Testing additivity vs. interactions I'm interested in differentiating the additivity of two factors versus if their interaction produces an effect.  For example:  


*

*Factor A produces effect of level 20. 

*Factor B produces effect of level 30. 

*Factors A + B produces effect of level 70.


How can I tell how much each factor and their interaction contribute to the total effect when factors A and B are used together?
 A: You would include an interaction term in your model and test it.  Here is a simple example, using your numbers and coded in R:  
set.seed(5571)                        # this makes the example exactly reproducible

N = 60                                # there are 60 data
A = rep(c(1,0), each=N/2)             # w/ 2 factors A & B
B = rep(c(1,0), times=N/2)
y.null = 0 + A*20 + B*30 +          rnorm(N, mean=0, sd=5)  # this is additive
y.int  = 0 + A*20 + B*30 + 20*A*B + rnorm(N, mean=0, sd=5)  # an interaction exists
options(digits=3)                     # this just makes the output cleaner
summary(lm(y.null~A*B))$coefficients  # this both fits the model & tests the variables
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)    -2.53        1.2   -2.11 3.93e-02 *
# A              22.72        1.7   13.39 4.24e-19 ***
# B              33.93        1.7   19.99 3.61e-27 ***
# A:B            -3.41        2.4   -1.42 1.61e-01          # not significant
summary(lm(y.int~A*B))$coefficients
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)   -0.279       1.34  -0.208 8.36e-01
# A             20.696       1.89  10.927 1.67e-15 ***
# B             33.843       1.89  17.868 8.46e-25 ***
# A:B           16.877       2.68   6.301 4.91e-08 ***      # highly significant

