from each of two populations and the mean of each sample is computed. The following is an example of means that would not be independent:

- 10 subjects are randomly sampled from a population,
- both simple and choice reaction time are measured for each subject, and
- the means of
these simple and choice reaction times are computed.

If, by chance, the mean
simple reaction time in the sample were much lower than the population mean
for simple reaction time, it is likely that the sample mean for choice reaction
time would also be lower than its corresponding population mean.

Two correlations are
independent if two independent samples are taken (from two populations) and
the correlation is computed in each. Correlations among variables taken from
the same sample are not independent.

Two proportions are independent if two
samples are taken and a proportion is computed in each. For example, if a
researcher were interested in whether the proportion of people who can solve
a problem depends on whether the problem is presented visually or aurally,
the researcher could sample 50 subjects and present the problem visually to a randomly chosen 25 of them and
aurally to the other 25.