Differences between experimental units

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

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 also affect their likelihood of responding to the letter.
Experiment on shops
The shops in a supermarket chain have different floor areas and are located in towns with different socio-economic characteristics. Even with no extra advertising (the treatment), weekly sales will vary from supermarket to supermarket.
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 the 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.

Speed of checkout operators

An experiment is to be conducted to estimate how much time is saved in supermarket checkouts by employing packers to fill groceries into bags for the customers. Sixteen checkout operators are available for use in the experiment and speeds are measured in seconds per dollar value of the purchased goods over a 3-hour period on Saturday. The checkout operators vary in their age and experience, as shown in the scatterplot below.

We initially consider the speeds of the checkout operators if none of the checkout operators use a packer. Even without packers, the speeds of the operators will vary and some of this variability is likely to be related to their age and experience.

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 speeds of the operators.

Click the y-x and the y-z rotation buttons and observe that speed is associated with both age and experience. (The operators who are older and have more experience tend to be faster.)

Click Repeat experiment to run the experiment with a similar group of checkout operators with the same ages and experiences.

Remember that we are not interested on the effect of age and experience on speed.

We want to use the data to assess the effect of using a packer on speed so the effect of age and experience only serves to complicate the experiment.