Assuming

statistical independence among the local test results is a best-case situation.

Sampling without replacement is well known to lead to violations of

statistical independence between trials, which the PEAR analyses did not take into account, and which can lead to p values incorrect by several orders of magnitude.

This also is mistaken: the article addresses randomness, expected or otherwise, in the sections on the error distribution,

statistical independence, Benford's law, rounding, and the systematic properties expressed by the equation for longevity.

Another important restriction which is imposed by the previous models is the

statistical independence assumption.

038), if we assume

statistical independence and the rules of conditional probabilities, would be the probability of winning the TC [P(TC)].

30) If the observed frequencies (survey results) differ significantly (< 0,5 per cent level of significance) from the expected frequencies, then the assumption of

statistical independence is contradicted, and at least some relationship between the two variables is implied.

Utilizing groups themselves as the unit of analysis, rather than the individual scores, decreases the possibility of the

statistical independence assumption being violated and systematic error being created (McMillan, 1999).

In addition, the faithfulness condition rules out those models in which

statistical independence relations follow was a result of special coincidences among the parameter values.

Approaching the jitter problem from this direction highlights the

statistical independence of each sample.

through external audit and

statistical independence.

This joint probability, a multiplication of three separate probabilities, requires

statistical independence of the three separate probabilities or events.