Supplementary Exercises 12.35 and 12.36 of IPS7e
------------------------------------------------

12.35:
------
Power calculation for a study on weight gains of pregnant women during 
the third trimester of pregnancy. Three groups of women will be
included, and for the planning we will assume these to be of the same
size. We assume sigma=2.4 (from the previous study), and the 3 means 
in the populations corresponding to the groups to be: 2.6, 3.0 and 3.4.
Note that only the maximal difference between group means is used by the
algorithm in Minitab; other software will use all 3 values.

Minitab gives:

---

 Power;
  OneWay 3;
   Sample 50 100 150 175 200;
   MaxDifference .8;
   Sigma 2.4.

One-way ANOVA
Alpha = 0.05  Assumed standard deviation = 2.4
Factors: 1  Number of levels: 3

   Maximum  Sample
Difference    Size     Power
       0.8      50  0.294836
       0.8     100  0.544909
       0.8     150  0.733193
       0.8     175  0.801385
       0.8     200  0.854468

Comments:
---------
The listing shows that with a sample size of 50 women per group 
there would be less than 33% chance of a significant result (at the 5%
level). A more appropriate sample size, in terms of attaining an acceptable
power, is somewhere between 150 and 200 women per group.

Addendum:
Calculations in Stata and R based on all three group means will give
powers ranging from 0.2945 to 0.8545, thus very similar results.


12.36:
------
The maximal difference between the means is the same for the new values,
therefore the power calculation in Minitab will evidently give exactly the 
same result. This is also true with other sample size calculations where
the individual means are entered, because all differences between the
three means are the same.