Hi,

I'm having difficulty  to replicate in R a nested (hierarchical) anova example found in p. 308 of
Zar, J.H. 1996. Bostatistical Analysis. Prentice Hall. 3rd ed.

The example (15.1) is as follows:
The variable is blood cholesterol concentration in women (in mg/100 ml of plasma). This
variable was measured after the administration of one of three different drugs, each drug
having been obtained from two sources

  DRUG 1   DRUG 2      DRUG 3
     A   Q       D      B          L   S
  102 103   108  1091   104 105
  104 104   110  1082   106 107

Zar results are these:
----------------------------------------------------------------------------
Source of variation             SS   DF      MS        F       P
----------------------------------------------------------------------------
*Total                              71.67   11
*Among all subgroups    62.67     5
  *Groups                        61.17     2   30.58   61.16  0.0037
  *Subgroups                    1.50     3     0.50     0.33   0.80
*Error                               9.00     6     1.50
----------------------------------------------------------------------------

It is straightforward to follow the equations from the book step by step to obtain those results.

Now, when trying the 'aov()' function in R:

## creating the data frame
zar <- data.frame(
       cChol=c(102, 104, 103, 104, 108, 110, 109, 108, 104, 106, 105, 107),
       drug=gl(3, 4, 12),
       dsource=gl(6, 2, 12, labels=c("A", "Q", "D", "B", "L", "S")) )


## This gives the relevant SS, DF and MS values, but only the F and P corresponding to drug
## effect (Zar's Groups)
summary( aov(cChol ~ drug + Error(dsource/drug), data=zar) )

## The F and P values corresponding to subgroups can be obtained by:
0.5/1.5 # F
pf(0.5/1.5, 3, 6, lower.tail=FALSE) # P

## or from the second row in the two way anova:
summary( aov(cChol ~  drug + dsource, data=zar) )


In order to avoid confussion in our students (and myself!) I wonder if we can obtain the
desired results in one step?

Thank you in advance for your kind help.

Héctor


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Héctor Villalobos <hvillalo@ipn.mx>
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