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Randomly
distributed
implies that the order of measured values in a set
does not impact the numerical value of its variance.
The variance of the set may be used
for short. Independently
measured values implies that measurement procedures
do not cause associative dependence between sequencies of measured
values.
Ordered
implies that the independently measured values in
a set display the same sequence as the selected
samples do in the sample space of interest. Ordered
sets of independently measured values may display
a statistically significant degree of associative
dependence or spatial dependence.
Apparently,
degrees of freedom are positive
integers for sets of independently measured values with
equal weights but become
positive irrationals
for sets of independently measured values with variable
weights.
Click here to find out how degrees of freedom are born.
Click here to prove heuristically that a set of n independently measured values has df(r)=n-1 degrees of freedom, and that the temporally or in situ ordered set has df(o)=2(n-1) degrees of freedom.
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