Different ANCOVA results in R using different functions

Question

before my actual ANCOVA I would like to test whether there is a significant interaction between the IV and the CV as this is one assumption for ANCOVA. I found 3 different ways in R to perform an ANCOVA. However, the result for one solution differs from the other two and I do not understand why. Here is my working code snippet:

library(lattice)

data <- data.frame(group = c(rep("CTRL", 10), rep("P", 10)), 

                   response = c(10,11,14,16,17,17,19,20,21,22, 10,11,11,11,12,13,14,14,15,16),

                   age = c(40,41,45,43,50,51,55,57,60,62, 30,32,34,35,40,41,42,44,43,46))

xyplot(response ~ age, data=data, groups=group, type=c("p","r"))

# 1. ANCOVA    
anova(lm(response ~ group + age + group : age, data = data))

# 2. ANCOVA
summary(aov(response ~ group + age + group : age, data = data))

# 3. ANCOVA
summary(lm(response ~ group + age + group : age, data = data))

I don't understand why the two p-values for group and age are identical for ANCOVA 1. and 2. but different for 3. even though the interaction p-value (group : age) is the same for all three. Doing the same thing in SPSS results in exactly the same p-values as ANCOVA 3.

Now, as you can imagine, I am pretty unsure what's right and what's wrong or what's actually the difference between them? Can anyone help?

Answer 1

I think that you would get a better idea what is going on if you tried the following:

data <- data.frame(group = rep( c("G1", "G2", "G3", "G4"), each= 5), 
        response = c(10,11,14,16,17,17,19,20,21,22, 10,11,11,11,12,13,14,14,15,16),
        age = c(40,41,45,43,50,51,55,57,60,62, 30,32,34,35,40,41,42,44,43,46))

You will see that the summary( lm( ... )) does not really give you overall factor effect, but instead effect for each factor level:

Call:
lm(formula = response ~ group + age + group:age, data = data)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.14331 -0.29665 -0.07703  0.17162  2.91720 

Coefficients:
        Estimate Std. Error t value Pr(>|t|)    
(Intercept) -14.7166     5.6759  -2.593 0.023536 *  
groupG2       9.0976     8.8559   1.027 0.324542    
groupG3      19.6954     7.3485   2.680 0.020030 *  
groupG4       6.9328    12.8274   0.540 0.598763    
age           0.6465     0.1292   5.005 0.000307 ***
groupG2:age  -0.2006     0.1756  -1.142 0.275744    
groupG3:age  -0.4704     0.1874  -2.510 0.027409 *  
groupG4:age  -0.1330     0.2958  -0.450 0.660993    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 1.024 on 12 degrees of freedom
Multiple R-squared: 0.9524, Adjusted R-squared: 0.9247 
F-statistic: 34.31 on 7 and 12 DF,  p-value: 5.218e-07