I’m analyzing data from an unbalanced factorial experiment both with

`SAS`

and`R`

. Both`SAS`

and`R`

provide similar Type I sum of squares but their Type III sum of squares are different from each other. Below are`SAS`

and`R`

codes and outputs.`DATA ASD; INPUT Y T B; DATALINES; 20 1 1 25 1 2 26 1 2 22 1 3 25 1 3 25 1 3 26 2 1 27 2 1 22 2 2 31 2 3 ; PROC GLM DATA=ASD; CLASS T B; MODEL Y=T|B; RUN;`

Type I SS from SAS`Source DF Type I SS Mean Square F Value Pr > F T 1 17.06666667 17.06666667 9.75 0.0354 B 2 12.98000000 6.49000000 3.71 0.1227 T*B 2 47.85333333 23.92666667 13.67 0.0163`

Type III SS from SAS`Source DF Type III SS Mean Square F Value Pr > F T 1 23.07692308 23.07692308 13.19 0.0221 B 2 31.05333333 15.52666667 8.87 0.0338 T*B 2 47.85333333 23.92666667 13.67 0.0163`

R Code`Y <- c(20, 25, 26, 22, 25, 25, 26, 27, 22, 31) T <- factor(x=rep(c(1, 2), times=c(6, 4))) B <- factor(x=rep(c(1, 2, 3, 1, 2, 3), times=c(1, 2, 3, 2, 1, 1))) Data <- data.frame(Y, T, B) Data.lm <- lm(Y~T*B, data = Data) anova(Data.lm) drop1(Data.lm,~.,test="F")`

Type I SS from R`Analysis of Variance Table Response: Y Df Sum Sq Mean Sq F value Pr(>F) T 1 17.067 17.067 9.7524 0.03543 * B 2 12.980 6.490 3.7086 0.12275 T:B 2 47.853 23.927 13.6724 0.01629 * Residuals 4 7.000 1.750 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1`

Type III SS from R`Single term deletions Model: Y ~ T * B Df Sum of Sq RSS AIC F value Pr(>F) <none> 7.000 8.4333 T 1 28.167 35.167 22.5751 16.0952 0.01597 * B 2 20.333 27.333 18.0552 5.8095 0.06559 . T:B 2 47.853 54.853 25.0208 13.6724 0.01629 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1`

Am I missing something here? If not which one is correct Type III SS?

**Answer**

Type III SS depend on the parameterization used. If I set

```
options(contrasts=c("contr.sum","contr.poly"))
```

before running `lm()`

and then `drop1()`

I get exactly the same type III SS as SAS does. For the R-community dogma on this issue, you should read Venables’ *Exegeses on linear models*.

See also: How does one do a Type-III SS ANOVA in R with contrast codes?

**Attribution***Source : Link , Question Author : MYaseen208 , Answer Author : Community*