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:
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.