The high variability of single trees can be illustrated, e.g., by drawing bootstrap samples from the original data set and investigating whether the trees built on the different samples have a different structure. The rationale of bootstrap samples, where a sample of the same size as the original sample is drawn with replacement (so that some observations are left out, while others may appear more than once in the bootstrap sample) is to reflect the variability inherent in any sampling process: Random sampling preserves the systematic effects present in the original sample or population, but in addition to this it induces random variability. Thus, if classification trees built on different bootstrap samples vary too strongly in their structure, this proves that their interpretability can be severely affected by the random variability present in any data set.
