(3) assumes

statistical independence among the local test results, the FDR procedure is (as will be illustrated in the following section) approximately valid (while being somewhat conservative) even when those results are strongly correlated, unlike the use of Eq.

Where the assumption of

statistical independence is not contradicted, no differences between the distributions exist, namely with none or limited (non-significant) statistical differences, indicating no or limited relationships between the variables.

Approaching the jitter problem from this direction highlights the statistical independence of each sample.

"To further ensure statistical independence, we randomize the hold-off time between measurements.

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.

In these tests, the mean values from each individual host tree (six clutches in each tree) were used to assure

statistical independence of the observations.

Consequently, the kriged variance for a set of measured (independent) data and some arbitrary but not over-smoothed set of kriged (dependent) data violate the requirement of

statistical independence. Mathematically, the set of measured data points determines the degrees of freedom.

This condition leads us to a very useful measure for investigating the

statistical independence of the k-tuple consisting of successive terms of a GFSR sequence.

The reason for this is that the latter increases the possibility of the

statistical independence being violated and systematic error being created (McMillan, 1999; Onwuegbuzie, in press).