding note: The key distinction is that Type I sums of squares are order-dependent, while Type II sums of squares focus on marginal contributions of main effects (and do not automatically account for interactions). The choice of type can change which effects appear significant in the analysis, especially in unbalanced designs.
Practical considerations and examples
To illustrate, imagine a simple two-factor design with factors A and B, possibly including an interaction term AB. If you use Type I sums of squares and you order the factors as A then B, the SS for A reflects A’s contribution after accounting for nothing (in the first stage) and B’s SS reflects B’s contribution after A has been accounted for. If you swap the order, the SS values can change, which can influence significance results. Type II SS, by contrast, tests each main effect after removing the other main effect(s) but typically without invoking the interaction term unless it is part of the model, yielding a different interpretation of each factor’s importance.
Because authors and software differ in notation, the safest approach is to look for explicit labels (Type I, Type II, Type III) or to read the methods section to see exactly how the sums of squares were computed. When reporting results, prefer explicit notation to avoid ambiguity.
Notes and cautions about notation
The shorthand 1SS/2SS is not universally standard. If you encounter these terms, look for a definitions box, a methods section, or software documentation that specifies whether they denote Type I or Type II sums of squares, and how interactions are handled. Without that clarification, conclusions drawn from these terms alone can be misleading, especially in unbalanced designs or models with interactions.
If you want, share the context or the source you're reading (journal article, textbook, or software output), and I can align the explanation to that specific usage and walk through a concrete example.
Summary
1SS and 2SS are not universal stand-ins for a single concept. In statistics, they are commonly encountered as shorthand for two approaches to partitioning variation: Type I (sequential) sums of squares and Type II (marginal) sums of squares. The exact interpretation depends on the source, especially regarding the treatment of interactions and the order of terms. Always check the explicit definitions in the text or software documentation you’re using to ensure accurate interpretation.
Conclusion
Understanding sums of squares and the distinctions between Type I and Type II is essential for interpreting ANOVA and regression results correctly. When 1SS or 2SS appear, verify the notation to ensure you’re assessing the right source of variation in your model, and be mindful of design balance and interactions that can affect conclusions.
Summary recap: 1SS/2SS are field-dependent shorthand that most often map to Type I and Type II sums of squares in statistics. Clear definitions from the source are crucial to avoid misinterpretation, especially in unbalanced designs or models with interactions.
