Which one to choose Type-I, Type-II, or Type-III ANOVA? [duplicate]

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)?

I want to check the interaction between my two factors (genotype*FuncBIN), but my output comes as Type II ANOVA with interaction. Is this normal?

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)


How can I run an ANOVA with interaction followed my Tukey PostHOC?

• Thank you, EdM, but I need a simple explanation to understand this + how to improve my R coding for this? – Kynda May 11 '18 at 14:53
• Read the "|" sign as "given. That is, for type II ANOVA, "SS(A|B)" means to test A given what is known about B; "SS(B|A)" means to test B given what is known about A; "SS (AB|A, B)" means to test the AB interaction given what is known about A and B individually. So type II (as recommended by @dbwilson) does provide a test for the interaction itself; in type II the interaction term, unlike in type III tests, is not included in the tests for main effects of A and B. – EdM May 11 '18 at 16:08
• I think you will find the information you need in the linked thread. Please read it. If it isn't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. – gung - Reinstate Monica May 11 '18 at 16:26

fit <- aov(k ~ genotype*FuncBIN, data=df)

• In practice, however, there will appear to be a difference when this is done with Anova() in the car package. Its Type II tests do not include an intercept term, while its Type III tests do. See this R-help thread. – EdM May 11 '18 at 18:02