# We began with some more discussion of power analysis.
# Here, we calculate the effect size f^2 for a regression
# with an R^2 of .05.  (This was used in G*Power.)
> .05/.95
[1] 0.05263158

# Note that this corresponds to a correlation of about .2:
> sqrt(.05)
[1] 0.2236068

# When we did a minimum detectable effect size analysis in
# G*Power, the result was stated in terms of f^2.  Here,
# we translate that back to R^2:
> f2 <- 0.1982296
> f2/(1+f2)
[1] 0.1654354

# Note that this correponds to a correlation of about .4:
> sqrt(.1654354)
[1] 0.4067375

# Here's another example of the same calculations:
> f2 <- 0.1438856
> f2/(1+f2)
[1] 0.1257867
> sqrt(f2/(1+f2))
[1] 0.3546642

# And another:
> f2 <- 0.1074744
> sqrt(f2/(1+f2))
[1] 0.3115198

 
 
 
# Here, we examine two methods for understanding continuous
# interactions.  First, we look at the regression of endurance
# on exercise for persons 1 sd above the mean age, persons at
# the mean age, and persons 1 sd below the mean age.  The
# information about slopes and intercepts comes from the
# SAS program "int2.sas".

> plot(c(-12,16), c(-2,56),type='n',xlab="Exercise",ylab="Endurance")
> points(Exercise,Endurance)
> abline(c(25.88872,.97272))
> abline(c(25.88872-.26169*10.1,.97272+.04724*10.1))
> abline(c(25.88872-.26169*-10.1,.97272+.04724*-10.1))
 
# Here, we take a similar approach, but instead of doing the fully
# continuous interaction, we approximate it by allowing separate
# regressions for the four age quartiles.  The numbers here come
# from the SAS program "int4.sas". 

> plot(c(-12,16), c(-2,56),type='n',xlab="Exercise",ylab="Endurance")
> points(Exercise,Endurance)
> abline(c(22.90663,1.39519))
> abline(c(22.90663+1.89862,1.39519-.11760))
> abline(c(22.90663+3.91087,1.39519-.69081))
> abline(c(22.90663+5.89785,1.39519-.97328))