Type 1 ANOVA is also called sequential sum of squares, because it considers the order effect of entering factors into the model. If you change the order of the factors in the model, the results will be different. The following uses an example in R to explain this.
Step 1: Prepare the data
The following is the data that will be using later, which has two IVs (cities and stores). Both IVs are categorical variable. The DV is sales.
# data will be used x_1 = rep(c('City1','City2'),each=5) x_2 = rep(c('store1','store2'), 5) sales=c(10,20,20,50,30,10,5,4,12,4) df <- data.frame (cities = x_1, stores = x_2, sales=sales) print(df)
cities stores sales 1 City1 store1 10 2 City1 store2 20 3 City1 store1 20 4 City1 store2 50 5 City1 store1 30 6 City2 store2 10 7 City2 store1 5 8 City2 store2 4 9 City2 store1 12 10 City2 store2 4
Step 2: Use aov() to test Type I ANOVA in R
Model 1: cities entering the model first
SS(cities) for factor
SS(stores | cities) for factor
stores) for interaction
# Model 1: cities entering the model first result_model1<-aov(sales ~ cities*stores, data = df) summary(result_model1)
Df Sum Sq Mean Sq F value Pr(>F) cities 1 902.5 902.5 7.752 0.0318 * stores 1 93.8 93.8 0.805 0.4041 cities:stores 1 183.7 183.7 1.578 0.2557 Residuals 6 698.5 116.4
Model 2: stores entering the model first
SS(stores) for factor stores
stores) for factor
) for interaction
# Model 2: stores entering the model first result_model2<-aov(sales ~ stores*cities, data = df) summary(result_model2)
Df Sum Sq Mean Sq F value Pr(>F) stores 1 12.1 12.1 0.104 0.7581 cities 1 984.1 984.1 8.454 0.0271 * stores:cities 1 183.7 183.7 1.578 0.2557 Residuals 6 698.5 116.4
As we can see, the Sum of Squares are different between these two models, due to the different orders of entering the model. That is why Type 1 ANOVA is also called sequential sum of squares.