# Interpreting interaction from two-way anova table

I've conducted three pairwise comparisons of variables and the results were as below:

Analysis of Variance Table

Response: Y
Df  Sum Sq Mean Sq F value    Pr(>F)
Dataset$$A 1 1140.57 1140.57 156.769 6.395e-11 *** Dataset$$B                           1  168.18  168.18  23.116 0.0001070 ***
Dataset$$A:Dataset$$B                 1  150.12  150.12  20.633 0.0001982 ***
Residuals                           20  145.51    7.28
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Analysis of Variance Table

Response: Y
Df  Sum Sq Mean Sq F value   Pr(>F)
Dataset$$A 1 1140.57 1140.57 64.7121 1.07e-07 *** Dataset$$C                       1   75.62   75.62  4.2904  0.05148 .
Dataset$$A:Dataset$$C             1   35.69   35.69  2.0247  0.17018
Residuals                       20  352.51   17.63
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Analysis of Variance Table

Response: Y
Df  Sum Sq Mean Sq F value Pr(>F)
Dataset$$B 1 168.18 168.184 2.4736 0.1315 Dataset$$C                       1   75.62  75.620  1.1122 0.3042
Dataset$$B:Dataset$$C             1    0.72   0.723  0.0106 0.9189
Residuals                       20 1359.86  67.993


From these tables, which interaction between variables would be said to be more interactive? I've interpreted that there is stronger interaction between A and B because Pr(>F) of Dataset$A:Dataset$B is lower.

Would this be a correct interpretation?

# if it is not in dataset
dataset$Y = Y anova(lm(Y ~ .*. ,data=dataset[,c("Y","A","B","C")]))  The reason for doing this is to properly estimate the variance and also properly account for the effects from all the variables. Although the term is an interaction term, having a smaller p-value or larger coefficient doesn't make it more "interactive". Let's take your example of Dataset$A:Dataset\$B. It means that by including another variable which is A multiplied by B, the model can explain more variance of Y.