Differences between experimental units

The experimental units are usually not identical — they have characteristics that affect the response.

Experiment on sheep
The sheep in a herd will have a variety of ages, weights and other characteristics. Even with no treatment applied, the weight gain in 6 months will vary from sheep to sheep.
Experiment on debtors
A dentist wants to assess whether a friendly letter or a threatening letter (the experimental treatment) is more effective at getting debtors to pay their bills. The experimental units are the debtors and they vary in age, gender and other characteristics that affect their likelihood of responding to the letter.
Experiment on flowers grown in a greenhouse
Some plants will be nearer to the windows, heat sources, ventilation, etc, than others. Some plants will also be naturally more vigorous than others.
Experiment about chemical reaction
In an experiment to assess the effect of an enzyme (the treatment) on a chemical reaction, the reaction will be repeated several times with different amounts of enzyme. The successive runs of the experiment are the experimental units and, although he experimenter will try to keep experimental conditions as constant as possible, some of aspects may change over the course of the experiment — the temperature may change during the day or the technician may improve the experimental technique in some subtle way.

Weight gain of calves

An experiment is to be conducted to assess whether a feed supplement improves the weight gain of calves over a 2-month period. Eighteen calves are available for use in the experiment. These calves vary in their age and weight at the start of the experiment, as shown in the scatterplot below.

We initially consider the weight gains of the calves if none of them are given the feed supplement. Even without being given a supplement, the weight gains of the calves will vary and some of this variability is likely to be related to the initial ages and weights.

The diagram is 3-dimensional, so move the mouse to the centre (marked by either a pink circle or the pointer changing to a hand) and drag towards the top left to rotate. (Or click the y-x-z rotation button.) The third dimension shows weight gains for the calves.

Click the y-x and the y-z rotation buttons and observe that weight gain is associated with both age and initial weight. (The calves that are older and heavier at the start of the experiment tend to gain more weight.)

Click Repeat experiment to run the experiment with a different group of 18 calves that have the same initial ages and weights.

Remember that we are not interested on the effect of age and initial weight on weight gain.

We want to use these calves to assess the effect of a feed supplement on weight gain so the effect of age and initial weight only serves to complicate the experiment.