It is likely that there is a strong relationship between whether a person shoplifts and whether or not their friends shoplift. Thus, a sample of 10 people chosen in this way would not consist of 10 independent pieces of information. The selection of the first person would have an influence on the selection of the remaining nine subjects. In short, the observations would not be independent.

When more than one measurement is taken from a subject, the two measurements are not independent since the score on the first measurement is likely to be related to the score on the second measurement. For example, if simple and choice reaction time are measured for each subject, one would almost certainly find that subjects who are fast at the simple reaction time task tend to be fast at the choice reaction time task. As a rule, only measurements taken from different subjects are considered independent.

Two statistics are independent if the observations that went into the statistics are independent. Thus, two means are independent if 10 subjects are randomly sampled