# R Language ANOVA Basic usage of Anova()

## Example

When dealing with an unbalanced design and/or non-orthogonal contrasts, Type II or Type III Sum of Squares are necessary. The `Anova()` function from the `car` package implements these. Type II Sum of Squares assumes no interaction between main effects. If interactions are assumed, Type III Sum of Squares is appropriate.

The `Anova()` function wraps around the `lm()` function.

Using the `mtcars` data sets as an example, demonstrating the difference between Type II and Type III when an interaction is tested.

``````> Anova(lm(wt ~ factor(cyl)*factor(am), data=mtcars), type = 2)
Anova Table (Type II tests)

Response: wt
Sum Sq Df F value    Pr(>F)
factor(cyl)            7.2278  2 11.5266 0.0002606 ***
factor(am)             3.2845  1 10.4758 0.0032895 **
factor(cyl):factor(am) 0.0668  2  0.1065 0.8993714
Residuals              8.1517 26
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> Anova(lm(wt ~ factor(cyl)*factor(am), data=mtcars), type = 3)
Anova Table (Type III tests)

Response: wt
Sum Sq Df F value    Pr(>F)
(Intercept)            25.8427  1 82.4254 1.524e-09 ***
factor(cyl)             4.0124  2  6.3988  0.005498 **
factor(am)              1.7389  1  5.5463  0.026346 *
factor(cyl):factor(am)  0.0668  2  0.1065  0.899371
Residuals               8.1517 26
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
``````