Assuming

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

Therefore, we showed that it is always possible to define hidden variables satisfying the 2 PBR axioms: i)

statistical independence at the sources or preparation

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.

In his next paragraph, Huebner states, "The author ignores the clear lack of expected randomness in many of the entries of Table 1." 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.

In case of diagonal covariance matrix (

statistical independence of the class of features) there is formularization of the distance by the standardized Euclidean distance and classification rule is

The product of these two probabilities (.454 x .083 = .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.