# Crossed vs. nested & fixed vs. random factors

A barn has 4 sections of animals. Within each section are 4 goats. Each goat is given one of four types of food. One of each goat's kidneys is randomly selected to be inspected after 3 days for level of carbohydrates. To measure the level, the goats' kidneys are divided into three pieces, and three measurement techniques are used.

I understand two treatments are applied: $\text{Food}$ (4 fixed levels) and $\text{Measurement Technique}$ (3 fixed levels). I am wondering a couple of things:

• Are the kidneys "factors"?
• If so, are they nested or fixed?

My original thinking is that they are fixed...We have a left and right kidney for each animal. Some of my classmates are arguing that the kidneys are nested because each kidney differs for every goat. I don't understand this logic, because EVERY experimental unit differs (even if they are homogeneous, they are different still). So, I'm thinking:

1. $\text{Kidney}$ is a crossed factor with 2 random levels.
2. $\frac 1 3$ of $\text{Kidney}$ is a split-plot experimental unit, that is, a factor that is crossed with $\text{Kidney}$ and has 3 fixed levels.

My classmates:

1. $\text{Kidney}$ is nested (2 levels) with the goat.
2. $\frac 1 3$ of $\text{Kidney}$ is nested, with the $\text{Kidney}$ (3 levels).