# ANOVA - Orthogonal Planned Comparisons

#### cxds

##### New Member
We've been given this question on a sample exam paper.

An experimenter is exploring the effects of two appetite suppressants in rats. Suppressant A induces mild nausea, while Suppressant B suppresses the sensation of hunger. Half the subjects receive a low dose of one suppressant, and half receive a high dose. The experimenter also runs a control group that receives an inert substance. There are thus five groups in the experiment, each with 4 rats assigned randomly. The rats are injected and then their eating behaviour is observed for a particular period of time. Construct a set of coefficients that will provide the following comparisons:
a) Control vs. experimental groups
b) Suppressant A vs. Suppressant B
c) Low vs. high dosage for Suppressant A
d) Low vs. high dosage for Suppressant B
Also show that these comparisons are mutually orthogonal.

Thought that it was one-way, so the answer would be
Five groups -
1. Sup. A, Low dose
2. Sup. A, High dose
3. Sup. B, Low dose
4. Sup. B, High dose
5. Control
Then comparison weightings
a) 1, 2, 3, 4 vs. 5 (0.25, 0.25, 0.25, 0.25, -1)
b) 1 & 2 vs. 3 & 4 (0.5, 0.5, -0.5, -0.5, 0)
c) 1 vs. 2 (1, -1, 0, 0, 0)
d) 3 vs. 4 (0, 0, 1, -1, 0)

BUT...someone asked our lecturer who said that it's a factorial ANOVA with 3 levels in each factor but won't give any more information - I am now thoroughly confused, can anyone shed any light?

#### Dragan

##### Super Moderator
You are correct. In short, it's a Single Factorial experiment (and not a Factorial Design).

In fact, the same question appears in the textbook: Keppel and Wickens (2004). Design and Analysis A Researcher's Handbook (4-th edition).

See problem 4.1 on page 84, which is under the auspices of Single Factor Experiments.