R-ticulate

4Replication and Randomisation

In Chapters 2 and 3, we have looked at variation, where it originates from, and how we can characterise it, both visually and numerically. We have also seen how to distinguish between different types of variation – random and systematic. Understanding the reason for systematic variation provides us with explanatory power, and we achieve this by trying to maximise the signal‐to‐noise ratio. Two fundamental tools that help us with the causal assignment of variance are replication and randomisation. Even a slight misunderstanding of these concepts can cause ripple effects far into your statistical analyses. Both are intricately related, and both also relate to the concept of statistical independence. To fully understand Boxes 4.1 and 4.2, you will have to read Chapter 5, but it should be possible to follow the argumentation without doing so.

4.1 Replication

Whilst the meaning of the word ‘replication’ may be clear to us in our day‐to‐day use of the English language, we need to understand what it means in a statistical sense. Consider this example:

You have three plants in three identical pots, and with homogenous soil (Figure 4.1a). To one pot, you add nitrogen (N), to another one you add N and water, and the third one remains as a control (see Chapter 2). After a certain time, you measure the height of the plants. A statistically uninformed experimenter might argue that the plant in the middle of Figure 4.1a grew best because it received additional ...