Hi,
Yes, the two methods are equivalent.
The p-value R calculates is based on the same t-statistic used in your
manual analysis. You can see this by doing the second method:
y2 = rbind(df1, df2)
y2 = cbind(c(0,0,0,1,1,1), y2)
summary(lm(y2[,3] ~ y2[,1] + y2[,2] + y2[,2]*y2[,1]))
Look at the values you previously calculated and see where they reappear...
print(td)
print(db)
print(sd)
Looked at from the other way, the models with the D's and so on is one
way to explain where the t-test comes from. Just do H0: b2=0 vs H1:
b2!=0, and sprinkle some independence and normality assumptions.
It's probably preferable to use the automatic lm based method, because
then you specify the model explicitly, while with the seemingly recipe
based approach the actual models and hypotheses your are testing may not
be clear. Plus you get nice diagnostic statistics and pretty graphs. The
downside is that you might get lured into complacency...
Zhou Fang
PS: Your model equation isn't right. In both, we are also allowing the
intercept to vary between groups. So really you want
y = c + D.b0 + b1.x + D.b2.x
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