To second Andrews answer:

In your type-I-SS table the order of the effects/factors/variables (can) matter (e.g. in unbalanced designs or in some models with inetractions). The contribution of each effect (to reduce the residual variance) is evaluated after all previous effects in the table are already considered.

In your case this particular effect, call it "A", has a "significant" contribution.

However, in your case it seems that another effect ("B") that comes in later in the table would also explain a part of the variance that is explained by A, when A was not already in the model. So if the contribution of A is evaluated after the contribution of B is already accounted for, then A has lesser variance to be explained and this may turn out to be not significant anymore.

And this is what type-III-SS tables do: the evaluate the contribution of each factor *after* considering the contributions of all the other factors/effects in the model.

The result you see can be interpreted as follows:

When A is used in a model where all tha latter factors shown in the table are not considered, then A does significantly reduce the residual variance ("over and above all factors that are at earlier positions in the table"). The Type-II-SS table shows that the contribution is not anymore significant when *all* other effetcs are considerd (the contribution of A is not significant "over and above all other factors").

You must decide what is relevant for you, possibly both results are relevant. When the order of the factors in the model is not thoughtfully chosen, then the result from the type-I-SS table might not be interesting. However, you may think about a sensible order and then look that this type-I-SS table again.

The links below may possibly help you

http://courses.ttu.edu/isqs5349-westfall/images/5349/type_i_or_type_iii_f_tests.htm

http://www.public.iastate.edu/~dnett/S402/wlsmeanssol.pdf

One thing you might try first is to see what a Type II SS reveals. Another is whether your samples sizes are unequal (unbalanced design), in which case Type III is probably superior. Type I SSs are sequential, in that for each effect is adjusted for previous effects. Type III treats every effect as if it were last (i.e., all affects are adjusted for all others). That's about as simple as I can get.

In reality, apart from whether the designed is balanced the key issues have to do with orthogonaliy and the nuances between how the two SSs treat interactions vs. effects. However, getting into these issues will not yield a "simplified" answer.

To second Andrews answer:

In your type-I-SS table the order of the effects/factors/variables (can) matter (e.g. in unbalanced designs or in some models with inetractions). The contribution of each effect (to reduce the residual variance) is evaluated after all previous effects in the table are already considered.

In your case this particular effect, call it "A", has a "significant" contribution.

However, in your case it seems that another effect ("B") that comes in later in the table would also explain a part of the variance that is explained by A, when A was not already in the model. So if the contribution of A is evaluated after the contribution of B is already accounted for, then A has lesser variance to be explained and this may turn out to be not significant anymore.

And this is what type-III-SS tables do: the evaluate the contribution of each factor *after* considering the contributions of all the other factors/effects in the model.

The result you see can be interpreted as follows:

When A is used in a model where all tha latter factors shown in the table are not considered, then A does significantly reduce the residual variance ("over and above all factors that are at earlier positions in the table"). The Type-II-SS table shows that the contribution is not anymore significant when *all* other effetcs are considerd (the contribution of A is not significant "over and above all other factors").

You must decide what is relevant for you, possibly both results are relevant. When the order of the factors in the model is not thoughtfully chosen, then the result from the type-I-SS table might not be interesting. However, you may think about a sensible order and then look that this type-I-SS table again.

The one and only way too choose between the sums-of-square you need is to carefully ask what exactly you want to use to make a whole comparison of your means, because all is about this. Another way to state it: you linear model makes use of a set of coefficients for each level of your factors (and interactions if you included them). These sums of squares test different combinations of coefficients, so not always the same thing. Difference come from different ways to project the data cloud to the factor subspaces, but this approach may be difficult to follow if you did not studied linear algebra, so I try another one below.

Type I sum of square tests the term in order of appearance and each sum of square include all coefficients of the below terms (including interactions). So you don't really see the effect of the factor, but the combined effect of the factor and the below ones. Consequently, it is strongly dependent of the order of the factors in the model.

Type II sum of square test (to be simple) are in fact type I sum of squares done in turn so that the term is the last before higher-order interactions. Hence, it does not depend of the order, nor of the coding of your model.

