Example 21. Two-Factor Unbalanced Model: Rations Data

The experiment consists of giving two types of feed rations to calves from three different sires. The response variable is the weight gained by each calf. Unequal numbers of calves from each sire were used in the experiment, although there are no empty cells. The data is shown below.

Source: Harvey, W.R. (1975). Least Squares Analysis of Data. Washington D.C. U.S. Dept. of Agriculture, ARS-H-4.

Table 21: Rations Data

 Sire
FeedS1S2S3
F15
6		2
3
5
6
7		3
F22
3		8
8
9		4
4
6
6
7

Questions:

  1. Discuss the effect of feed ration and sire on weight gain.

  2. Is there an interaction between the two effects?

Keywords: Unbalanced data, two-way ANOVA, estimable functions, four types of SS, main effects, interaction effects

Numerical Examples for use with
A First Course in Linear Model Theory by Ravishanker and Dey
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