Psyc 480 -- Dr. King

Answers to ANCOVA Practice Questions

1) Why did the effect of Gender disappear (p=0.176) when HSGPA was added
to the model as a covariate?

> summary(aov(GPA91~Gender,data=tres))
             Df Sum Sq Mean Sq F value  Pr(>F)   
Gender        1   6.61   6.615   9.999 0.00176 **
Residuals   249 164.73   0.662                   

> summary(aov(GPA91~HSGPA+Gender,data=tres))
             Df Sum Sq Mean Sq F value   Pr(>F)    
HSGPA         1  37.62   37.62  70.295 3.87e-15 ***
Gender        1   0.99    0.99   1.842    0.176    
Residuals   248 132.74    0.54

The effect of Gender virtually disappeared when HSGPA was added because women
had higher mean HSGPA than men. When HSGPA is entered into the model first, it
gets first crack at the variability in GPA91.

> cor(tres[,c(8,6,5)])
             sex      HSGPA      GPA91
sex    1.0000000 -0.2631519 -0.1964826
HSGPA -0.2631519  1.0000000  0.4685921
GPA91 -0.1964826  0.4685921  1.0000000

HSGPA is clearly related to GPA91, and when it is entered first, it essentially
"steals" the effect from its correlated variable, Gender.

2) Did the effect of CSEI change when gender was added to the model
as a categorical IV? Why not? Did the effect of gender change when CSEI was
added to the model as a covariate? Why? Why did it change in the direction
in which it did?

The effect of CSEI did not change when Gender was added because CSEI was
entered first. pse~CSEI and pse~CSEI+gender both show the same effect of
CSEI, which is CSEI ignoring gender. The effect of gender did change when
CSEI was entered first into the model. In fact, the effect of gender was
cut more than in half.

> cor(milne)
             CSEI        pse     gender
CSEI    1.0000000  0.5385038 -0.1938515
pse     0.5385038  1.0000000 -0.3129385
gender -0.1938515 -0.3129385  1.0000000

CSEI is strongly positively correlated with pse. When entered first, it's
going to take a big chunk of the total variability for itself. Because of
the correlation between CSEI and gender (negative, meaning women have lower
mean CSEI scores than men), some of that big chunk is going to have belonged
to gender in the previous analysis, because women also have lower mean pse
scores. Therefore, CSEI is essentially saying, "Hey! I can explain some of
that!"

3) Did the effect of csa change when cpa was added to the model as
a covariate? Why?

It decreased quite a bit, easier to see in this analysis.

> summary(aov(ptsd~csa,data=my.data))
            Df Sum Sq Mean Sq F value   Pr(>F)    
csa          1  963.7   963.7   79.92 2.16e-13 ***
Residuals   74  892.3    12.1                     

> summary(aov(ptsd~cpa+csa,data=my.data))
            Df Sum Sq Mean Sq F value   Pr(>F)    
cpa          1  450.1   450.1   42.02 9.36e-09 ***
csa          1  624.0   624.0   58.25 6.89e-11 ***
Residuals   73  781.9    10.7 

What this is suggesting (is consistent with) is that some of the ptsd suffered
in adulthood by sexually abused girls is due to the fact that they also tend to
be physically abused as girls.