The justicespecific data on individual canons is more difficult to interpret compared with the aggregate canon data, however, not only because of the nonrandomness
of other justices who may have joined the opinion, but because of the relatively small numbers involved and the nonrandomness
of opinion assignments.
In practice, a two-tail test is most commonly used as a significant result that implies nonrandomness
T-Square estimators evolved as methods to remove some bias due to nonrandomness
associated with the nearest neighbor distance measurement .
Although previous studies of cross-judge disparities have asserted that assignment to judges is random in practice, (145) I find that assignment is not random and consider the likely causes of the nonrandomness
. Relying on interviews with lawyers and court personnel, evidence of case clustering, and the replication of results within a subset of the data in which assignment appears random, I argue that case assignment is arbitrary with respect to the merits of cases.
We also recognize the possibility that the number of restrictions on the data might introduce nonrandomness
to our sample.
But if there is truly no engagement in this setup, then any nonrandomness
before this deterministic screen would get destroyed; event-correlated nonrandomness
emerging after that screen could then only have been produced by a contrivance--a prior fitting of the bits so that the (constantly updated) deterministic algorithm would produce nonrandom bits on the other end.
It is transformation of time series into sequences of such inconsistent histograms, revealing well-reproducible cosmo-physical regularities, indicating nonrandomness
of "stochastic" physical processes .
More succinctly, the analysis below demonstrates the effect of using an imputation model (or swapping rule) that does not contain a regressor of interest, and thus is not conflated with any bias that could arise from nonrandomness
of the suppression rule.
In this equation, [[phi].sub.i] and [w.sub.i] are the volume and weight fractions, espectively, [[??].sub.i] and [??] are the reduced volume of species i and the nixture, q, is the effective chain length of species i, [[theta].sub.i,p], and [theta] are he surface area fractions of pure species i and the mixture, T, and r are the reduce temperature of species i and the mixture, z is the coordination number, and [[??].sub.ii], is the nonrandomness
of point mutation as rejected in nucleotide substitutions in pseudogenes and its evolutionary implications.
Although Little's MCAR test revealed that data was not missing completely at random, [x.sup.2] ( 129809)= 133367.09, p<0.0001, a visual analysis of Missing Values Patterns revealed that data appeared to be missing towards the end of the questionnaire (potentially due to response fatigue), which contributed to a pattern of nonrandomness
. A pattern in this direction was not expected to influence subsequent analyses.
Additionally, industry-specific or regional-specific variables may also be needed to alleviate the nonrandomness