Type III sum of square tests only the coefficients of the term used. Hence, it does not depend of the order of introduction. However, it is strongly dependent on how the model was coded (reference model [R by default, some SAS procedures by default], central mean model [some SAS procedures by default]....). Most often, it makes sense mainly if the central mean model is used, but not always, it depends of what exactly you ask.

I think, but it is to be checked, that type III SS checks unweighted combinations of the means, whereas type II SS checks combination of the means weighted by the sample sizes. Hence, choice between the two also depends on the reason of the unbalancedness...

All 3 _must_ be equal in balanced designed, and more generally in orthogonal designs.

In all 3 cases, this makes sense only in the absence of interaction, as always. Interations terms (at least, the highest order one) should be the same.

If this seems difficult... It is indeed ;) and yoy may instead think about using nested models approaches to make your tests.

Note that strong differences between the approaches mean either strong unbalance or strong correlation between the factors... Both case leading to difficult to interpret results anyway!

Thank you all.

i guess your data are unbalanced (meaning you have different numbers of replicates for different treatments). When handling unbalanced data, PROC GLM outputs for Type I and Type III sums of square are different and type III SS is the one you should look at. When data are balanced, both type I and type III SS yield same results. Please see the link below from SAS support:

http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glm_sect005.htm

From SPSS Help

Type I. This method is also known as the hierarchical decomposition of the sum-of-squares method. Each term is adjusted for only the term that precedes it in the model. Type I sums of squares are commonly used for:

• A balanced ANOVA model in which any main effects are specified before any first-order interaction effects, any first-order interaction effects are specified before any second-order interaction effects, and so on.

• A polynomial regression model in which any lower-order terms are specified before any higher-order terms.

• A purely nested model in which the first-specified effect is nested within the second-specified effect, the second-specified effect is nested within the third, and so on. (This form of nesting can be specified only by using syntax.)

Type II. This method calculates the sums of squares of an effect in the model adjusted for all other "appropriate" effects. An appropriate effect is one that corresponds to all effects that do not contain the effect being examined. The Type II sum-of-squares method is commonly used for:

• A balanced ANOVA model.

• Any model that has main factor effects only.

• Any regression model.

• A purely nested design. (This form of nesting can be specified by using syntax.)

Type III. The default. This method calculates the sums of squares of an effect in the design as the sums of squares adjusted for any other effects that do not contain it and orthogonal to any effects (if any) that contain it. The Type III sums of squares have one major advantage in that they are invariant with respect to the cell frequencies as long as the general form of estimability remains constant. Hence, this type of sums of squares is often considered useful for an unbalanced model with no missing cells. In a factorial design with no missing cells, this method is equivalent to the Yates' weighted-squares-of-means technique. The Type III sum-of-squares method is commonly used for:

• Any models listed in Type I and Type II.

• Any balanced or unbalanced model with no empty cells.

Type IV. This method is designed for a situation in which there are missing cells. For any effect F in the design, if F is not contained in any other effect, then Type IV = Type III = Type II. When F is contained in other effects, Type IV distributes the contrasts being made among the parameters in F to all higher-level effects equitably. The Type IV sum-of-squares method is commonly used for:

• Any models listed in Type I and Type II.

• Any balanced model or unbalanced model with empty cells.

Thank you all

I thank you all --- NSTC

I thank all for your answers. So if we have missing data, we should go for type III. Does it correct?

Not neccesarily. It depends what you are interested in. If the order of variables that are accounted for is important, then type III is wrong. If the order should not matter and always all other variables should be accounted for, then type III is correct.

Thanks Dr Jochen Wilhelm. I am comparing the means of treatments using Tukey test, what is the difference between Lines and cldiff (I have got some difference in some traits). In addition would you please explain

the difference between Pooled SEM ( in papers) and also SEM when we use proc univariate.

Sorry, I don't use SAS.

Pooled SEM means that the standard error of the means (SEM) is calculated based on all the residuals of all groups in your model (i.e. pooling the information from different groups).

@A. Karimi

1) the reason for choosing type I, II or III is never the missingness of the data, but the way your question translates in terms of linear combinations of means

2) if you're using Tukey's all pairwise comparisons, the question of which type of sum of square to use is irrelevant, since the Tukey's test only uses the residual sum of square and the cell means, both of them being unrelated to the sum of squares (for a given model, of course).

Thanks for your input Emmanuel Curis.