I want to check the interaction between my two factors (genotype*FuncBIN), but my output comes as Type II ANOVA with interaction. I don't understand what the difference is between TypeI and TypeIII? Since my background is not very mathematics, it's very difficult for me to understand this mathematical notation; Type I SS: SS(A) SS(B|A) SS (AB|A, B) Type II SS: SS(A|B) SS(B|A) SS (AB|A, B) Type III SS: SS (A|B, AB) SS (B|A, AB) SS (A*B|A, B)?

structure( list(genotype = structure(c(3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("WT", "Mut2", "Mut1" ), class = "factor"), FuncBIN = structure(c(1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L), .Label = c("Mitochondria ", "Golgi", "ER"), class = "factor"), k = c(0.2, 0.3, 0.4, 0.5, 0.3, 0.2, 0.5, 0.6, 0.7, 0.4, 0.6, 0.9, 0.2, 0.3, 0.5, 0.4, 0.2, 0.3, 0.5, 0.6, 0.8, 0.5, 0.4, 0.6, 0.2, 0.3, 0.1)), .Names = c("genotype", "FuncBIN", "k"), class = "data.frame", row.names = c(NA, -27L) )


library(car)
library(lsmeans)
library(multcomp)
fit <- lm(k ~ genotype + FuncBIN + genotype*FuncBIN, df) 
plot(fit) shapiro.test(residuals(fit)) 
Anova(fit) 
lsmip(fit, FuncBIN ~ genotype) 
lsmeans(fit, pairwise ~ genotype)[[2]]
fit.tukey <- lsmeans(fit, pairwise ~ genotype | FuncBIN)[[2]]
fit.tukey
cld(fit.tukey)